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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenSat, 13 Apr 2024 00:55:45 +0000Dynamic fracture problems involving highly transient crack growth histories : an investigation of dynamic failure in homgeneous and bimaterial systems
https://resolver.caltech.edu/CaltechETD:etd-12122007-141145
Authors: {'items': [{'id': 'Liu-C', 'name': {'family': 'Liu', 'given': 'Cheng'}, 'show_email': 'NO'}]}
Year: 1994
DOI: 10.7907/k32y-0450
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Highly transient elastodynamic fracture processes in both homogeneous and bimaterial systems have been investigated. It is found that due to the wave character of the mechanical fields during transient and dynamic crack growth, the customarily assumptions of steady state and K[superscript d]-dominance may be violated. This may be particularly true during crack growth in laboratory size specimens where crack growth seldom reaches steady state conditions due to the persistence of the initiation transients and the influence of reflected stress waves from the specimen boundaries. By relaxing both restrictions of steady state and of K[superscript d]-dominance, and by permitting the crack-tip speed and the dynamic stress intensity factor to be arbitrary functions of time, the transient asymptotic elastodynamic field near the moving crack-tip was established in the form of higher order expansion for both homogeneous solids and bimaterial systems. In homogeneous solids, we considered cracks that propagated along arbitrary smooth paths, while in bimaterial systems, we only considered crack growth along a straight interface. The higher order coefficients of the asymptotic expansion were found to depend on the time derivative of crack-tip speed, the time derivative of the dynamic stress intensity factors, and for crack propagating along curved paths, on the instantaneous value of the local curvature of the crack path.
The issue of K[superscript d]-dominance during dynamic crack initiation and transient crack growth was further investigated by solving a particular transient initial/boundary value problem. This corresponds to a planar dilatational wave impinging on a semi-infinite crack in an unbounded elastic solid. The crack initiates under the influence of the wave, and then propagates dynamically. Through comparison of this full field solution and the equivalent K[superscript d]-dominant field or the field represented by the higher order transient terms, it is found that even for points which are relatively far away from the crack-tip, or for times very close to the crack initiation, the higher order transient representation provides a very good description of the actual stress field.
The K[superscript d]-dominant field, however, is incapable of approximating the complete stress field with any accuracy (lack of K[superscript d]-dominance).
The implications of the above observations (possible lack of K[superscript d]-dominance) on the interpretability of dynamic fracture experiments are also explored. The interpretation of experimental data in past laboratory investigations of dynamic fracture events is based on the assumption of K[superscript d]-dominance. However, as we have seen theoretically this assumption may often fail in laboratory situations. As a result, experimental measurements must be analyzed by techniques that allow for the possibility of the existence of transient higher order term effects. Several types of experiments are considered as examples. Plate impact experiments involving very high rates of loading are first analyzed by both a K[...]-dominant and a high order transient approach. The results clearly show the strong effects of transients on the interpretation of the data. As a second example, the optical method of caustics is reanalyzed. A new way of extracting the instantaneous value of the dynamic stress intensity factor K[...](t), which takes transients into account, is proposed and verified theoretically. For the bimaterial system, the issues are equivalent but much more complicated analytically. Here transient effects are found to be magnified by the material property mismatch between the constituent solids. It is shown however, that the higher order transient analysis can predict accurately the fringe patterns from actual experiment performed by means of the CGS (Coherent Gradient Sensing) technique and high speed photography.
The observations of this thesis suggest that a variety of conclusions made in the literature based on interpretations of experimental data on the basis of steady state or K[superscript d]-dominance may be suspect.https://thesis.library.caltech.edu/id/eprint/4976Continuum dynamics of solid-solid phase transitions
https://resolver.caltech.edu/CaltechETD:etd-10222007-135103
Authors: {'items': [{'email': 'allanzhong@hotmail.com', 'id': 'Zhong-Xiaoguang-Allan', 'name': {'family': 'Zhong', 'given': 'Xiaoguang Allan'}, 'show_email': 'NO'}]}
Year: 1995
DOI: 10.7907/PW4M-9B73
<p>This work focuses on the applications in dynamics of recently developed continuum-mechanical models of solid-solid phase transitions. The dynamical problems considered here involve only one space coordinate, and attention is limited to hyperelastic materials that involve two phases. This investigation has two purposes. The first is to determine the predictions of the models in complicated situations. Secondly, the present study attempts to develop analytical and numerical approaches to problems that may be relevant to the interpretation and understanding of experiments involving phase transitions under dynamical conditions.</p>
<p>The first problem studied involves the study of a semi-infinite bar initially in an equilibrium state that involves two material phases separated by a phase boundary at a given location. The end of the bar is suddenly subject to a constant impact velocity that persists for a finite time and is then removed. Interaction between the phase boundary and the elastic waves generated by the impact and subsequent reflections are studied in detail, and the trajectory of the phase boundary is determined exactly. The second task addressed involves the development of a Riemann solver to be applied to the numerical solution of Riemann problems for two-phase elastic materials. Riemann problems for such materials involve complications not present in the corresponding problems that arise, for example, in classical gas dynamics. Finally, a finite-difference method of Godunov type is developed for the numerical treatment of boundary-initial-value problems arising in the model of Abeyaratne and Knowles. The method is applied to specific problems.</p>https://thesis.library.caltech.edu/id/eprint/4215Shock Wave Processing of Transitional Metal Silicides
https://resolver.caltech.edu/CaltechETD:etd-09202002-154801
Authors: {'items': [{'id': 'Montilla-Edmonds-Karina-Luciel', 'name': {'family': 'Montilla Edmonds', 'given': 'Karina Luciel'}, 'show_email': 'NO'}]}
Year: 1998
DOI: 10.7907/9g63-5c59
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Shock wave consolidation is an innovative processing technique for the densification of initially porous media. A compressive shock wave is introduced in the material by the impact of a high velocity flyer plate. Densification is achieved via intense inhomogeneous plastic deformation, pore collapse, and localized melting around particle surface. The passage of the shock wave may also induce chemical reactions within the material. The chemical reactivity of the powders are enhanced through dislocation nucleation, plastic flow, grain fracture and mass mixing as a result of the shock wave.
A systematic investigation is performed to examine the effects of particle size and porosity on the initiation of the Ti[subscript 5]Si[subscript 3] reaction from the elemental powder mixture (i.e., 5 Ti + 3 Si). The initial powder porosity is varied from 40% to 49% of the theoretical density for two different size powders. The threshold shock energy necessary for complete silicide reaction is established. The powders are consolidated with shock energies up to 671 J/g and shock pressures up to 7.3 GPa. The threshold shock energy for the large powder mixture is found to be approximately 80% higher than that for the smaller powder mixture. For both sized powders, an increase in the threshold shock energy of 75% is observed in decreasing the initial porosity of the powders from 49% to 40%. Evidence for the reaction of solid Ti and liquid Si is observed in isolated regions at shock energies slightly below the threshold energy.
Mechanical alloying and shock wave consolidation are examined as viable alternatives for the synthesis and consolidation of MoSi [subscript 2]. Mechanic alalloying of Mo + 2Si is monitored with X-ray diffraction and differential scanning calorimetry (DSC). The milling time is varied from two hours to one hundred forty-four hours. Nanocrystalline MoSi [subscript 2] is observed after sixteen hours of ball milling. X-ray diffraction is used to follow the extent of alloying and average grain size as a function of ball milling time. DSC is utilized to determine the onset endothermic and exothermic reactions in the ball milled powder. MoSi [subscript 2] is produced from the elemental powder mixture by shock wave consolidation.https://thesis.library.caltech.edu/id/eprint/3655An Experimental Investigation of High-Shear-Strain-Rate Behavior of Metals
https://resolver.caltech.edu/CaltechETD:etd-02062008-080229
Authors: {'items': [{'id': 'Deshpande-Nitin-Ashok', 'name': {'family': 'Deshpande', 'given': 'Nitin Ashok'}, 'show_email': 'NO'}]}
Year: 1999
DOI: 10.7907/naah-mx91
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
The present study investigated the mechanical behavior of metals under high-shear-strain-rates and large shear strains. Numerical and experimental investigation of different specimen geometries for shear testing of materials was carried out. Results of numerical simulations showed that shear stress-strain curves calculated from boundary measurement of load and displacement did not match with the constitutive law for the material. The yield stress for the shear stress-strain curve from the boundary measurement was considerably lower than that of the constitutive law whereas hardening exponent was almost the same for two curves. Considerable bending was observed in the shear zone. The results from the boundary measurements were close to the constitutive law for H specimen, an analogue of axisymmetric top hat specimen with top replaced by tool steel punch. A planar version of axisymmetric top hat specimen geometry was studied using finite element analysis. The plane specimen was chosen since it is suitable for temperature measurements in the shear zone. In order to reduce the bending, three types of constraints were considered in the experiments.
Quasi-static and high strain rate experiments were carried out on different geometries in the strain rate range, 10[...] to 10[...] s[...]. Relatively rate insensitive material, 2024-T3 aluminum was used to establish the relationship between numerical and experimental results. Experimental results for the axisymmetric top hat specimen were found to be in good agreement with the finite element results, but there was discrepancy between the stress-strain curve from the boundary measurements and the constitutive law. Shear stress-strain curve from the quasi-static test for the plane specimen with external constraint reproduced the results of numerical simulation. A planar specimen with built-in constraint was fabricated using wire EDM. Both quasi-static and high strain rate results matched with the numerical simulation of the same specimen geometry. High shear strains of the order of 1.5 were reached in the experiments on the Kolsky pressure bar. Some amount of thermal softening was observed in high strain rate experiments.
It was concluded that both numerical simulations and experiments are required in order to obtain accurate constitutive behavior of the material using top hat specimen geometries. A relationship can be established between the numerical tests and the experiments by conducting the experiments at strain rates where the constitutive behavior of the metal is well known. This relationship then can be used to predict the constitutive law at higher strain rates from the experimental data obtained at high strain rates.https://thesis.library.caltech.edu/id/eprint/524Shape-memory effect in bulk and thin-film polycrystals
https://resolver.caltech.edu/CaltechETD:etd-02212008-114547
Authors: {'items': [{'email': 'yichung@iam.ntu.edu.tw', 'id': 'Shu-Y', 'name': {'family': 'Shu', 'given': 'Yi-Chung'}, 'show_email': 'NO'}]}
Year: 1999
DOI: 10.7907/4NW5-3Q89
Shape-memory effect (SME) is a phenomenon where deformation suffered below a critical temperature can be recovered on heating. About 20-30 alloys are known to exhibit SME in single crystals. However, the degree to which they retain their shape-memory behavior in polycrystals is widely varied. In particular, Ti-Ni and Cu-Zn-Al undergo cubic to monoclinic transformation and recover similar strains as single crystals; yet, the observed shape-memory behavior in the former is much better than that in the latter. We develop a model based on energy minimization to understand this difference. Using this model, we establish that texture is the very important reason why the strains recoverable in Ti-Ni are so much larger than those in Cu-based shape-memory alloys in rolled, extruded and drawn specimens. We find that even the qualitative behavior of combined tension-torsion can critically depend on the texture. The results are in good agreement with experimental observations.
We extend our analysis to the behavior of very thin films with three competing length scales: the film thickness, the length scales of heterogeneity and material microstructure. We start with three-dimensional nonhomogeneous nonlinear elasticity enhanced with an interfacial energy of the van der Waals type, and derive the effective energy density as all length scales tend to zero with given limiting ratios. We do not require any priori selection of asymptotic expansion or ansatz in deriving our results. Depending on the dominating length scale, the effective energy density can be identified by three procedures: averaging, homogenization and thin-film limit. We apply our theory to martensitic thin films and use a model example to show that the shape-memory behavior can crucially depend on the relative magnitudes of these length scales. Using this theory, we show that sputtering textures in both Ti-Ni and Cu-based shape-memory thin films are not favorable for large recoverable strain. We comment on multilayers made of shape-memory and elastic materials.
Finally, we suggest textures for improved SME in bulk and thin-film polycrystals.https://thesis.library.caltech.edu/id/eprint/705Micromechanical Aspects of Failure in Unidirectional Fiber Reinforced Composites
https://resolver.caltech.edu/CaltechTHESIS:10082010-091323238
Authors: {'items': [{'email': 'oguni@sd.keio.ac.jp', 'id': 'Oguni-Kenji', 'name': {'family': 'Oguni', 'given': 'Kenji'}, 'orcid': '0000-0003-0425-9784', 'show_email': 'NO'}]}
Year: 2000
DOI: 10.7907/3VSA-QN96
<p>Micromechanical aspects of failure in unidirectional fiber reinforced composites are investigated using combined experimental and analytical methods. Results from an experimental investigation on mechanical behavior of a unidirectional fiber reinforced polymer composite (E-glass/vinylester) with 50% fiber volume fraction under quasi-static uniaxial and proportional multiaxial compression are presented. Detailed examination of the specimen during and after the test reveals the failure mode transition from axial splitting to kink band formation as the loading condition changes from uniaxial to multiaxial compression.</p>
<p>Motivated by the experimental observations, an energy-based model is developed to provide an analytical estimate of the critical stress for axial splitting observed in unidirectional fiber reinforced composites under uniaxial compression in the fiber direction (also with weak lateral confinement). The analytic estimate for the compressive strength is used to illustrate its dependence on material properties, surface energy, fiber volume fraction, fiber diameter and lateral confining pressure.</p>
<p>To understand the effect of flaws on the strength of unidirectional fiber reinforced composites, a fracture mechanics based model for failure is developed. Based on this model, failure envelope, dominant initial flaw orientation and failure mode for the composites under a wide range of stress states are predicted. Parametric study provides quantitative evaluation of the effect of various mechanical and physical properties on failure behavior and identifies their influence on strength.</p>
<p>Finally, results from an experimental investigation on the dynamic mechanical behavior of unidirectional E-glass/vinylester composites with 30%, 50% fiber volume fraction under uniaxial compression are presented. Limited experimental results are also presented for the 50% fiber volume fraction composite under dynamic proportional lateral confinement. Specimens are loaded in the fiber direction using a modified Kolsky (split Hopkinson) pressure bar. The results indicate that the compressive strength of the composite increases with increasing strain rate and confinement. Post-test scanning electron microscopy reveals that axial splitting is the dominant failure mechanism in the composites under uniaxial compression in the entire range of strain rates. Based on the experimental results and observations, the energy-based analytic model is extended to predict the compressive strength of these composites under dynamic uniaxial loading conditions.</p>https://thesis.library.caltech.edu/id/eprint/6119Investigation of Large Strain Actuation in Barium Titanate
https://resolver.caltech.edu/CaltechETD:etd-10232001-192042
Authors: {'items': [{'email': 'burcsu@alumni.caltech.edu', 'id': 'Burcsu-Eric-Noboru', 'name': {'family': 'Burcsu', 'given': 'Eric Noboru'}, 'show_email': 'YES'}]}
Year: 2001
DOI: 10.7907/XT3Y-Z860
<p>Sensors and actuators based on ferroelectric materials have become indispensable in the fields of aerospace, high technology, and medical instruments. Most devices rely on the linear piezoelectric behavior of formulations of PZT which offer high bandwidth, linear actuation but very low strains of around 0.1%. The nonlinear electromechanical behavior of these materials is largely governed by the motion of domains and is highly affected by stress as well as electric field. The recent theories of Shu and Bhattacharya have sought to address some of the issues related to the structure and behavior of these materials at the mesoscale. One result of the theories is the prediction of another mode of actuation in ferroelectric crystals based on a combined electrical and mechanical loading that could result in strains of up to 6%.</p>
<p>Descriptions of the phenomenological theories of ferroelectrics are presented including the classical Landau-Ginsburg-Devonshire theory and the more recent theory of Shu and Bhattacharya. Predictions are made, based on the theory, of the electromechanical behavior of ferroelectric crystals that are addressed by the experiments. An experimental setup has been designed to investigate large strain actuation in single crystal ferroelectrics based on combined electrical and mechanical loading. An investigation of the stress dependence of the electrostrictive response has been carried out with in situ observations of the domain patterns under constant compressive stress and variable electric field. Experiments have been performed on initially single domain crystals of barium titanate with (100) and (001) orientation at compressive stresses between 0 and 5 MPa. Global strain and polarization histories have been recorded. The electrostrictive response is shown to be highly dependent on the level of applied stress with a maximum strain of 0.9% measured at a compressive stress of about 2 MPa. An unusual secondary hysteresis has been observed in the polarization signal at high levels of stress that indicates an intermediate structural configuration, possibly the orthorhombic state. Polarized light microscopy has been used to observe the evolution of the domain pattern simultaneously with the strain and polarization measurement. These results are discussed and suggestions for future work are proposed.</p>https://thesis.library.caltech.edu/id/eprint/4218Time-dependent compressibility of poly (methyl methacrylate) (PMMA) : an experimental and molecular dynamics investigation
https://resolver.caltech.edu/CaltechTHESIS:04262011-100757709
Authors: {'items': [{'id': 'Sane-S-B', 'name': {'family': 'Sane', 'given': 'Sandeep Bhalchandra'}, 'show_email': 'NO'}]}
Year: 2001
DOI: 10.7907/saw5-7p32
This thesis contains three chapters, which describe different aspects of an investigation of the bulk response of Poly(Methyl Methacrylate) (PMMA). The first chapter describes the physical measurements by means of a Belcher/McKinney-type apparatus. Used earlier for the measurement of the bulk response of Poly(Vinyl Acetate), it was now adapted for making measurements at higher temperatures commensurate with the glass transition
temperature of PMMA. The dynamic bulk compliance of PMMA was measured at atmospheric pressure over a wide range of temperatures and frequencies, from which the master curves for the bulk compliance were generated by means of the time-temperature superposition principle. It was found that the extent of the transition ranges for the bulk and shear response were comparable. Comparison of the shift factors for bulk and shear responses supports the idea that different molecular mechanisms contribute to shear and
bulk deformations.
The second chapter delineates molecular dynamics computations for the bulk response for a range of pressures and temperatures. The model(s) consisted of 2256 atoms
formed into three polymer chains with fifty monomer units per chain per unit cell. The time scales accessed were limited to tens of pico seconds. It was found that, in addition to the typical energy minimization and temperature annealing cycles for establishing equilibrium models, it is advantageous to subject the model samples to a cycle of
relatively large pressures (GPa-range) for improving the equilibrium state. On comparing the computations with the experimentally determined "glassy" behavior, one finds that,
although the computations were limited to small samples in a physical sense, the primary limitation rests in the very short times (pico seconds). The molecular dynamics computations do not model the physically observed temperature sensitivity of PMMA, even if one employs a hypothetical time-temperature shift to account for the large
difference in time scales between experiment and computation. The values computed by the molecular dynamics method do agree with the values measured at the coldest
temperature and at the highest frequency of one kiloHertz.
The third chapter draws on measurements of uniaxial, shear and Poisson response conducted previously in our laboratory. With the availability of four time or frequency-dependent material functions for the same material, the process of interconversion between different material functions was investigated. Computed material functions were
evaluated against the direct experimental measurements and the limitations imposed on successful interconversion due to the experimental errors in the underlying physical data
were explored. Differences were observed that are larger than the experimental errors would suggest.
https://thesis.library.caltech.edu/id/eprint/6354In-Situ Diagnostics for Metalorganic Chemical Vapor Deposition of YBCO
https://resolver.caltech.edu/CaltechETD:etd-09262005-143545
Authors: {'items': [{'email': 'dj_lightzout@hotmail.com', 'id': 'Tripathi-Ashok-Burton', 'name': {'family': 'Tripathi', 'given': 'Ashok Burton'}, 'show_email': 'NO'}]}
Year: 2001
DOI: 10.7907/3ZJS-BE38
<p>A new stagnation flow MOCVD research reactor is described that is designed to serve as a testbed to develop tools for "intelligent" thin film deposition, such as in-situ sensors and diagnostics, control algorithms, and thin film growth models. The reactor is designed in particular for the deposition of epitaxial YBa<sub>2</sub>Cu<sub>3</sub>O<sub>7-δ</sub> on MgO, although with minor modifications it would be suitable for deposition of any metal-oxide thin films.</p>
<p>The reactor is specifically designed to permit closed-loop thermal and stoichiometric control of the film growth process. Closed-loop control of precursor flow rates is accomplished by using ultraviolet absorption spectroscopy on each precursor line. Also integrated into the design is a Fourier Transform Infrared (FTIR) spectroscopy system which collects real-time, in-situ infrared polarized reflectance spectra of the film as it grows. Numerical simulation was used extensively to optimize the fluid dynamics and heat transfer to provide uniform fluxes to the substrate. As a result, thickness uniformity across the substrate is typically within 3% from the center to the edge of the substrate.</p>
<p>Experimental studies of thin films grown in the Y/Ba/Cu/O system have been carried out. The films have been characterized by Rutherford Backscattering Spectrometry and X-ray Diffraction. Results indicate c-axis oriented grains with pure 1:2:3 phase YBCO, good spatial uniformity, and a low degree of c-axis wobble. Experimental growth data is used in a gas phase and surface chemistry model to calculate sticking coefficients for yttrium oxide, barium oxide, and copper oxide on YBCO.</p>
<p>In-situ FTIR and Coherent Gradient Sensing (CGS) analysis of growing films has been performed, yielding accurate substrate temperature, film thickness monitoring, and full-field, real-time curvature maps of the films. In addition, we have implemented CGS to obtain full-field in-situ images of local curvature during oxygenation and deoxygenation of YBCO films. An analysis of the oxygen diffusion is performed, and diffusivity constants are presented for a variety of temperature and film conditions.</p>https://thesis.library.caltech.edu/id/eprint/3785The Cu47Ti34Zr11Ni8 glass-forming alloy : thermophysical properties, crystallization, and the effect of small alloying additions on the thermal stability
https://resolver.caltech.edu/CaltechETD:etd-05242005-084824
Authors: {'items': [{'email': 'sglade@alumni.caltech.edu', 'id': 'Glade-Stephen-Clarke', 'name': {'family': 'Glade', 'given': 'Stephen Clarke'}, 'show_email': 'YES'}]}
Year: 2001
DOI: 10.7907/4ZJQ-RP66
The thermophysical properties, crystallization, and the effect of small alloying additions on the thermal stability of Cu47Ti34Zr11Ni8 were investigated. The thermophysical properties studied were specific heat capacity and viscosity. From the specific heat capacity data, the differences in the thermodynamic functions between the liquid and the crystalline states of Cu47Ti34Zr11Ni8 were calculated. A lower Gibbs free energy difference between the liquid and the crystalline states generally indicates a better glass-forming ability of an alloy. A lower entropy of fusion indicates a better glass-forming ability as well. The viscosity data, using the strong/fragile classification of glasses, also give a measure of the glass-forming ability of the alloy.
The crystallization of amorphous Cu47Ti34Zr11Ni8 was studied with many experimental techniques. Similar to other metallic glass-forming alloys, Cu47Ti34Zr11Ni8 phase separates prior to crystallization. Cu47Ti34Zr11Ni8 decomposes to copper-enriched and titanium-enriched regions (the copper-enriched regions are low in titanium and vice versa). Primary crystallization of Cu47Ti34Zr11Ni8 consists of face centered cubic nanocrystals growing in an amorphous matrix.
The glass-forming ability of certain metallic glass-forming alloys has been improved with small silicon additions, which has been attributed to silicon destabilizing oxide nucleation sites. To investigate this further, a study of the effect of silicon on the crystallization of Cu47Ti34Zr11Ni8 was performed. Prior to crystallization, both Cu47Ti34Zr11Ni8 and Cu47Ti33Zr11Ni8Si1 phase separate to copper-enriched and titanium-enriched regions. A face centered cubic phase then nucleates and grows in both alloys. No change in the local composition around a silicon atom in Cu47Ti33Zr11Ni8Si1 was detected.
Small additions of magnesium and germanium were added to Cu47Ti34Zr11Ni8 to observe the effect on the thermal stability of the alloy. In contrast to the results observed with silicon, no improvement in the glass-forming ability was observed. However, there was an improvement in the thermal stability of the alloy against crystallization in the supercooled liquid regime with both the magnesium and germanium additions.https://thesis.library.caltech.edu/id/eprint/1993Phase Boundary Propagation in Heterogeneous Media
https://resolver.caltech.edu/CaltechTHESIS:10082010-142653040
Authors: {'items': [{'id': 'Craciun-Bogdan', 'name': {'family': 'Craciun', 'given': 'Bogdan'}, 'show_email': 'NO'}]}
Year: 2002
DOI: 10.7907/JXG6-W865
<p>There has been much recent progress in the study of free boundary problems motivated by phase transformations in materials science. Much of this literature considers fronts propagating in homogeneous media. However, usual materials are heterogeneous due to the presence of defects, grains and precipitates. This thesis addresses the propagation of phase boundaries in heterogeneous media.</p>
<p>A particular motivation is a material undergoing martensitic phase transformation. Given a martensitic material with many non-transforming inclusions, there are well established microscopic laws that give the complex evolution of a particular twin or phase boundary as it encounters the many inclusions. The issue of interest is the overall evolution of this interface and the effect of defects and impurities on this evolution. In particular, if the defects are small, it is desirable to find the effective macroscopic law that governs the overall motion, without having to follow all the microscopic details but implicitly taking them into account. Using a theory of phase transformations based on linear elasticity, we show that the normal velocity of the martensitic phase or twin boundary may be written as a sum of several terms: first a homogeneous (but non-local) term that one would obtain for the propagation of the boundary in a homogeneous medium, second a heterogeneous term describing the effects of the inclusions but completely independent of the phase or twin boundary and third an interfacial energy term proportional to the mean curvature of the boundary.</p>
<p>As a guide to understanding this problem, we begin with two simplified settings which are also of independent interest. First, we consider the homogenization for the case when the normal velocity depends only on position (the heterogeneous term only). This is equivalent to the homogenization of a Hamilton-Jacobi equation. We establish several variational principles which give useful formulas to characterize the effective Hamiltonian. We illustrate the usefulness of these results through examples and we also provide a qualitative study of the effective normal velocity.</p>
<p>Second, we address the case when the interfacial energy is not negligible, so we keep the heterogeneous and curvature terms. This leads to a problem of homogenization of a degenerate parabolic initial value problem. We prove a homogenization theorem and obtain a characterization for the effective normal velocity, which however proves not to be too useful a tool for actual calculations. We therefore study some interesting examples and limiting cases and provide explicit formula in these situations. We also provide some numerical examples.</p>
<p>We finally address the problem in full generality in the setting of anti-plane shear. We explicitly evaluate the term induced by the presence of the inclusions and we propose a numerical method that allows us to trace the evolution of the phase boundary. We use this numerical method to evaluate the effect of the inclusions and show that their effect is quite localized. We use it to explain some experimental observations in NiTi.</p>https://thesis.library.caltech.edu/id/eprint/6122Mechanical Behavior of a Bulk Metallic Glass and Its Composite Over a Wide Range of Strain Rates and Temperatures
https://resolver.caltech.edu/CaltechETD:etd-06082005-151713
Authors: {'items': [{'email': 'junlu@alumni.caltech.edu', 'id': 'Lu-Jun', 'name': {'family': 'Lu', 'given': 'Jun'}, 'show_email': 'NO'}]}
Year: 2002
DOI: 10.7907/3SZ8-Y947
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
The development of bulk metallic glasses (BMG), which have exceptional mechanical properties such as high strength, high hardness and corrosion resistance, as well as good glass forming and shaping abilities, using relatively expensive materials and processing techniques, offers great opportunities to use this class of solids as structural amorphous materials (SAM). In this thesis, the mechanical behavior of a bulk metallic glass [...] (Vitreloy 1) and its composite [beta]-phase Vitreloy 1 composite, i.e., [...]) is investigated.
The stress-strain relations for Vitreloy 1 over a broad range of temperatures (from room temperature up to the crystallization temperature) and strain rates [...] were established in uniaxial compression using both quasi-static and dynamic Kolsky pressure bar loading systems. The effect of strain rate and temperature on steady state flow stress, viscosity and peak stress, as well as the effect of jump-in-strain-rate on the stress-strain behavior, were investigated. Based on the experimental results, boundaries between three main deformation modes are proposed, namely, Newtonian flow and nonlinear flow resulting in homogeneous deformation and shear-localized failure constituting inhomogeneous deformation. To characterize the constitutive behavior of the bulk metallic glass, a free volume based model as well as a fictive stress model are utilized to analyze the stress-strain behavior and a mechanism for shear band formation.
A unique deformation characteristic of a bulk metallic glass is the shear localization of the material in response to external mechanical loading, which may lead to catastrophic shear failure immediately after yielding under uniaxial loading and at low temperatures. A dynamic indentation experimental setup was developed to evaluate the high-strain-rate inelastic post yield deformation behavior of Vitreloy 1 and its [beta]-phase composite. Time-resolved depth and load responses during the process of indentation on the materials were obtained. Both materials are found to be strain rate insensitive up to 2,000 [...]. Numerical simulations of the indentation experiments, using both pressure insensitive (J2 von Mises) and pressure dependent (Drucker-Prager) flow models, reveal that both materials are pressure (or normal stress) dependent. Intense multiple shear bands are observed in the indentation craters and are responsible for the observed overall inelastic deformation.
To further examine the inelastic deformation and as well as whether a pressure sensitive or normal stress is more appropriate for Vitreloy 1, multiaxial compression experiments using a confining sleeve technique were performed. In contrast to the catastrophic shear failure behavior in uniaxial compression, Vitreloy 1 exhibits large inelastic deformation of more than 10 percent under confinement, indicating the nature of ductile deformation under constrained conditions. It is found that the metallic glass follows a pressure dependent Tresca criterion, [...], and the coefficient of the pressure dependence, [beta], is 0.17. Multiple parallel shear bands are observed on the outer surfaces of the deformed specimens.
Motivated by potential use of Vitreloy 1 in impact related applications, the shock compression characteristics of both Vitreloy 1 and [beta]-Vitreloy composite were studied using planar impact loading. A surprisingly low amplitude elastic precursor bulk wave, corresponding to the elastic response of the 'frozen structure' of the intact metallic glasses, was observed to precede the rate-dependent large deformation shock wave. A concave downward curvature after the initial increase of the [...] shock Hugoniots suggests that a phase-change-like transition occurred during shock compression. In addition, compression damage occurred due to the shear localization. The spalling inside Vitreloy 1 was induced by shear localization, while in [beta]-Vitreloy 1, it was due to debonding of the [beta]-phase boundary from the matrix. The spall strengths at strain rate of [...] were 2.35 GPa and 2.11 GPa for Vitreloy I and [beta]-Vitreloy 1, respectively.https://thesis.library.caltech.edu/id/eprint/2515Global Fracture Analysis of Laminated Composite Materials for Aerospace Structures
https://resolver.caltech.edu/CaltechTHESIS:05032011-085654224
Authors: {'items': [{'id': 'González-Liñero-Luis', 'name': {'family': 'González Liñero', 'given': 'Luis'}, 'show_email': 'NO'}]}
Year: 2002
DOI: 10.7907/FCJ8-EW63
The failure process of laminated composite materials originating from precut sharp cracks, as well as their propagation, is studied from a "global" perspective,
appropriate for structural analysis. The size effect in the damage development is explored and the question of "scaling" of the results is addressed.
Two globally orthotropic sets of panels with the notches aligned along the axes of orthrotopy are studied. The internally evolving damage in the crack tip region is
examined through enhanced x-ray radiographic inspection and surface strain fields are measured by means of the Digital Image Correlation method (the applicability and limitations of which are analyzed and discussed). The results obtained from these two experimental techniques are joined to assess the feasibility of identifying internal damage solely from surface measurements.
The shape of the region of influence of the crack is described and its extension measured. A simplified model for damage progression analysis is proposed.
The process of initiation of the damage propagation is described in detail and the different responses for the two different layups are discussed. The maximum stress/strain and the Tsai-Hill failure criteria are compared with the experimental results on the laminates, and their reliability and limitations are addressed.
The effective properties of the two sets of laminates are measured at three different loading rates and compared to theory, and the relevance of the time dependence of the material is studied.
https://thesis.library.caltech.edu/id/eprint/6371Dynamics of Phase Transitions in Strings, Beams and Atomic Chains
https://resolver.caltech.edu/CaltechETD:etd-11072006-100058
Authors: {'items': [{'email': 'purohit@seas.upenn.edu', 'id': 'Purohit-Prashant-Kishore', 'name': {'family': 'Purohit', 'given': 'Prashant Kishore'}, 'show_email': 'NO'}]}
Year: 2002
DOI: 10.7907/DP97-XH80
This thesis presents a theory for dynamical martensitic phase transitions in strings and beams. Shape memory alloys that rely on such phase transitions for their unique properties are often used in slender configurations like beams and rods. Yet most studies of phase transformations are in one dimension and consider only extension. The theory presented in this thesis to model these slender structures is based on the general continuum mechanical framework of thermoelasticity with a non-convex Helmholtz free energy. This non-convexity allows for the simultaneous existence of several metastable phases in a material; in particular, it leads to the formation of phase boundaries. The study of the laws governing the propagation of phase boundaries is the object of this thesis.
Phase boundaries in strings are studied first. It is demonstrated that the motion of phase boundaries is not fully described by the usual balance laws of mass, momentum and energy. Additional constitutive information must be furnished from outside, and this additional information is referred to as the kinetic relation. While this notion is well-accepted in continuum theory, there is no definitive experiment or theoretical framework to determine the kinetic relation. This study of strings proposes a simple experiment to determine the kinetic relation. It also proposes a numerical method that accurately describes the complex behaviour of strings with phase boundaries.
The kinetic relation can also be viewed from the atomic scale. Phase transformations involve a complex rearrangement of the atoms the explicit details of which are averaged in a continuum theory. The kinetic relation may be viewed as an aggregate of those aspects of the atomistic rearrangement that have a bearing on macroscopic phenomena. This view is explored using a simple one dimensional model of an atomic chain with non-convex interaction potentials. A kinetic relation is obtained from dynamic simulations of impact experiments on the chain.
The latter part of this thesis studies beams made of materials capable of phase transitions. It develops a conceptual framework that accounts for extension, shear and flexure in such beams using a non-convex stored energy function. Specific constitutive assumptions that relate to the underlying crystallography are developed. The theory is applied to design a simple experiment on single crystals of martensitic materials with the objective of measuring the kinetic relation.
Finally, propulsion at small scales is discussed as an application of beams made of phase transforming material. The goal is to mimic the flagellum of a micro-organism by propagating phase boundaries through a shearbale rod.https://thesis.library.caltech.edu/id/eprint/4442Experimental Investigation of Quasistatic and Dynamic Fracture Properties of Titanium Alloys
https://resolver.caltech.edu/CaltechETD:etd-02112002-153745
Authors: {'items': [{'id': 'Anderson-David-Deloyd', 'name': {'family': 'Anderson', 'given': 'David Deloyd'}, 'show_email': 'NO'}]}
Year: 2002
DOI: 10.7907/NHZS-D271
<p>The goal of this work is to investigate the quasistatic and dynamic fracture properties of three titanium alloys: 6Al-4V titanium, 6Al-4V titanium ELI, and Timetal 5111. While standard tests exist for measuring quasistatic fracture toughness, the dynamic investigation requires that several measurement techniques are employed including Coherent Gradient Sensing (CGS), Crack Opening Displacement (COD), and the use of strain gages. The use of these methods with difficult engineering materials in the dynamic loading regime requires methodologies to be advanced beyond that previously required with model materials having properties ideal for experimental measurements techniques.</p>
<p>After a description of each measurement technique is given, stress intensity factor measurements made on 12.7 mm thick pre-cracked 6Al-4V titanium specimens are compared. These specimens were dynamically impacted in three point bend in a drop weight tower. Specimens with and without side-grooves were tested as each measurement technique allows. Side-grooves are useful to increase the degree of plane strain experienced in proximity of the crack tip, allowing plane strain (geometry independent) fracture toughnesses to be obtained from specimens that may be otherwise too thin in cross section. Resulting stress intensity factor-time histories from the different techniques are compared to verify that their results mutually agree.</p>
<p>Advancements in employing CGS, a shearing interferometric technique, are described in more detail. First, the analysis of CGS interferograms is extended to allow experimental fringe data to be fit to very general analytical asymptotic crack tip solution to determine mixed mode stress intensity factors. As formulated in this work, the CGS technique can be used to measure stress intensity factors for non-uniformly propagating dynamic mixed mode cracks moving along arbitrary paths in homogeneous linear elastic isotropic materials. Other advancements are also detailed which improve analysis accuracy, objectivity, and efficiency.</p>
<p>Finally, with the equivalence of the three measurement technique results established, tests were performed on 8--17 mm thick pre-cracked three point bend specimens of the three materials to measure critical stress intensity values for crack initiation. Side-grooves are necessary for the more ductile 6Al-4V titanium ELI and Timetal 5111 materials to obtain plane strain fracture toughness values. It is found that both the 6Al-4V titanium ELI and Timetal 5111 alloys are 50-70% tougher than the 6Al-4V titanium, and for all three materials their initiation toughness does not vary significantly with loading rate over the domain tested.</p>https://thesis.library.caltech.edu/id/eprint/601Variational Arbitrary Lagrangian-Eulerian Method
https://resolver.caltech.edu/CaltechETD:etd-05292003-113845
Authors: {'items': [{'id': 'Thoutireddy-Pururav', 'name': {'family': 'Thoutireddy', 'given': 'Pururav'}, 'show_email': 'NO'}]}
Year: 2003
DOI: 10.7907/DQT0-5104
This thesis is concerned with the development of Variational Arbitrary Lagrangian-Eulerian method (VALE) method. VALE is essentially finite element method generalized to account for horizontal variations, in particular, variations in nodal coordinates. The distinguishing characteristic of the method is that the variational principle simultaneously supplies the solution, the optimal mesh and, in case problems of shape optimization, optimal shape. This is accomplished by rendering the functional associated with the variational principle stationary with respect to nodal field values as well as with respect to the nodal positions of triangulation of the domain of analysis. Stationarity with respect to the nodal positions has the effect of the equilibriating the energetic or configurational forces acting in the nodes. Further, configurational force equilibrium provides precise criterion for mesh optimality. The solution so obtained corresponds to minimum of energy functional (minimum principle) in static case and to the stationarity of action sum (discrete Hamilton's stationarity principle) in dynamic case, with respect to both nodal variables and nodal positions. Further, the resulting mesh adaption scheme is devoid of error estimates and mesh-to-mesh transfer interpolation errors. We illustrate the versatility and convergence characteristics of the method by way of selected numerical tests and applications, including the problem of semi-infinite crack, the shape optimization of elastic inclusions and free vibration of 1-d rod.https://thesis.library.caltech.edu/id/eprint/2227A Phase-Field Model of Dislocations in Ductile Single Crystals
https://resolver.caltech.edu/CaltechETD:etd-05302003-094155
Authors: {'items': [{'email': 'marisol@purdue.edu', 'id': 'Koslowski-Marisol', 'name': {'family': 'Koslowski', 'given': 'Marisol'}, 'orcid': '0000-0001-9650-2168', 'show_email': 'YES'}]}
Year: 2003
DOI: 10.7907/SFMJ-1B50
<p>A phase-field theory of dislocations, strain hardening and hysteresis in ductile single crystals is developed. The theory accounts for an arbitrary number and arrangement of dislocation lines over a slip plane; the long-range elastic interactions between dislocation lines; the core structure of the dislocations; the interaction between the dislocations and an applied resolved shear stress field; and the irreversible interactions with short-range obstacles, resulting in hardening, path dependency and hysteresis.</p>
<p>We introduce a variational formulation for the statistical mechanics of dissipative systems. The influence of finite temperature as well as the mechanics in the phase-field theory are modeled with a Metropolis Monte Carlo algorithm and a mean field approximation.</p>
<p>A chief advantage of the present theory is that at zero temperature it is analytically tractable, in the sense that the complexity of the calculations may be reduced, with the aid of closed form analytical solutions, to the determination of the value of the phase field at point-obstacle sites. The theory predicts a range of behaviors which are in qualitative agreement with observation, including hardening and dislocation multiplication in single slip under monotonic loading; the Bauschinger effect under reverse loading; the fading memory effect; the evolution of the dislocation density under cycling loading; temperature softening; strain rate dependence; and others.</p>
<p>The model also reproduces the formation of dislocation networks observed in grain boundaries for different crystal structures and orientations. Simultaneously with the stable configurations the theory naturally predicts the equilibrium dislocation density independently of initial values or sources.</p>https://thesis.library.caltech.edu/id/eprint/2287Electronic Environments and Electrochemical Properties in Lithium Storage Materials
https://resolver.caltech.edu/CaltechETD:etd-05162003-142018
Authors: {'items': [{'email': 'jagraetz@hrl.com', 'id': 'Graetz-Jason-Allan', 'name': {'family': 'Graetz', 'given': 'Jason Allan'}, 'orcid': '0000-0002-2584-2357', 'show_email': 'YES'}]}
Year: 2003
DOI: 10.7907/CS3R-RW08
<p>The local electronic environments and energy storage properties of lithium electrodes are investigated through inelastic electron scattering and electrochemical measurements. Experimental and computational methods are developed to characterize the electronic structure of lithiated compounds during electrochemical cycling. An electrochemical investigation of new lithium alloys has led to a better understanding of the thermodynamics, kinetics, and mechanical properties of nanostructured materials. These studies have also inspired the development of new anode materials for rechargeable lithium batteries.</p>
<p>One of the large controversies regarding lithium cathodes concerns the arrangement of the local electronic environments in the host material and how these environments are affected by lithium intercalation. To investigate this issue, the core edges of the 3d transition-metal oxides were studied using electron energy-loss spectrometry. A number of techniques were developed to better understand how characteristics of the electronic structure are reflected in the core edge and near-edge structure of metal oxides. An empirical relationship is established between the transition-metal L23 white line intensity and the transition-metal 3d occupancy. In addition, the near-edge structure of the oxygen K-edge was used to investigate the 2p electron density about the oxygen ions. The results of these investigations were used to study charge compensation in lithiated transition-metal oxides (e.g., LiCoO2 and LiNi0.8Co0.2O2) during electrochemical cycling. These results show a large increase in state occupancy of the oxygen 2p band during lithiation, suggesting that much of the lithium 2s electron is accommodated by the anion. Ab initio calculations of the oxygen 2p partial density of states curves confirm the increase in unoccupied states that accompany lithium extraction. In contrast with the large changes observed in the oxygen K-edge, much smaller changes were observed in the transition-metal L23 white lines. Surprisingly, for layered LiCoO2 and Li(Ni, Co)O2, the transition-metal valence changes little during the charge compensation accompanying lithiation. These results have led to a better understanding of intercalation hosts and the role of oxygen in these layered structures.</p>
<p>Recent demand for alternatives to graphitic carbon for lithium anodes motivated an investigation into novel binary lithium alloys. The large volume expansions associated with lithium insertion is known to generate tremendous microstructural damage, making most alloys unsuitable for rechargeable lithium batteries. Electrodes of nanostructured lithium alloys were prepared in an attempt to mitigate the particle decrepitation that occurs during cycling and to shorten diffusion times for lithium. Anodes of silicon and germanium were prepared in thin film form as nanocrystalline particles (10 nm mean diameter) and as continuous amorphous thin films (60-250 nm thick). These nanostructured materials exhibited stable capacities up to six times larger than what is found in graphitic carbons, which are currently the industry standard. In addition, these electrodes do not suffer from particle decrepitation and therefore exhibit excellent cycle life. Nanocrystalline electrodes of silicon and germanium were found to transform into a glassy phase via an electrochemically driven solid-state amorphization during the initial alloying. The disordered structure is believed to assuage strains of intercalation by bypassing multiple crystallographic phases. However, the primary reason for the improved reversibility in these electrodes is attributed to the nanoscale dimensions, which circumvent conventional mechanisms of mechanical deterioration. Nanostructured Li-Si and Li-Ge exhibit the highest reversible electrochemical capacities yet reported for an alloy electrode.</p>
<p>Future investigations of the local electronic environments in cathodes could be extended to include more complicated systems such as Li(Ni, Mn)O2 and Li(Fe, X)PO4. Our results suggest that the electronic stability of the metal ion is necessary to maintain a prolonged cycle life. Therefore, an understanding of charge compensation in these complex oxides will be important for understanding new cathode materials. The electronic environments will also be a critical component in the development of alternative anodes, such as binary and ternary lithium alloys. Chemical and valence maps will be used to determine how the lithium is distributed and how its chemical potential varies throughout the electrode. In addition, a better understanding of the thermodynamics, kinetics, and mechanical properties of lithium hosts will be necessary for the development of lithium electrodes with high capacities and high rate capabilities.</p>https://thesis.library.caltech.edu/id/eprint/1833Variational Time Integrators in Computational Solid Mechanics
https://resolver.caltech.edu/CaltechETD:etd-05262003-200254
Authors: {'items': [{'email': 'lewa@stanford.edu', 'id': 'Lew-Adrián-José', 'name': {'family': 'Lew', 'given': 'Adrián José'}, 'show_email': 'YES'}]}
Year: 2003
DOI: 10.7907/6C74-GC16
<p>This thesis develops the theory and implementation of variational integrators for computational solid mechanics problems, and to some extent, for fluid mechanics problems as well. Variational integrators for finite dimensional mechanical systems are succinctly reviewed, and used as the foundations for the extension to continuum systems. The latter is accomplished by way of a space-time formulation for Lagrangian continuum mechanics that unifies the derivation of the balance of linear momentum, energy and configurational forces, all of them as Euler-Lagrange equations of an extended Hamilton's principle. In this formulation, energy conservation and the path independence of the J- and L-integrals are conserved quantities emanating from Noether's theorem. Variational integrators for continuum mechanics are constructed by mimicking this variational structure, and a discrete Noether's theorem for rather general space-time discretizations is presented. Additionally, the algorithms are automatically (multi)symplectic, and the (multi)symplectic form is uniquely defined by the theory. For instance, in nonlinear elastodynamics the algorithms exactly preserve linear and angular momenta, whenever the continuous system does.</p>
<p>A class of variational algorithms is constructed, termed asynchronous variational integrators (AVI), which permit the selection of independent time steps in each element of a finite element mesh, and the local time steps need not bear an integral relation to each other. The conservation properties of both synchronous and asynchronous variational integrators are discussed in detail. In particular, AVI are found to nearly conserve energy both locally and globally, a distinguishing feature of variational integrators. The possibility of adapting the elemental time step to exactly satisfy the local energy balance equation, obtained from the extended variational principle, is analyzed. The AVI are also extended to include dissipative systems. The excellent accuracy, conservation and convergence characteristics of AVI are demonstrated via selected numerical examples, both for conservative and dissipative systems. In these tests AVI are found to result in substantial speedups, at equal accuracy, relative to explicit Newmark.</p>
<p>In elastostatics, the variational structure leads to the formulation of discrete path-independent integrals and a characterization of the configurational forces acting in discrete systems. A notable example is a discrete, path-independent J-integral at the tip of a crack in a finite element mesh.</p>https://thesis.library.caltech.edu/id/eprint/2077Constrained Sequential Lamination: Nonconvex Optimization and Material Microstructure
https://resolver.caltech.edu/CaltechETD:etd-05142004-144712
Authors: {'items': [{'id': 'Fago-Matthew-Justin', 'name': {'family': 'Fago', 'given': 'Matthew Justin'}, 'show_email': 'YES'}]}
Year: 2004
DOI: 10.7907/P1PK-E179
<p>A practical algorithm has been developed to construct, through sequential lamination, the partial relaxation of multiwell energy densities such as those characteristic of shape memory alloys. The resulting microstructures are in static and configurational equilibrium, and admit arbitrary deformations. The laminate topology evolves during deformation through branching and pruning operations, while a continuity constraint provides a simple model of metastability and hysteresis. In cases with strict separation of length scales, the method may be integrated into a finite element calculation at the subgrid level. This capability is demonstrated with a calculation of the indentation of a Cu-Al-Ni shape memory alloy by a spherical indenter.</p>
<p>In verification tests the algorithm attained the analytic solution in the computation of three benchmark problems. In the fourth case, the four-well problem (of, e.g., Tartar), results indicate that the method for microstructural evolution imposes an energy barrier for branching, hindering microstructural development in some cases. Although this effect is undesirable for purely mathematical problems, it is reflective of the activation energies and metastabilities present in applications involving natural processes.</p>
<p>The method was further used to model Shield's tension test experiment, with initial calculations generating reasonable transformation strains and microstructures that compared well with the sequential laminates obtained experimentally.</p>https://thesis.library.caltech.edu/id/eprint/1799Investigation of Thermal Tempering in Bulk Metallic Glasses
https://resolver.caltech.edu/CaltechETD:etd-04192004-120604
Authors: {'items': [{'email': 'can.aydiner@boun.edu.tr', 'id': 'Aydiner-Cahit-Can', 'name': {'family': 'Aydiner', 'given': 'Cahit Can'}, 'orcid': '0000-0001-8256-6742', 'show_email': 'YES'}]}
Year: 2004
DOI: 10.7907/ZC9Z-5Y06
<p>Bulk metallic glasses are recent advanced materials which generate residual stresses due to rapid cooling from their surfaces during processing. These stresses arise from the thermal gradients that form within the sample at and above the glass transition region. A typical processing of BMGs involves feeding the alloy melt into a mold followed by severe quenching. The formation and nature of these stresses are analogous to the residual stresses due to the thermal tempering of silicate glasses. This analytical-experimental study investigates the thermal tempering phenomenon in BMGs for the first time.</p>
<p>One of the best glass forming metallic alloys, Zr<sub>41.2</sub>Ti<sub>13.8</sub>Cu<sub>12.5</sub>Ni<sub>10</sub>Be<sub>22.5</sub> (Vitreloy 1<sup>TM</sup>), is employed in this study. First, the best technique for the high-resolution measurement of residual stresses in BMGs is determined to be the crack compliance method. Second, the formation of the stresses is modeled with three different levels of viscoelastic phenomenology, namely, an instant freezing model, a viscoelastic model and a structural model. The first is a simplistic analytical model to estimate residual stresses whereas the structural model accounts for the temperature history dependence of the glassy structure. The constitutive laws for the viscoelastic and structural models are incorporated into the finite element method (ABAQUS<sup>TM</sup> software package) allowing the application of these models to complex geometries. To increase the accuracy of the analysis, the 'correct' temperature evolution in the sample during processing has to be input to these 'mechanical' models. Therefore, the heat transfer problem during the casting process of the BMG is analyzed in detail. Accuracy also requires a detailed knowledge of the thermal parameters of the material as a function of temperature; thus, some attention is also devoted to their measurement.</p>
<p>At the end, calculated and measured stresses are compared and good agreement is achieved. BMGs are demonstrated to be capable of generating very high (around 400 MPa) compression on their surfaces. The study also yielded valuable physical insight into the thermal tempering process itself. It is seen that this process exhibits significant discrepancies in BMGs compared to its analogy in silicate glasses. For instance, the transient tensile stresses that develop in the latter are shown to be lacking in the BMGs. Another discrepancy between the two materials is that the density of BMGs is uniform across the sample cross section in contrast to that found in silicate glasses. Overall, this investigation developed sufficient understanding of the thermal tempering phenomenon in BMGs to establish it as a viable process to manipulate properties.</p>
https://thesis.library.caltech.edu/id/eprint/1409Energy-Minimizing Microstructures in Multiphase Elastic Solids
https://resolver.caltech.edu/CaltechETD:etd-05252004-131315
Authors: {'items': [{'email': 'Isaac.Chenchiah : bristol.ac.uk', 'id': 'Chenchiah-Isaac-Vikram', 'name': {'family': 'Chenchiah', 'given': 'Isaac Vikram'}, 'orcid': '0000-0002-8618-620X', 'show_email': 'YES'}]}
Year: 2004
DOI: 10.7907/RXE5-9A33
<p>This thesis concerns problems of microstructure and its macroscopic consequences in multiphase elastic solids, both single crystals and polycrystals.</p>
<p>The elastic energy of a two-phase solid is a function of its microstructure. Determining the infimum of the energy of such a solid and characterizing the associated extremal microstructures is an important problem that arises in the modeling of the shape memory effect, microstructure evolution (precipitation, coarsening, etc.), homogenization of composites and optimal design. Mathematically, the problem is to determine the relaxation under fixed volume fraction of a two-well energy.</p>
<p>We compute the relaxation under fixed volume fraction for a two-well linearized elastic energy in two dimensions with no restrictions on the elastic moduli and transformation strains; and show that there always exist rank-I or rank-II laminates that are extremal. By minimizing over the volume fraction we obtain the quasiconvex envelope of the energy. We relate these results to experimental observations on the equilibrium morphology and behavior under external loads of precipitates in Nickel superalloys. We also compute the relaxation under fixed volume fraction for a two-well linearized elastic energy in three dimensions when the elastic moduli are isotropic (with no restrictions on the transformation strains) and show that there always exist rank-I, rank-II or rank-III laminates that are extremal.</p>
<p>Shape memory effect is the ability of a solid to recover on heating apparently plastic deformation sustained below a critical temperature. Since utility of shape memory alloys critically depends on their polycrystalline behavior, understanding and predicting the recoverable strains of shape memory polycrystals is a central open problem in the study of shape memory alloys. Our contributions to the solution of this problem are twofold:</p>
<p>We prove a dual variational characterization of the recoverable strains of shape memory polycrystals and show that dual (stress) fields could be signed Radon measures with finite mass supported on sets with Lebesgue measure zero. We also show that for polycrystals made of materials undergoing cubic-tetragonal transformations the strains fields associated with macroscopic recoverable strains are related to the solutions of hyperbolic partial differential equations.</p>https://thesis.library.caltech.edu/id/eprint/2044Investigation of the Multiscale Constitutive Behavior of Ferroelectric Materials Using Advanced Diffraction Techniques
https://resolver.caltech.edu/CaltechETD:etd-05282004-105848
Authors: {'items': [{'id': 'Rogan-Robert-Cashman', 'name': {'family': 'Rogan', 'given': 'Robert Cashman'}, 'show_email': 'NO'}]}
Year: 2004
DOI: 10.7907/BT3T-F608
<p>Ferroelectric ceramics are widely used in a diverse set of devices including sensors, actuators, and transducers. The technological importance of ferroelectrics originates from their large electromechanical coupling. Ferroelectric materials exhibit a complicated behavior in response to both electrical and mechanical loads which produce large internal stresses that eventually lead to failure. Efforts to model and predict the behavior of ferroelectrics have been hindered by the lack of suitable constitutive relations that accurately describe the electromechanical response of these materials. While many measurements have been conducted on the macroscopic response of single-crystals or polycrystals, multiaxial (and multiscale) data about the in situ internal strain and texture response of these materials is lacking; this information is critical to the development of accurate models, and diffraction techniques which directly measure internal crystal strains and material texture are aptly suited to supply it.</p>
<p>A neutron diffraction technique was employed which allowed for the simultaneous measurement of material texture and lattice strains in directions parallel and transverse to an applied mechanical load. By comparing the behaviors of single-phase tetragonal, single-phase rhombohedral, and dual-phase morphotropic compositions, information concerning mechanics of average macroscopic behavior was inferred. In an effort to probe more of the multiaxial constitutive behavior, a high-energy X-ray diffraction technique was employed. Using transmission geometry and a 2-D image plate detector, 36 different directions of sample behavior were measured simultaneously. Polychromatic scanning X-ray microdiffraction was used to investigate the microscale three-dimensional strain tensor in single-crystals. One investigation yielded the first ever direct measurement of the tri-axial strain fields associated with single domain walls in ferroelectrics. The second investigation recorded the domain switching mechanisms activated to accommodate indentation-induced fracture stresses. Finally, 3-D XRD was used to probe the mesoscale constitutive behavior of single, embedded grains of BaTiO3 within a polycrystalline matrix.</p>
<p>The experimental methods described in this thesis provide access to two-dimensional and three-dimensional multiaxial constitutive strain behavior in ferroelectrics for each of the microscopic, mesoscopic, and macroscopic length scales. Results from each of these length scales will provide critical data for models attempting to accurately describe the behavior of ferroelectric materials.</p>
https://thesis.library.caltech.edu/id/eprint/2187Gaseous Detonation-Driven Fracture of Tubes
https://resolver.caltech.edu/CaltechETD:etd-04062004-165940
Authors: {'items': [{'id': 'Chao-Tong-Wa', 'name': {'family': 'Chao', 'given': 'Tong Wa'}, 'show_email': 'NO'}]}
Year: 2004
DOI: 10.7907/TEZP-YC46
<p>An experimental investigation of fracture response of aluminum 6061-T6 tubes under internal gaseous detonation loading has been carried out. The pressure load, with speeds exceeding 2 km/s, can be characterized as a pressure peak (ranging from 2 to 6 MPa) followed by an expansion wave. The unique combination of this particular traveling load and tube geometry produced fracture data not available before in the open literature. Experimental data of this type are useful for studying the fluid-structure-fracture interaction and various crack curving and branching phenomena, and also for validation for multi-physics and multi-scale modeling.</p>
<p>Axial surface flaws were introduced to control the crack initiation site. Fracture threshold models were developed by combining a static fracture model and an extensively studied dynamic amplification factor for tubes under internal traveling loads. Experiments were also performed on hydrostatically loaded preflawed aluminum 6061-T6 tubes for comparison. Significantly different fracture behavior was observed and the difference was explained by fluid dynamics and energy considerations. The experiments yielded comparison on crack speeds, strain, and pressure histories.</p>
<p>In other experiments, the specimens were also pre-torqued to control the propagation direction of the cracks. Measurements were made on the detonation velocity, strain history, blast pressure from the crack opening, and crack speeds. The curved crack paths were digitized. The Chapman-Jouguet pressure, initial axial flaw length, and torsion level were varied to obtain different crack patterns. The incipient crack kinking angle was found to be consistent with fracture under mixed-mode loading. High-speed movies of the fracture events and blast wave were taken and these were used in interpreting the quantitative data.</p>
<p>Numerical simulations were performed using the commercial explicit finite-element software LS-Dyna. The detonation wave was modeled as a traveling boundary load. Both non-fracturing linear elastic simulations and elastoplastic simulations with fracture were conducted on three-dimensional models. The simulated fracture was compared directly with an experiment with the same conditions. The overall qualitative fracture behavior was captured by the simulation. The forward and backward cracks were observed to branch in both the experiment and simulation.</p>https://thesis.library.caltech.edu/id/eprint/1276A Director-Field Theory of DNA Packaging in Bacteriophage Viruses
https://resolver.caltech.edu/CaltechETD:etd-10132003-150122
Authors: {'items': [{'id': 'Klug-William-Scott', 'name': {'family': 'Klug', 'given': 'William Scott'}, 'show_email': 'NO'}]}
Year: 2004
DOI: 10.7907/E0V6-4Y97
<p>This thesis is concerned with the formulation of a continuum theory of packaging of DNA in bacterial viruses based on a director-field representation of the encapsidated DNA. The point values of the director field give the local direction and density of the DNA. The continuity of the DNA strand requires that the director field be divergence-free and tangent to the capsid wall. The energy of the DNA is defined as a functional of the director field which accounts for bending, torsion, and for electrostatic interactions through a density-dependent interaction energy. The operative principle which determines the encapsidated DNA conformation is assumed to be energy minimization.</p>
<p>The director-field theory is used for the direct formulation and study of two low-energy DNA conformations: the inverse spool and torsionless toroidal solenoids. Analysis of the inverse spool configuration yields predictions of the interaxial spacing and the dependence of the packing force on the packed genome fraction which are found to be in agreement with experiments. Further analysis shows that torsionless toroidal solenoids can achieve lower energy than the inverse spool configuration.</p>
<p>Also, the theory is adapted to a framework of numerical optimization, wherein all fields are discretized on a computational lattice, and energy minimizing configurations are sought via simulated annealing and the nonlinear conjugate gradient method. It is shown that the inverse spool conformation is stable in all regions of the virus capsid except in a central core, where the DNA tends to buckle out of the spooling plane.</p>https://thesis.library.caltech.edu/id/eprint/4059Quantitative Biaxial Texture Analysis with Reflection High-Energy Electron Diffraction for Ion Beam-Assisted Deposition of MgO and Heteroepitaxy of Perovskite Ferroelectrics
https://resolver.caltech.edu/CaltechETD:etd-08182003-150957
Authors: {'items': [{'email': 'rhett@alumni.caltech.edu', 'id': 'Brewer-Rhett-Ty', 'name': {'family': 'Brewer', 'given': 'Rhett Ty'}, 'show_email': 'YES'}]}
Year: 2004
DOI: 10.7907/J5PY-RS79
<p>To facilitate ferroelectric-based actuator integration with silicon electronics fabrication technology, we have developed a route to produce biaxially textured ferroelectrics on amorphous layers by using biaxially textured MgO templates.</p>
<p>Using a kinematical electron scattering model, we show that the RHEED pattern from a biaxially textured polycrystalline film can be calculated from an analytic solution to the electron scattering probability. We found that diffraction spot shapes are sensitive to out-of-plane orientation distributions and in-plane RHEED rocking curves are sensitive to the in-plane orientation distribution. Using information from the simulation, a RHEED-based experimental technique was developed for in situ measurement of MgO biaxial texture. The accuracy of this technique was confirmed by comparing RHEED measurements of in-plane and out-of-plane orientation distribution with synchrotron x-ray rocking curve measurements.</p>
<p>Biaxially textured MgO was grown on amorphous Si3N4 by ion beam-assisted deposition (IBAD). MgO was e-beam evaporated onto the amorphous substrate with a simultaneous 750-1200 eV Ar⁺ ion bombardment at 45° from normal incidence. We observed a previously unseen, dramatic texture evolution in IBAD MgO using transmission electron microscopy (TEM) and RHEED-based quantitative texture measurements of MgO. The first layers of IBAD MgO are diffraction amorphous until the film is about 3.5 nm thick. During the next 1 nm of additional growth, we observed rapid biaxial texture evolution. RHEED and TEM studies indicate that biaxially textured MgO film results from a solid phase crystallization of biaxially textured MgO crystals in an amorphous matrix.</p>
<p>Biaxially textured perovskite ferroelectrics were grown on biaxially textured MgO templates using sol-gel, metallorganic chemical vapor deposition (MOCVD), and molecular beam epitaxy (MBE). Through RHEED-based biaxial texture analysis we observed that the heteroepitaxial ferroelectric in-plane orientation distribution, deposited using ex situ techniques (not performed in the same high vacuum growth environment where the MgO was deposited), narrowed significantly with respect to the in-plane orientation distribution of its MgO template (from 11° to 6° FWHM). Evidence from cross section TEM and RHEED suggest that atmospheric moisture degrades the crystallinity of highly defective, misaligned MgO grains and that heteroepitaxially grown ferroelectrics preferentially nucleate on well-aligned grains and over grow misaligned regions of MgO.</p>https://thesis.library.caltech.edu/id/eprint/3160The Influence of Oxygen Vacancies on Domain Patterns in Ferroelectric Perovskites
https://resolver.caltech.edu/CaltechETD:etd-01032005-140446
Authors: {'items': [{'id': 'Xiao-Yu', 'name': {'family': 'Xiao', 'given': 'Yu'}, 'show_email': 'NO'}]}
Year: 2005
DOI: 10.7907/5QSX-9Y68
<p>This thesis investigates the role of oxygen vacancies in determining ferroelectric properties and domain patterns of ferroelectric perovskites. Being non-polar (paraelectric) above their Curie temperature but spontaneously polarized (ferroelectric) below it, ferroelectric perovskites offer a tantalizing potential for applications: large actuation through domain switching and memory storage via switchable electric polarization. Oxygen vacancies, commonly present and mobile at high temperature, are the primary defects and thus play a central role in these applications.</p>
<p>We develop a model that combines the ferroelectric and semiconducting nature of ferroelectric perovskites. Oxygen vacancies act as n-type dopants and thus affect the semiconducting properties. We show that the ferroelectric and semiconducting features interact and lead to the formation of depletion layers near the electrodes and double layers at the 90° domain walls. We find a potential drop across 90° domain walls even in a perfect crystal. This potential drop marks the essential difference between a 90° and an 180° domain wall, drives the formation of a space charge double layer in a doped crystal, promotes electronic charge injection and trapping, and leads to the redistribution of oxygen vacancies at 90° domain walls. The rearrangement of oxygen vacancies near 90° domain walls may form a basis for domain memory and provides a potentially new mechanism for large electrostriction.</p>
<p>We also rigorously justify the continuum theory by calculating the Coulomb energy of a spontaneously polarized solid starting from a periodic distribution of charges based on the classical interpretation of ferroelectrics and with a definite choice of polarization per unit cell. We prove that in the limit where the size of the body is large compared to the unit cell, the energy of Coulombic interactions may be approximated by a sum of a local part and a nonlocal part. The local part depends on the lattice structure, but is different from the Lorentz formula for a lattice of dipoles. The nonlocal part is identical to the Lorentz formula.</p>https://thesis.library.caltech.edu/id/eprint/8Development of Novel Binary and Multi-Component Bulk Metallic Glasses
https://resolver.caltech.edu/CaltechETD:etd-05272005-160315
Authors: {'items': [{'id': 'Xu-Donghua', 'name': {'family': 'Xu', 'given': 'Donghua'}, 'orcid': '0000-0001-5018-5603', 'show_email': 'NO'}]}
Year: 2005
DOI: 10.7907/XD2M-WW51
<p>Bulk Metallic Glasses (BMGs) have been drawing increasing attention in recent years due to their scientific and engineering significance. A great deal of effort in this area has been devoted to developing BMGs in different alloy systems. BMGs based on certain late transition metals (e.g. Fe, Co, Ni, Cu) have many potential advantages over those based on early transition metals. These include even higher strength and elastic modulii, and lower materials cost, to name a few, which are highly preferable for a broad application of BMGs as engineering materials. Nevertheless, these ordinary-late-transition-metal-based BMGs generally have quite limited glass-forming ability (GFA). In particular, for the Ni-based and Cu-based alloys reported prior to this research, the maximum casting thickness allowed to retain their amorphous structures is only ~2 mm (or lower) and ~5 mm (or lower), respectively.</p>
<p>During this research it was first found that certain quinary Ni-based alloys in the Ni-Cu-Ti-Zr-Al system can be cast into 5 mm diameter amorphous rods. This critical casting thickness is the highest for any reported Ni-based BMG’s indicating that these alloys are the easiest metallic glass formers based on Ni discovered to date. Secondly, certain binary alloys in the Cu-Zr and Cu-Hf systems were found to form bulk glasses with casting thickness as high as 2 mm. The discovery of these binary BMGs was very surprising since it had been widely considered that only multi-component (containing at least three elements) alloys could form bulk metallic glasses. These new binary BMGs provide interesting subjects for future theoretical studies such as molecular dynamics simulations since they possess both the simplicity of binary alloys and the good GFA of multi-component BMGs. In fact, these binary BMGs have led to the third but perhaps the most significant progress during this research, i.e., the discovery of a family of Cu-based BMGs in the Cu-Zr-Al-Y system which possess a critical casting thickness up to 1 cm. These quaternary Cu-based alloys, together with some complicated Fe-based alloys reported by two other groups during the course of this research, are the first centimeter level BMGs based on the ordinary late transition metals.</p>
<p>This thesis first reviews the fundamentals related to BMG development, then reports in detail the formation and properties of the above-mentioned binary and multi-component BMGs based on Ni and Cu. A generalized geometric model for the critical-value problem of nucleation developed in this research is also presented.</p>https://thesis.library.caltech.edu/id/eprint/2158Sol-Gel Synthesis of Highly Oriented Lead Barium Titanate and Lanthanum Nickelate Thin Films for High Strain Sensor and Actuator Applications
https://resolver.caltech.edu/CaltechETD:etd-03282005-113506
Authors: {'items': [{'email': 'Stacey.W.Boland@jpl.caltech.edu', 'id': 'Boland-Stacey-Walker', 'name': {'family': 'Boland', 'given': 'Stacey Walker'}, 'show_email': 'YES'}]}
Year: 2005
DOI: 10.7907/7H7R-6X26
Piezoelectric materials, capable of 0.1% strains, have been extensively used in sensor and actuator applications. Ferroelectric materials, a subset of the piezoelectric class, are capable of strains an order of magnitude larger. For a ferroelectric material with tetragonal crystal structure, large strains can be achieved through 90 degree domain switching between a and c domains. Bulk barium titanate has been shown to produce strains of 0.9% through such domain switching under combined electromechanical loading. Lead titanate has a larger c/a ratio and would be expected to produce 6% strains, though it is prone to brittle fracture. By examining the solid solution lead barium titanate, larger strains can be achieved while maintaining mechanical integrity. The work presented here covers the development of multiple sol-gel processes for producing powder and highly oriented thin film lead barium titanate, and a detailed discussion of their parametric optimization towards low temperature crystallization. Finally, results of early efforts toward integrating these films into useful structures and devices are discussed, including sol-gel synthesis of highly oriented conductive oxide electrodes. Thin film barium lead oxide and lanthanum nickelate electrodes were produced using sol-gel processing. (100)-oriented lanthanum nickelate electrodes were produced on a wide variety of amorphous and crystalline substrates, and subsequently deposited PBT showed excellent (100/001)-orientation regardless of substrate. The ability to produce highly oriented ferroelectric films on oxide electrodes deposited directly on Si promises to improve fatigue characteristics and greatly facilitate efforts to integrate ferroelectric thin films into MEMS process.https://thesis.library.caltech.edu/id/eprint/1186Deformation Mechanisms of Bulk Metallic Glass Matrix Composites
https://resolver.caltech.edu/CaltechETD:etd-05272005-131120
Authors: {'items': [{'email': 'sylee@caltech.edu', 'id': 'Lee-Seung-Yub', 'name': {'family': 'Lee', 'given': 'Seung-Yub'}, 'show_email': 'NO'}]}
Year: 2005
DOI: 10.7907/X74S-3H47
<p>Bulk metallic glasses (BMGs) possess a unique set of mechanical properties that make them attractive structural materials: yield strength > 2 GPa, fracture toughness ~20 MPa.m1/2 and elastic strain limit ~2%. BMGs can also be cast into intricate shapes which retain their dimensional integrity and require no further machining. Unfortunately, monolithic BMGs fail catastrophically under unconstrained loading by forming shear bands. To overcome this problem, BMG matrix composites with fiber and dendritic reinforcements were proposed. The former type includes metallic fibers of Ta, Mo and stainless steel. The latter composites develop precipitates during casting and are thus called in-situ composites. Here, the reinforcements form an interpenetrating dendritic structure and enhance the ductility of the composite.</p>
<p>This study investigated the deformation behavior of these two types of BMG composites. Loading measurements were performed during neutron or high-energy X-ray diffraction to determine lattice strains in the crystalline reinforcements. The diffraction data were then combined with finite element and self-consistent modeling to deduce the behavior of the amorphous matrix, as well as to understand the effective deformation mechanisms in the composite.</p>
<p>The deformation of the wire composites was studied using an integrated neutron diffraction and finite element (FE) approach. The FE model yielded a reasonable version of in-situ stress-strain plots for both reinforcements and the matrix. It was found that the reinforcements yielded first and started transferring load to the matrix which remained elastic throughout the whole loading experiment. The reinforcements were seen to possess yield strengths lower than their monolithic forms, likely due to annealing during processing. After optimizing material properties to fit experimental data, the FE model developed was reasonably successful in describing both the macroscopic composite deformation and the lattice strain evolution in the reinforcements.</p>
<p>In the case of the in-situ composites, a detailed neutron and high energy X-ray diffraction study was conducted combined with a self-consistent deformation model. The compressive behavior of the composite and the second phase (in its monolithic form) were investigated. It was shown that the ductile second phase yields first upon loading the composite followed by multiple shear band formation in the BMG matrix, a process which enhances the ductility of the composite. It was also discovered that the mechanical properties of the reinforcements, and indirectly the composite, are highly variable and quite sensitive to processing conditions. This resulted from the unstable nature of the BCC beta phase reinforcements which tend to transform into an ordered phase leading to significant stiffening, but also loss of ductility. An additional heat treatment study confirmed this phase evolution.</p>
<p>The overall conclusion of this study is that BMG composites with high ductility require reinforcements that yield first and induce multiple shear bands in the amorphous matrix, which in turn enhances the latter’s ductility. To also retain a high yield point, the reinforcements need to be stiff. These two properties can best be optimized in beta phase composites via a judicious combination of microstructure control and heat treatment.</p>https://thesis.library.caltech.edu/id/eprint/2149Atomic Structure of Ferroelectric Domain Walls, Free Surfaces and Steps
https://resolver.caltech.edu/CaltechETD:etd-12142004-121255
Authors: {'items': [{'email': 'arash.yavari@ce.gatech.edu', 'id': 'Yavari-Arash', 'name': {'family': 'Yavari', 'given': 'Arash'}, 'orcid': '0000-0002-7088-7984', 'show_email': 'YES'}]}
Year: 2005
DOI: 10.7907/jdy3-1m77
The goal of this thesis is to develop a general framework for lattice statics analysis of defects in ferroelectric Perovskites. The techniques presented here are general and can be easily applied to other systems as well. We present all the calculations and numerical examples for two technologically important ferroelectric materials, namely, PbTiO3 and BaTiO3. We use shell potentials, that are derived using quantum mechanics calculations, and analyze three types of defects: (i) 180° and 90° domain walls, (ii) free surfaces and (iii) steps in 180° domain walls. Our formulation assumes that an interatomic potential is given. In other words, there is no need to have the force constants or restrict the number of nearest neighbor interactions a priori. Depending on the defect and symmetry, the discrete governing equations are reduced to those for representatives of some equivalence classes. The idea of symmetry reduction in lattice statics calculations is one of the contributions of this thesis. We call our formulation of lattice statics 'inhomogeneous lattice statics' as we consider the fact that close to defects force constants (stiffness matrices) change. For defects with one-dimensional symmetry reduction we solve the discrete governing equations directly using a novel method in the setting of the theory of difference equations. This will be compared with the solutions obtained using discrete Fourier transform. For defects with two-dimensional symmetry reduction we solve the discrete governing equations using discrete Fourier transform. We calculate the fully nonlinear solutions using modified Newton-Raphson iterations and call the method 'inhomogeneous anharmonic lattice statics'. This work is aimed to fill the gap between quantum mechanics ab initio calculations and continuum models (based on Landau-Ginzberg-Devonshire theory) of ferroelectric domain walls.https://thesis.library.caltech.edu/id/eprint/4991Atomistic Simulation of Barium Titanate
https://resolver.caltech.edu/CaltechETD:etd-10292004-152709
Authors: {'items': [{'id': 'Zhang-Qingsong', 'name': {'family': 'Zhang', 'given': 'Qingsong'}, 'show_email': 'NO'}]}
Year: 2005
DOI: 10.7907/SQ9J-4H73
<p>We present the Polarizable Charge Equilibration (P-QEq) force field to include self-consistent atomic polarization and charge transfer in molecular dynamics of materials. The short-range Pauli repulsion effects are described by two body potentials without exclusions. A linear self-consistent field solution to the charge transfer is proposed for charge transfer in large systems. The P-QEq is parameterized for BaTiO₃ based on quantum mechanics calculations (DFT with GGA) and applied to the study of the phase transitions, domain walls and oxygen vacancies.</p>
<p>Frozen phonon analysis reveals that the three high-temperature BaTiO₃ phases in the displacive model are unstable. Within their corresponding macroscopic phase symmetries, the smallest stable phase structures are achieved by antiferroelectric distortions from unstable phonons at the Brillouin zone boundaries. The antiferroelectric distortions soften phonons, reduce zero point energies and increase vibrational entropies. A correct BaTiO₃ phase transition sequence and comparable transition temperatures are obtained by free energy calculations. The inelastic coherent scattering functions of these phases agree with X-ray diffraction experiments.</p>
<p>BaTiO₃ 180° domain wall is Ba-centered with abrupt polarization switching across the wall. The center of BaTiO₃ 90° domain wall is close to its orthogonal phase. There are transition layers from the wall centers to the internal domains in the types of domain walls. Polarization variation in these transition layers induces polarization charge and free charge transfer. This effect causes a strong bipolar electric field in BaTiO₃ 90° domain wall.</p>
<p>Oxygen vacancies are frozen at room temperature, and mobile near the Curie temperature. In the tetragonal phase, the broken Ti-O chains are frozen, reducing switchable polarization. Due to charge redistribution and local relaxation, oxygen vacancy interaction is short-range and anisotropic. Two oxygen vacancies can form a stable pair state, where two broken Ti-O chains are aligned parallel. Oxygen vacancy clusters can form dendritic structures as a result of local relaxation and charge interaction.</p>https://thesis.library.caltech.edu/id/eprint/4303Theory of Complex Lattice Quasicontinuum and Its Application to Ferroelectrics
https://resolver.caltech.edu/CaltechETD:etd-12202004-182638
Authors: {'items': [{'email': 'okowalewsky@ggu.edu', 'id': 'Kowalewsky-Olga', 'name': {'family': 'Kowalewsky', 'given': 'Olga'}, 'show_email': 'NO'}]}
Year: 2005
DOI: 10.7907/rb0c-9534
<p>Complex lattice Quasicontinuum theory is developed and applied to the description of ferroelectric phenomena. Quasicontinuum theory is a multiscale theory that provides a unified description of materials by combining atomistic and continuum approaches. It provides a seamless transition between atomistics and continuum, but the description of the material is derived directly from the underlying atomic structure, using the computationally expensive atomistics only where needed, at the location of phenomena of atomistic origin.</p>
<p>Complex Lattice Quasicontinuum theory can be applied to complex lattice crystals consisting of many kinds of atoms. One highlight of it is treatment of each component lattice as separately and independently as possible. The component Quasicontinua are coupled through the microscopic forces within nodal clusters, making the complex atomistics of the heterogeneous lattice the basis of the description.</p>
<p>Ferroelectrics are especially suited to the application of Quasicontinuum theory. The nature of defects in ferroelectric materials is atomistic, but their influence over the material is long ranged due to induced elastic fields. Many different ferroelectric phenomena involving the perovskite ferroelectrics Barium Titanate and Lead Titanate are investigated and simulated. For Barium Titanate: the 180 degree domain wall structure and quasistatic crack under load. For Lead Titanate: the 180 degree domain wall structure and a domain wall step.</p>
<p>The results for the domain walls show that the domain wall thickness is atomistically small, of the order of few lattice constants, which is in agreement with recent ab initio molecular dynamics simulations, but we also observe long range effects resulting from the presence of the wall. During crack loading in the sample of Barium Titanate we observe polarization changes around the crack tip which are consistent with experimental observations of an increase of fracture toughness. The quasicontinuum study of a domain wall step gives an atomistical view into the equilibrium structure of the step.</p>
<p>Quasicontinuum is able to model these phenomena with atomistic precision around the defects and non-homogeneities, and also capture the influence of long-ranging effects in the samples. These studies could also give valuable modeling input for larger scale continuum approaches.</p>https://thesis.library.caltech.edu/id/eprint/5084Configurational Forces and Variational Mesh Adaption in Solid Dynamics
https://resolver.caltech.edu/CaltechETD:etd-05112006-162905
Authors: {'items': [{'id': 'Zielonka-Matias-Gabriel', 'name': {'family': 'Zielonka', 'given': 'Matias Gabriel'}, 'show_email': 'NO'}]}
Year: 2006
DOI: 10.7907/V6RB-FR94
This thesis is concerned with the exploration and development of a variational finite element mesh adaption framework for non-linear solid dynamics and its conceptual links with the theory of dynamic configurational forces. The distinctive attribute of this methodology is that the underlying variational principle of the problem under study is used to supply both the discretized fields and the mesh on which the discretization is supported. To this end a mixed-multifield version of Hamilton's principle of stationary action and Lagrange-d'Alembert principle is proposed, a fresh perspective on the theory of dynamic configurational forces is presented, and a unifying variational formulation that generalizes the framework to systems with general dissipative behavior is developed. A mixed finite element formulation with independent spatial interpolations for deformations and velocities and a mixed variational integrator with independent time interpolations for the resulting nodal parameters is constructed. This discretization is supported on a continuously deforming mesh that is not prescribed at the outset but computed as part of the solution. The resulting space-time discretization satisfies exact discrete configurational force balance and exhibits excellent long term global energy stability behavior. The robustness of the mesh adaption framework is assessed and demonstrated with a set of examples and convergence tests.https://thesis.library.caltech.edu/id/eprint/1724Dissipative Nanomechanics
https://resolver.caltech.edu/CaltechETD:etd-03272006-142956
Authors: {'items': [{'email': 'mandarinamdar78@gmail.com', 'id': 'Inamdar-Mandar-Mukund', 'name': {'family': 'Inamdar', 'given': 'Mandar Mukund'}, 'orcid': '0000-0001-8549-8490', 'show_email': 'NO'}]}
Year: 2006
DOI: 10.7907/P5K9-BD68
<p>Due to thermal fluctuations, systems at small length scales are remarkably different than their large length scale counterparts. For example, bacterial viruses (phages) have thousands of nanometers of DNA packed inside a hollow capsid of tens of nanometers. This tight compaction leads to large forces on the phage DNA (tens of piconewtons). These forces can be subsequently utilized to instigate the DNA ejection during the infection phase. Developments in optics, biochemistry, microfluidics, etc., have enabled the experimental quantification of these forces, and the rate of DNA packing and ejection. Similarly, eukaryotic genome is compacted into nanometer size structures called nucleosomes. The conformational changes in the nucleosome due to the thermal fluctuations of the DNA are instrumental in making the DNA accessible for key genomic processes. Developments in FRET, gel electrophoresis, spectroscopy etc. have made it possible to quantify the equilibrium constant and the rates of these fluctuations. The first part of the thesis involves formulation of simple models for the phage and nucleosome to respond to the existing experimental data and predict results to stimulate further experimentation.</p>
<p>One of the next frontiers in biology is to understand the "small numbers" problem: how does a biological cell function given that most of its proteins and nucleotide polymers are present in numbers much smaller than Avogadro's number? For example, one of the most important molecules, a cell's DNA, occurs in only a single copy. Also, it is the flow of matter and energy through cells that makes it possible for organisms to maintain a relatively stable form. Hence, cells must be in this stable state far from equilibrium to function. Many problems of current interest thus involve small systems that are out of equilibrium. Unfortunately, there is no general theoretical frame-work to model these dissipative systems. E. T. Jaynes suggested the use of dynamical microtrajectories to write down the trajectory entropy, or caliber, for such systems. Maximization of this trajectory entropy, subject to the external constraints, provides one with the probabilities of the underlying microtrajectories. Jaynes calls this the "principle of maximum caliber." Advances in optics, video-microscopy, etc. have made it possible to experimentally measure these microtrajectories for various systems. In the second part of the thesis we develop simple microtrajectory models for small systems like molecular motors, ion-channels, etc., and apply the maximum caliber principle to obtain the probabilities of the underlying microtrajectories. Our goal is to respond to these experiments and make new predictions.</p>https://thesis.library.caltech.edu/id/eprint/1165Vibrational Entropy Contributions to the Phase Stability of Iron- and Aluminum-Based Binary Alloys
https://resolver.caltech.edu/CaltechETD:etd-09012005-143247
Authors: {'items': [{'email': 'tabitha.swanwood@csuci.edu', 'id': 'Swan-Wood-Tabitha-Liana', 'name': {'family': 'Swan-Wood', 'given': 'Tabitha Liana'}, 'show_email': 'NO'}]}
Year: 2006
DOI: 10.7907/3PTA-J395
<p>This work considers phonon entropy effects on phase stability of three binary alloys: Fe-Cr, FeAl, and Al-Ag. In all cases the vibrational entropy plays an interesting role.</p>
<p>The phonon density of states was measured on body-centered cubic Fe<sub>0.50</sub>Cr<sub>0.50</sub> prepared as a solid solution, and in increasingly un-mixed states induced by annealing the solid solution at 773 K. Mossbauer spectrometry was used to characterize the extent of decomposition after annealing. A neutron-weight correction was performed, using results from the Mossbauer spectra and recent data on inelastic nuclear resonant scattering from <sub>57</sub>Fe-Cr. The vibrational entropy of decomposition was found to be 0.17 ± 0.01 k<sub>B</sub>/atom, nearly equal to the change in configurational entropy after spinodal decomposition. Vibrational entropy has a large effect on the critical temperature for spinodal decomposition in equi-atomic Fe<sub>0.50</sub>Cr<sub>0.50</sub>.</p>
<p>The vibrational entropy of formation of vacancies in FeAl is studied in detail. Born von Karman calculations show that the point defects due to vacancy formation have a strong stiffening effect on one of the transverse acoustic branches in the (1 1 0) direction. The vibrational entropy of vacancy formation is measured to be 0.75 k<sub>B</sub>/vacancy.</p>
<p>The anharmonic vibrational entropy of FeAl is measured in the temperature range of 10 K to 1323 K. It is shown that there is an abnormally large softening between 10 K and 300 K, which is attributed to a local magnetic moment corresponding to Fe anti-site defects at 10 K. Also measured is an anomalously small anharmonic entropy between 300 K and 1323 K. This could be caused by thermal vacancies and point defects.</p>
<p>The anharmonic entropy of Al<sub>0.40</sub>Ag<sub>0.60</sub> have been measured to be extremely large between 20 C and 520 C. The origins of this anharmonicity are unclear. The origins of this anharmonic entropy of Al<sub>0.93</sub>Ag<sub>0.07</sub> between 20°C and 520°C was found to be fully described by lattice expansion. A large Ag resonance peak was measured in Al<sub>0.93</sub>Ag<sub>0.07</sub> at 20°C. The Mannheim method was used to show that this peak could make a large contribution to the increased solubility of Ag in Al at high temperatures.</p>https://thesis.library.caltech.edu/id/eprint/3306Mechanical Characterization of Thin Films with Application to Ferroelectrics
https://resolver.caltech.edu/CaltechETD:etd-01312006-170959
Authors: {'items': [{'email': 'rongjing@gmail.com', 'id': 'Zhang-Rongjing', 'name': {'family': 'Zhang', 'given': 'Rongjing'}, 'show_email': 'NO'}]}
Year: 2006
DOI: 10.7907/CJR5-DK94
<p>One important part of the motivation for this research work comes from the microelectromechanical systems (MEMS) technology. Its basic concept of high volume production and low unit cost can only be achieved when the devices made by microelectronics technique are reliable. The success in this area largely depends on the understanding of materials. However, the mechanical characterization is lagged behind the theoretical work and designing software development. The standard characterization method is still not established. For MEMS actuators, especially for active materials, the desired characterization system for obtaining mechanical properties requires load control feature and the capability of doing dynamic tests. However, there is no such method among the currently available tools for mechanical characterization.</p>
<p>The other part of the motivation comes from the comprehensive research work of Caltech ferroelectric group. This group, which consists of nine faculty members, is aiming to develop new devices, especially new actuators, by the aid of multi-scale theory tools and selected experimental methods. The work presented in this dissertation is an important and key step of this ambitious project: the electromechanical characterization of devices. This will provide validation for the multi-scale materials modeling framework and help to increase the reliability of the actuators and devices.</p>
<p>In this work, two techniques were developed for mechanical characterization, which satisfy the challenging requirements for thin film structures and devices: being able to do dynamic study on fragile ceramic thin film samples with load control feature. The first technique is a new method to characterize mechanical properties of released thin films under concentrated load. This technique can be used to apply load in the ?N?mN range with displacement measured with high accuracy of 0.1 ?m. The successful characterization of Si3N4 free-standing membranes demonstrated the capability and reliability of this new technique. The elastic modulus and residual stress of Si3N4 free-standing thin film were measured to be around 250 GPa and 450 MPa, respectively. These values were in close agreement with values obtained using a different technique as well as those found in the literature. This technique has the potential application on elastic-plastic characterization and characterization of other functional thin film materials such as shape memory alloys.</p>
<p>Pressure bulge test technique, which is another type of load control method suitable for dynamic test, was also developed. The apparatus was designed to be compact to fit into the x-ray diffractometer for in-situ XRD study and had additional compatibility for polarized light microscopy study. Characterization of free standing thin film of single layer amorphous silicon nitride (Si3N4) and multi-layered PBT/Si3N4, and thick film of single crystal barium titanate (BaTiO3) showed the capability and reliability of this technique. Excellent agreement of the Si3N4 Young’s modulus between these two developed methods gave the confidence for using these techniques to understand new materials.</p>
<p>In situ x-ray diffraction study was carried out on the single crystal thick films which were loaded with distributed mechanical loading by pressure bulge setup. Direct evidence of 90o domain switching was obtained from the in situ XRD results with the intensity changing in both (002) and (200) orientations. Obvious changes in domain patterns were observed by using the polarized light microscope. The Young’s modulus of this barium titanate single crystal thick film with thickness of 100 ?m was characterized before the XRD exam. Using this information, in-plane stress can be analyzed, and the relation between the driving force (the stress) and the microstructural change (volume fraction change in a-domain or c-domain) can be determined.</p>https://thesis.library.caltech.edu/id/eprint/420A Micromechanics-Inspired Three-Dimensional Constitutive Model for the Thermomechanical Response of Shape-Memory Alloys
https://resolver.caltech.edu/CaltechETD:etd-05112006-162948
Authors: {'items': [{'id': 'Sadjadpour-Amir', 'name': {'family': 'Sadjadpour', 'given': 'Amir'}, 'show_email': 'NO'}]}
Year: 2006
DOI: 10.7907/MB1W-1V17
<p>The goal of this thesis is to develop a full dimensional micromechanics-inspired constitutive model for polycrystalline shape-memory alloys. The model is presented in two forms: (1) The one-dimensional framework where we picture the ability of the model in capturing main properties of shape memory alloys such as superelasticity and shape-memory effect; (2) The full dimensional model where micromechanics origins of the model, the concepts emerged from those analysis and their relation to macroscopic properties in both single and polycrystals are presented.</p>
<p>We use this framework to study the effects of the texture and anisotropy in the material behavior. Since phase transformation often competes with plasticity in shape-memory alloys, we incorporate that phenomenon into our model. We also demonstrate the ability of the model to predict the response of the material and track the phase transformation process for multi-axial, proportional and non-proportional loading and unloading experiments. We consider both stress-controlled and strain-controlled experiments and develop the model for isothermal, adiabatic and non-adiabatic thermal conditions. Adiabatic heating and loading rate both lead to the apparent hardening at high rates. We also visit this problem and examine the relative role of these two factors.</p>
<p>Finally we extend our model to study the reversible "bcc" to "hcp" martensitic phase transformation in pure iron. We consider a wide range of loading rates ranging from quasistatic to high rate dynamic loading and use our model to describe the evolution of the microstructure along with the effects of the rate hardening and thermal softening.</p>https://thesis.library.caltech.edu/id/eprint/1725High Temperature Deformation of Vitreloy Bulk Metallic Glasses and Their Composite
https://resolver.caltech.edu/CaltechETD:etd-03022006-005723
Authors: {'items': [{'email': 'mint@caltech.edu', 'id': 'Tao-Min', 'name': {'family': 'Tao', 'given': 'Min'}, 'show_email': 'YES'}]}
Year: 2006
DOI: 10.7907/27SN-R187
<p>A complete understanding of the deformation mechanisms of BMGs and their composites requires investigation of the microstructural changes and their interplay with the mechanical behavior. In this dissertation, the deformation mechanisms of a series of Vitreloy glasses and their composites are experimentally investigated over a wide range of strain rates and temperatures, with focus on the supercooled liquid regime, by combining uniaxial mechanical testing with calorimetric and microscopic examinations. Various theories of deformation of metallic glasses and the composites are examined in light of the experimental data.</p>
<p>A comparative structural relaxation study was performed on two closely related Vitreloy alloys, Zr41.2Ti13.8Cu12.5Ni10Be22.5 (Vit 1) and Zr46.7Ti8.3Cu7.5Ni10Be27.5 (Vit 4). Differential scanning calorimetric studies on the specimens deformed in compression at constant-strain-rate in supercooled liquid regime showed that mechanical loading accelerated the spinodal phase separation and nanocrystallization process in Vit 1, while the relaxation in Vit 4 featured local chemical composition fluctuation accompanied by annealing out of free volume. The effect of the structural relaxation on their mechanical behavior was further studied via single and multiple jump-in-strain-rate tests.</p>
<p>The deformation and viscosity of a new Vitreloy alloy were characterized using uniaxial compression tests in its supercooled liquid regime. A new theoretical model named Cooperative Shear Model, which correlates the evolution of the macroscopic mechanical/thermal variables such as shear modulus and viscosity with the configurational energies of atom clusters in an amorphous alloy, was critically examined in this investigation. The model was successful in predicting the Newtonian and non-Newtonian viscosities of the material, as well as the shear moduli of the deformed specimens, in a self-consistent manner.</p>
<p>The plastic flow of an in-situ metallic glass composite, beta-Vitreloy, was investigated under uniaxial compression in its supercooled liquid regime and at various strain rates. The composite, with ~0.25 volume fraction of crystalline beta-phase dendrites exhibited superplastic behavior similar to that of amorphous Vit 1. Significant strain hardening was observed when the material was deformed at high temperatures and low strain rates. A dual-phase composite model was employed in finite element simulations to understand the effect of the composite microstructure on its mechanical behavior.</p>https://thesis.library.caltech.edu/id/eprint/834Wiener Chaos Expansion and Numerical Solutions of Stochastic Partial Differential Equations
https://resolver.caltech.edu/CaltechETD:etd-05182006-173710
Authors: {'items': [{'id': 'Luo-Wuan', 'name': {'family': 'Luo', 'given': 'Wuan'}, 'show_email': 'NO'}]}
Year: 2006
DOI: 10.7907/RPKX-BN02
<p>Stochastic partial differential equations (SPDEs) are important tools in modeling complex phenomena, and they arise in many physics and engineering applications. Developing efficient numerical methods for simulating SPDEs is a very important while challenging research topic. In this thesis, we study a numerical method based on the Wiener chaos expansion (WCE) for solving SPDEs driven by Brownian motion forcing. WCE represents a stochastic solution as a spectral expansion with respect to a set of random basis. By deriving a governing equation for the expansion coefficients, we can reduce a stochastic PDE into a system of deterministic PDEs and separate the randomness from the computation. All the statistical information of the solution can be recovered from the deterministic coefficients using very simple formulae.</p>
<p>We apply the WCE-based method to solve stochastic Burgers equations, Navier-Stokes equations and nonlinear reaction-diffusion equations with either additive or multiplicative random forcing. Our numerical results demonstrate convincingly that the new method is much more efficient and accurate than MC simulations for solutions in short to moderate time. For a class of model equations, we prove the convergence rate of the WCE method. The analysis also reveals precisely how the convergence constants depend on the size of the time intervals and the variability of the random forcing. Based on the error analysis, we design a sparse truncation strategy for the Wiener chaos expansion. The sparse truncation can reduce the dimension of the resulting PDE system substantially while retaining the same asymptotic convergence rates.</p>
<p>For long time solutions, we propose a new computational strategy where MC simulations are used to correct the unresolved small scales in the sparse Wiener chaos solutions. Numerical experiments demonstrate that the WCE-MC hybrid method can handle SPDEs in much longer time intervals than the direct WCE method can. The new method is shown to be much more efficient than the WCE method or the MC simulation alone in relatively long time intervals. However, the limitation of this method is also pointed out.</p>
<p>Using the sparse WCE truncation, we can resolve the probability distributions of a stochastic Burgers equation numerically and provide direct evidence for the existence of a unique stationary measure. Using the WCE-MC hybrid method, we can simulate the long time front propagation for a reaction-diffusion equation in random shear flows. Our numerical results confirm the conjecture by Jack Xin that the front propagation speed obeys a quadratic enhancing law.</p>
<p>Using the machinery we have developed for the Wiener chaos method, we resolve a few technical difficulties in solving stochastic elliptic equations by Karhunen-Loeve-based polynomial chaos method. We further derive an upscaling formulation for the elliptic system of the Wiener chaos coefficients. Eventually, we apply the upscaled Wiener chaos method for uncertainty quantification in subsurface modeling, combined with a two-stage Markov chain Monte Carlo sampling method we have developed recently.</p>https://thesis.library.caltech.edu/id/eprint/1861Mechanical Characterization of Damage and Failure in Polymeric Foams and Glass/Epoxy Composites
https://resolver.caltech.edu/CaltechETD:etd-11102006-182329
Authors: {'items': [{'id': 'Kidd-Theresa-Hiromi', 'name': {'family': 'Kidd', 'given': 'Theresa Hiromi'}, 'show_email': 'NO'}]}
Year: 2007
DOI: 10.7907/G25Y-KE07
<p>The mechanical characterization including evolution of damage and failure of foams and composites are becoming increasingly important, as they form the basic components of sandwich structures. Sandwich structures consist of two faceplates that surround a core material. In many modern applications, faceplates and cores are typically comprised of composite materials and polymeric foam, respectively. Knowledge of the failure behavior of these individual components is necessary for understanding the failure behavior and design of sandwich structures. A systematic investigation of the damage evolution and failure behavior of foams and composites was conducted using a variety of experimental techniques.</p>
<p>In-situ ultrasonic measurements were used to track the damage behavior in PVC polymeric foams with densities ranging from 130 to 250 kg/m³. The wave speeds were measured by two quartz piezoelectric shear transducers with a resonant frequency of 5 MHz in the transmission mode. A fixture was developed and constructed to protect the transducers during compression, while allowing them to take sound speed measurements of the sample along the axis of the load train. This fixture was placed in a servo-hydraulic MTS (Materials Testing System) machine, where the load-displacement response of the foam was recorded. A digital image correlation (DIC) method was used to capture the progression of failure under compression. Two dominant failure modes, elastic buckling and plastic collapse, were identified – and their onsets corresponded to the change in elastic wave speeds in the material, measured by the in-situ ultrasonic technique.</p>
<p>The transverse response of S-Glass/Epoxy unidirectional composites was investigated under varying degrees of confinement and strain rates. The experimental setup utilizes a fixture that allowed for independent measurement of the three principal stresses in a confined specimen. A servo-hydraulic materials testing system and a Kolsky (split Hopkinson) pressure bar generated strain rates between 10⁻³ to 10⁴ s⁻¹. Post-test scanning electron microscopy (SEM) observations suggest that under transverse loading at low-strain rates, confinement contributes to localized band formation. In addition, micrographs indicated that macroscopic transverse failure is dominated by shear stress, and occurs within these localized bands. These shear dominated failure bands were found inclined in a direction approximately 35° to the direction of loading. Implications of this orientation deviation of failure bands from maximum shear trajectories at 45° are discussed in reference to the state of confinement.</p>https://thesis.library.caltech.edu/id/eprint/4500Deformation and Fracture of Thin Sheets of Nitinol
https://resolver.caltech.edu/CaltechETD:etd-05252007-000127
Authors: {'items': [{'email': 'samdaly@engineering.ucsb.edu', 'id': 'Daly-Samantha-Hayes', 'name': {'family': 'Daly', 'given': 'Samantha Hayes'}, 'orcid': '0000-0002-7297-1696', 'show_email': 'YES'}]}
Year: 2007
DOI: 10.7907/RATX-WG46
Nickel-Titanium (Nitinol) is a Shape Memory Alloy (SMA) that exhibits superelasticity (pseudoelasticity) and shape memory by a solid-solid state diffusion-less phase transformation. Phase transformation and the resulting strain localization in Nitinol has long been a topic of study, both for its inherent scientific interest and also because of the large number of practical applications of this bimetallic alloy. Although Nitinol devices are extensively used in the medical industry, there is a fundamental gap in the amount of high-quality quantitative experimental data detailing strain localization. The numerous applications of shape memory alloys provide the motivation to understand the deformation and failure mechanisms of these materials, particularly their fatigue and fracture behavior. By using an in-situ optical technique called Digital Image Correlation (DIC), quantitative measures of strain localization in Nitinol are presented for the first time in both deformation and failure modes. In addition, a finite element small-scale transformation analysis near a crack tip in Nitinol subjected to mode-I loading under plane stress conditions is performed for the first time. The experimental results and finite element analysis provide new and detailed insights concerning the structure of phase transformation and crack tip fields in Nitinol.https://thesis.library.caltech.edu/id/eprint/2067Correlating Microscopic Ferroelectric Properties and Macroscopic Thin Film Device Performance
https://resolver.caltech.edu/CaltechETD:etd-02252007-153131
Authors: {'items': [{'email': 'jenrug@gmail.com', 'id': 'Ruglovsky-Jennifer-Lynn', 'name': {'family': 'Ruglovsky', 'given': 'Jennifer Lynn'}, 'show_email': 'NO'}]}
Year: 2007
DOI: 10.7907/K3BG-N315
<p>The relationship between thin film device performance and crystallographic microstructure is one of fundamental importance in materials science. Ferroelectric materials that show an electromechanical response via domain switching, such as the perovskites BaTiO<SUB>3</SUB> and PbTiO<SUB>3</SUB>, are discussed. In this work, we focus on thin film MEMS actuators fabricated from four different ferroelectric thin film microstructures: poorly oriented, fiber textured, biaxially textured, and single crystal. The microscale properties of these thin film materials are characterized and correlated to macroscale mechanical device behavior.</p>
<p>We have modeled each of these four microstructures to determine the effect of grain-scale crystallographic texture on device-scale electromechanical constants. The method enables the effective electromechanical properties to be obtained for a polycrystalline film via a self-consistent approach. Using this model, we show that most electromechanical constants depend primarily on the out-of-plane texture of the ferroelectric thin film.</p>
<p>We have used surface micromachining to create free-standing bridge geometries in ferroelectric thin films of polycrystalline and biaxially textured PbTiO<sub>3</sub>. The material properties of these thin films are characterized with various techniques to confirm the texture at the grain scale. We have utilized a custom experimental apparatus that can apply a loading force to a single microdevice via magnetostatic interaction while measuring the resulting displacement. The force-displacement curves that we measure provide insight into the initial stress and modulus of our composite beam devices and the role of the underlying crystalline microstructure.</p>
<p>In order to study cantilever actuators, BaTiO<SUB>3</SUB> active layers are grown monolithically on SrRuO<SUB>3</SUB> electrodes and devices are patterned via focused ion beam (FIB) milling exclusively or with a subsequent XeF<SUB>2</SUB> etch. Using this fabrication method, we study cantilevers consisting of fiber, biaxial, and single crystalline microtextures. The cantilevers are actuated by applying a voltage across the active layer and the resulting displacement is measured via inspection with optical microscopy. We are able to relate the macroscopic device performance to the microscopic piezoelectric constants via multimorph calculations.</p>
<p>Our experiments show that ferroelectric thin film device performance may be enhanced by improving the underlying grain scale crystalline microstructure - from fiber to biaxial to single crystal texture.</p>https://thesis.library.caltech.edu/id/eprint/766Electronic Structure Calculations at Macroscopic Scales
https://resolver.caltech.edu/CaltechETD:etd-05152007-121823
Authors: {'items': [{'email': 'vikram.gavini@gmail.com', 'id': 'Gavini-Vikram', 'name': {'family': 'Gavini', 'given': 'Vikram'}, 'orcid': '0000-0002-9451-2300', 'show_email': 'YES'}]}
Year: 2007
DOI: 10.7907/1R69-YY30
<p>Electronic structure calculations, especially those using density-functional theory have provided many insights into various materials properties in the recent decade. However, the computational complexity associated with electronic structure calculations has restricted these investigations to periodic geometries with small cell-sizes (computational domains) consisting of few atoms (about 200 atoms). But material properties are influenced by defects---vacancies, dopants, dislocations, cracks, free surfaces---in small concentrations (parts per million). A complete description of such defects must include both the electronic structure of the core at the fine (sub-nanometer) scale and also elastic and electrostatic interactions at the coarse (micrometer and beyond) scale. This in turn requires electronic structure calculations at macroscopic scales, involving millions of atoms, well beyond the current capability. This thesis presents the development of a seamless multi-scale scheme, Quasi-Continuum Orbital-Free Density-Functional Theory (QC-OFDFT) to address this significant issue. This multi-scale scheme has enabled for the first time a calculation of the electronic structure of multi-million atom systems using orbital-free density-functional theory, thus, paving the way to an accurate electronic structure study of defects in materials.</p>
<p>The key ideas in the development of QC-OFDFT are (i) a real-space variational formulation of orbital-free density-functional theory, (ii) a nested finite-element discretization of the formulation, and (iii) a systematic means of adaptive coarse-graining retaining full resolution where necessary, and coarsening elsewhere with no patches, assumptions, or structure. The real-space formulation and the finite-element discretization gives freedom from periodicity, which is important in the study of defects in materials. More importantly, the real-space formulation and its finite-element discretization support unstructured coarse-graining of the basis functions, which is exploited to advantage in developing the QC-OFDFT method. This method has enabled for the first time a calculation of the electronic structure of samples with millions of atoms subjected to arbitrary boundary conditions. Importantly, the method is completely seamless, does not require any ad hoc assumptions, uses orbital-free density-functional theory as its only input, and enables convergence studies of its accuracy. From the viewpoint of mathematical analysis, the convergence of the finite-element approximation is established rigorously using Gamma-convergence, thus adding strength and validity to the formulation.</p>
<p>The accuracy of the proposed multi-scale method under modest computational cost, and the physical insights it offers into properties of materials with defects, have been demonstrated by the study of vacancies in aluminum. One of the important results of this study is the strong cell-size effect observed on the formation energies of vacancies, where cells as large as tens of thousands of atoms were required to obtain convergence. This indicates the prevalence of long-range physics in materials with defects, and the need to calculate the electronic structure of materials at macroscopic scales, thus underscoring the importance of QC-OFDFT.</p>
<p>Finally, QC-OFDFT was used to study a problem of great practical importance: the embrittlement of metals subjected to radiation. The brittle nature of metals exposed to radiation is associated with the formation of prismatic dislocation loops---dislocation loops whose Burgers vector has a component normal to their plane. QC-OFDFT provides an insight into the mechanism of prismatic dislocation loop nucleation, which has remained unclear to date. This study, for the first time using electronic structure calculations, establishes vacancy clustering as an energetically favorable process. Also, from direct numerical simulations, it is demonstrated that vacancy clusters collapse to form stable prismatic dislocation loops. This establishes vacancy clustering and collapse of these clusters as a possible mechanism for prismatic dislocation loop nucleation. The study also suggests that prismatic loops as small as those formed from a 7-vacancy cluster are stable, thus shedding new light on the nucleation size of these defects which was hitherto unknown.</p>
https://thesis.library.caltech.edu/id/eprint/1822Measuring Stress in Thin-Film - Substrate Systems Featuring Spatial Nonuniformities of Film Thickness and/or Misfit Strain
https://resolver.caltech.edu/CaltechETD:etd-06042007-171342
Authors: {'items': [{'email': 'michalamaris@yahoo.com', 'id': 'Brown-Michal-Amaris', 'name': {'family': 'Brown', 'given': 'Michal Amaris'}, 'show_email': 'YES'}]}
Year: 2007
DOI: 10.7907/9GD9-A088
<p>It is very important to be able to accurately determine the film stress distribution in a thin film structure, since stress can lead directly to failure and as such is intimately related to reliability and process yield. The most common way of inferring film stress caused by a given process is by measuring system curvature before and after the process; the change in curvature is directly related to the stress caused by that process, usually through the Stoney formula. This formula was derived based on a number of restrictive assumptions. Two of these are the assumptions of a spatially uniform film thickness and a spatially uniform misfit strain; taken together, these assumptions imply constant curvature and film stress over the entire wafer. In practice, these conditions are rarely met, and yet the Stoney formula is still the film stress measurement standard.</p>
<p>Recently, extensions to this formula were derived which allow for spatial non-uniformities in film thickness and misfit strain. The resulting Stoney-like relations which relate film stress and wafer curvature, known as the HR relations, require knowledge of not only the curvature at a single point, but also full-field curvature information. In this work, the HR relations are verified by comparison with X-ray microdiffraction. Two independent XRD measurements are used; one measures substrate curvature and the other determines film stress. Since these measurements are independent, the substrate curvature data are used as an input to the Stoney and HR stress/curvature relations. The resulting film stresses are then compared with XRD film stress data. From this, it is established that the HR relations result in substantially more accurate film stress predictions than does the Stoney analysis.</p>
<p>Next, a full-field curvature measurement technique, Coherent Gradient Sensing, is introduced as an ideally suited measurement tool for inferring film stress through the HR analysis. CGS measurements are taken of several progressively more interesting test wafers and the curvature is used through the HR relations to determine film stress.</p>https://thesis.library.caltech.edu/id/eprint/2451Nonlocal Microstructural Mechanics of Active Materials
https://resolver.caltech.edu/CaltechETD:etd-06122006-161234
Authors: {'items': [{'email': 'kaushikdayal@gmail.com', 'id': 'Dayal-Kaushik', 'name': {'family': 'Dayal', 'given': 'Kaushik'}, 'orcid': '0000-0002-0516-3066', 'show_email': 'YES'}]}
Year: 2007
DOI: 10.7907/YGR6-H428
<p>This thesis deals with two aspects of the mechanics of symmetry-breaking defects such as phase boundaries, inclusions and free surfaces, and their role in the macroscopic response of active materials. We first examine the problem of kinetics using a nonlocal theory, and then study the role of geometry in active materials with fields that are not confined to the material.</p>
<p>Classical PDE continuum models of active materials are not closed, and require nucleation and kinetic information or regularization as additional constitutive input. We examine this problem in the peridynamic formulation, a nonlocal continuum model that uses integral equations to account for long-range forces that are important at small scales, and allows resolution of the structure of interfaces. Our analysis shows that kinetics is inherent to the theory. Viewing nucleation as a dynamic instability at small times, we obtain interesting scaling results and insight into nucleation in regularized theories. We also exploit the computational ease of this theory to study an unusual mechanism that allows a phase boundary to bypass an inclusion.</p>
<p>Shifting focus to problems of an applied nature, we consider issues in the design of ferroelectric optical/electronic circuit elements. Free surfaces and electrodes on these devices generate electrical fields that must be resolved over all space, and not just within the body. These fields greatly enhance the importance of geometry in understanding the electromechanical response of these materials, and give rise to strong size and shape dependence. We describe a computational method that transforms this problem into a local setting in an accurate and efficient manner. We apply it to three examples: closure domains, a ferroelectric slab with segmented electrodes and a notch subjected to electro-mechanical loading.</p>https://thesis.library.caltech.edu/id/eprint/2558Structure and Evolution of Martensitic Phase Boundaries
https://resolver.caltech.edu/CaltechETD:etd-05292007-211950
Authors: {'items': [{'email': 'patrick.dondl@mathematik.uni-freiburg.de', 'id': 'Dondl-Patrick-Werner', 'name': {'family': 'Dondl', 'given': 'Patrick Werner'}, 'orcid': '0000-0003-3035-7230', 'show_email': 'YES'}]}
Year: 2007
DOI: 10.7907/89AW-3S87
<p>This work examines two major aspects of martensitic phase boundaries. The first part studies numerically the deformation of thin films of shape memory alloys by using subdivision surfaces for discretization. These films have gained interest for their possible use as actuators in microscale electro-mechanical systems, specifically in a pyramid-shaped configuration. The study of such configurations requires adequate resolution of the regions of high strain gradient that emerge from the interplay of the multi-well strain energy and the penalization of the strain gradient through a surface energy term. This surface energy term also requires the spatial numerical discretization to be of higher regularity, i.e., it needs to be continuously differentiable. This excludes the use of a piecewise linear approximation. It is shown in this thesis that subdivision surfaces provide an attractive tool for the numerical examination of thin phase transforming structures. We also provide insight in the properties of such tent-like structures.</p>
<p>The second part of this thesis examines the question of how the rate-independent hysteresis that is observed in martensitic phase transformations can be reconciled with the linear kinetic relation linking the evolution of domains with the thermodynamic driving force on a microscopic scale. A sharp interface model for the evolution of martensitic phase boundaries, including full elasticity, is proposed. The existence of a solution for this coupled problem of a free discontinuity evolution to an elliptic equation is proved. Numerical studies using this model show the pinning of a phase boundary by precipitates of non-transforming material. This pinning is the first step in a stick-slip behavior and therefore a rate-independent hysteresis.</p>
<p>In an approximate model, the existence of a critical pinning force as well as the existence of solutions traveling with an average velocity are proved rigorously. For this shallow phase boundary approximation, the depinning behavior is studied numerically. We find a universal power-law linking the driving force to the average velocity of the interface. For a smooth local force due to an inhomogeneous but periodic environment we find a critical exponent of 1/2.</p>
https://thesis.library.caltech.edu/id/eprint/2251Coarse-Graining of Atomistic Description at Finite Temperature
https://resolver.caltech.edu/CaltechETD:etd-11102006-152125
Authors: {'items': [{'email': 'ykulkarni@uh.edu', 'id': 'Kulkarni-Yashashree', 'name': {'family': 'Kulkarni', 'given': 'Yashashree'}, 'show_email': 'YES'}]}
Year: 2007
DOI: 10.7907/W9M0-HX47
<p>This thesis presents a computational method for seamlessly bridging the atomistic and the continuum realms at finite temperature. The theoretical formulation is based on the static theory of the quasicontinuum and extends it to model non-equilibrium finite temperature material response.</p>
<p>At non-zero temperature, the problem of coarse-graining is compounded by the presence of multiple time scales in addition to multiple spatial scales. We address this problem by first averaging over the thermal motion of atoms to obtain an effective temperature-dependent energy on the macroscopic scale. Two methods are proposed to this end. The first method is developed as a variational mean field approximation which yields local thermodynamic potentials such as the internal energy, the free energy, and the entropy as phase averages of appropriate phase functions. The chief advantage of this theory is that it accounts for the anharmonicity of the interaction potentials, albeit numerically, unlike many methods based on statistical mechanics which require the quasi-harmonic approximation for computational feasibility. Furthermore, the theory reduces to the classical canonical ensemble approach of Gibbs under the quasi-harmonic approximation for perfect, isotropic, infinite crystals subjected to uniform temperature. In the second method, based on perturbation analysis, the internal energy is derived as an effective Hamiltonian of the atomistic system by treating the thermal fluctuations as perturbations about an equilibrium configuration.</p>
<p>These energy functionals are then introduced into the quasicontinuum theory, which facilitates spatial coarse-graining of the atomistic description. Finally, a variational formulation for simulating rate problems, such as heat conduction, using the quasicontinuum method is developed. This is achieved by constructing a joint incremental energy functional whose Euler-Lagrange equations yield the equilibrium equations as well as the time-discretized heat equation.</p>
<p>We conclude by presenting the results for numerical validation tests for the thermal expansion coefficient and the specific heat for some materials and compare them with classical theory, molecular dynamics results, and experimental data. Some illustrative examples of thermo-mechanical coupled problems such as heat conduction in a deformable solid, adiabatic tension test, and finite temperature nanoindentation are also presented which show qualitative agreement with expected behavior and demonstrate the applicability of the method.</p>https://thesis.library.caltech.edu/id/eprint/4498Experimental Studies of Elasticity, Plastic Flow, and Anelasticity in Metallic-Glass-Forming-Liquids
https://resolver.caltech.edu/CaltechETD:etd-05072007-150354
Authors: {'items': [{'email': 'John.Harmon@WolfGreenfield.com', 'id': 'Harmon-John-Shelby-III', 'name': {'family': 'Harmon', 'given': 'John Shelby, III'}, 'show_email': 'NO'}]}
Year: 2007
DOI: 10.7907/53AD-3G15
A rheological law based on the concept of cooperatively-sheared flow zones is presented, in which the thermodynamic state variable controlling flow is identified to be the isoconfigurational shear modulus of the liquid. The law captures Newtonian as well as non-Newtonian viscosity data for glass-forming metallic liquids over a broad range of fragility. Acoustic measurements on specimens deformed at constant strain rates correlate with the measured steady-state viscosities, and define the relative effects of the “elastic” and “cooperative volume” indices on the liquid fragility. The steady state deformation material properties are evaluated to obtain a relationship between the shear modulus and configurational enthalpy. Furthermore, the material properties are evaluated through steady state in an effort to probe the relaxation mechanisms governing flow.https://thesis.library.caltech.edu/id/eprint/1661Textured Ferroelectric Thin Films: Synthesis, Characterization, and Influence of Compositional Grading on the Dielectric Behavior
https://resolver.caltech.edu/CaltechETD:etd-09222006-131741
Authors: {'items': [{'email': 'mnaggar@usc.edu', 'id': 'El-Naggar-Mohamed-Y', 'name': {'family': 'El-Naggar', 'given': 'Mohamed Y.'}, 'show_email': 'NO'}]}
Year: 2007
DOI: 10.7907/WMJW-H724
<p>This dissertation focuses on two topics concerning the connections between structure and property in ferroelectric thin films. First, the synthesis of highly oriented ferroelectric thin films is addressed, where the texture is needed to generate high strains that rely on electromechanical domain switching. The ferroelectric films are integrated with oxide electrodes onto single crystal MgO and Si substrates using biaxially-textured MgO as buffer layers. The second topic focuses on modeling the dielectric behavior of compositionally graded ferroelectrics.</p>
<p>The functional ferroelectric (Pb,Ba)TiO3 films are deposited by metalorganic chemical vapor deposition (MOCVD). SrRuO3, grown by pulsed laser deposition (PLD), is a lattice-matching electrode. Both the ferroelectric and oxide electrode layers are found to inherit the biaxial texture of the underlying MgO template, which can be deposited by ion beam assisted deposition (IBAD) directly on Si-based substrates. In addition, we demonstrated control of the ferroelectric film stoichiometry using a spectroscopic control loop that monitors the ultraviolet spectra of the gas-phase MOCVD precursors during growth. Detailed studies of the microstructural details of these films will be presented.</p>
<p>The second topic of this thesis explores the dielectric behavior of functionally graded ferroelectric thin films. Homogenous ferroelectrics offer the possibility of engineering a tunable dielectric response for components in microwave circuits. However, this approach often leads to an undesired temperature sensitivity. Compositionally-graded (Ba,Sr)TiO3 ferroelectric films have been explored as a means of redressing this sensitivity, but experimental observations vary depending on geometry and other details. A continuum model is presented to calculate the capacitive response of graded ferroelectric films with realistic electrode geometries by accurately accounting for the polarization distribution and long-range electrostatic interactions. We show preferred designs that are extremely effective in obtaining high and temperature-stable dielectric properties.</p>https://thesis.library.caltech.edu/id/eprint/3697A Plasticity Model to Predict the Effects of Confinement on Concrete
https://resolver.caltech.edu/CaltechETD:etd-05212008-221749
Authors: {'items': [{'email': 'julie@wolfkatz.com', 'id': 'Wolf-Julie-Anne', 'name': {'family': 'Wolf', 'given': 'Julie Anne'}, 'show_email': 'NO'}]}
Year: 2008
DOI: 10.7907/XMA5-MK90
A plasticity model to predict the behavior of confined concrete is developed. The model is designed to implicitly account for the increase in strength and ductility due to confining a concrete member. The concrete model is implemented into a finite element (FE) model. By implicitly including the change in the strength and ductility in the material model, the confining material can be explicitly included in the FE model. Any confining material can be considered, and the effects on the concrete of failure in the confinement material can be modeled. Test data from a wide variety of different concretes utilizing different confinement methods are used to estimate the model parameters. This allows the FE model to capture the generalized behavior of concrete under multiaxial loading. The FE model is used to predict the results of tests on reinforced concrete members confined by steel hoops and fiber reinforced polymer (FRP) jackets. Loading includes pure axial load and axial load-moment combinations. Variability in the test data makes the model predictions difficult to compare but, overall, the FE model is able to capture the effects of confinement on concrete. Finally, the FE model is used to compare the performance of steel hoop to FRP confined sections, and of square to circular cross sections. As expected, circular sections are better able to engage the confining material, leading to higher strengths. However, higher strains are seen in the confining material for the circular sections. This leads to failure at lower axial strain levels in the case of the FRP confined sections. Significant differences are seen in the behavior of FRP confined members and steel hoop confined members. Failure in the FRP members is always determined by rupture in the composite jacket. As a result, the FRP members continue to take load up to failure. In contrast, the steel hoop confined sections exhibit extensive strain softening before failure. This comparison illustrates the usefulness of the concrete model as a tool for designers. Overall, the concrete model provides a flexible and powerful method to predict the performance of confined concrete.https://thesis.library.caltech.edu/id/eprint/1929Quantitative Characterization of 3D Deformations of Cell Interactions with Soft Biomaterials
https://resolver.caltech.edu/CaltechETD:etd-05292008-163638
Authors: {'items': [{'email': 'cfranck@wisc.edu', 'id': 'Franck-Christian', 'name': {'family': 'Franck', 'given': 'Christian'}, 'show_email': 'YES'}]}
Year: 2008
DOI: 10.7907/VMN5-SP86
<p>In recent years, the importance of mechanical forces in directing cellular function has been recognized as a significant factor in biological and physiological processes. In fact, these physical forces are now viewed equally as important as biochemical stimuli in controlling cellular response. Not only do these cellular forces, or cell tractions, play an important role in cell migration, they are also significant to many other physiological and pathological processes, both at the tissue and organ level, including wound healing, inflammation, angiogenesis, and embryogenesis. A complete quantification of cell tractions during cell-material interactions can lead to a deeper understanding of the fundamental role these forces play in cell biology. Thus, understanding the function and role of a cell from a mechanical framework can have important implications towards the development of new implant materials and drug treatments.</p>
<p>Previous research has contributed significant descriptions of cell-tissue interactions by quantifying cell tractions in two-dimensional environments; however, most physiological processes are three-dimensional in nature. Recent studies have shown morphological differences in cells cultured on two-dimensional substrates versus three-dimensional matrices, and that the intrinsic extracellular matrix interactions and migration behavior are different in three dimensions versus two dimensions. Hence, measurement techniques are needed to investigate cellular behavior in all three dimensions.</p>
<p>This thesis presents a full-field imaging technique capable of quantitatively measuring cell traction forces in all three spatial dimensions, and hence addresses the need of a three-dimensional quantitative imaging technique to gain insight into the fundamental role of physical forces in biological processes. The technique combines laser scanning confocal microscopy (LSCM) with digital volume correlation (DVC) to track the motion of fluorescent particles during cell-induced or externally applied deformations. This method is validated by comparing experimentally measured non-uniform deformation fields near hard and soft spherical inclusions under uniaxial compression with the corresponding analytical solution. Utilization of a newly developed computationally efficient stretch-correlation and deconvolution algorithm is shown to improve the overall measurement accuracy, in particular under large deformations.</p>
<p>Using this technique, the full three-dimensional substrate displacement fields are experimentally determined during the migration of individual fibroblast cells on polyacrylamide gels. This is the first study to show the highly three-dimensional structure of cell-induced displacement and traction fields. These new findings suggest a three-dimensional push-pull cell motility, which differs from the traditional theories based on two-dimensional data. These results provide new insight into the dynamic cell-matrix force exchange or mechanotransduction of migrating cells, and will aid in the development of new three-dimensional cell motility and adhesion models.</p>
<p>As this study reveals, the mechanical interactions of cells and their extracellular matrix appear to be highly three-dimensional. It also shows that the LSCM-DVC technique is well suited for investigating the mechanics of cell-matrix interactions while providing a platform to access detailed information of the intricate biomechanical coupling for many cellular responses. Thus, this method has the capability to provide direct quantitative experimental data showing how cells interact with their surroundings in three dimensions and might stimulate new avenues of scientific thought in understanding the fundamental role physical forces play in regulating cell behavior.</p>https://thesis.library.caltech.edu/id/eprint/5216Effective Behavior of Dielectric Elastomer Composites
https://resolver.caltech.edu/CaltechETD:etd-08272007-145455
Authors: {'items': [{'email': 'lixiutian@gmail.com', 'id': 'Tian-Lixiu', 'name': {'family': 'Tian', 'given': 'Lixiu'}, 'show_email': 'YES'}]}
Year: 2008
DOI: 10.7907/CZNF-JB47
<p>The class of electroactive polymers has been developed to a point where real life applications as ``artificial muscles" are conceivable. These actuator materials provide attractive advantages: they are soft, lightweight, can undergo large deformation, possess fast response time and are resilient. However, widespread application has been hindered by their limitations: the need for a large electric field, relatively small forces and energy density. However, recent experimental work shows great promise that this limitation can be overcome by making composites of two materials with high contrast in their dielectric modulus. In this thesis, a theoretical framework is derived to describe the electrostatic effect of the dielectric elastomers. Numerical experiments are conducted to explain the reason for the promising experimental results and to explore better microstructures of the composites to enhance the favorable properties.</p>
<p>The starting point of this thesis is a general variational principle, which characterizes the behavior of solids under combined mechanical and electrical loads. Based on this variational principle, we assume the electric field is small as of order ε½, assume further the deformation is caused by the electrostatic effects; the deformation field is then of order ε. Using the tool of Γ-convergence, we derive a small-strain model in which the electric field and the deformation field are decoupled which results in a huge simplification of the problem.</p>
<p>Based on this small-strain model, employing the powerful tool of two-scale convergence, we derive the effective properties for dielectric composites conducting small strains. A formula of the effective electromechanical coupling coefficients is given in terms of the unit cell solutions.</p>
<p>Armed with these theoretical results, we carry out numerical experiments about the effective properties of different kind of composites. A very careful analysis of the numerical results provides a deep understanding of the mechanism of the enhancement in strain by making composites of different microstructures.</p>https://thesis.library.caltech.edu/id/eprint/3248Low-Cost High-Efficiency Solar Cells with Wafer Bonding and Plasmonic Technologies
https://resolver.caltech.edu/CaltechETD:etd-05272008-123439
Authors: {'items': [{'email': 'ka2aki@gmail.com', 'id': 'Tanabe-Katsuaki', 'name': {'family': 'Tanabe', 'given': 'Katsuaki'}, 'orcid': '0000-0002-0179-4872', 'show_email': 'NO'}]}
Year: 2008
DOI: 10.7907/4W2B-RD63
<p>III-V compound multijunction solar cells enable ultrahigh efficiency performance in designs where subcells with high material quality and high internal quantum efficiency can be employed. However the optimal multijunction cell bandgap sequence cannot be achieved using lattice-matched compound semiconductor materials. Most current compound semiconductor solar cell design approaches are focused on either lattice-matched designs or metamorphic growth (i.e., growth with dislocations to accommodate subcell lattice mismatch), which inevitably results in less design flexibility or lower material quality than is desirable. An alternative approach is to employ direct bonded interconnects between subcells of a multijunction cell, which enables dislocation-free active regions by confining the defect network needed for lattice mismatch accommodation to tunnel junction interfaces.</p>
<p>We fabricated for the first time a direct-bond interconnected multijunction solar cell, a two-terminal monolithic GaAs/InGaAs dual-junction cell, to demonstrate a proof-of-principle for the viability of direct wafer bonding for solar cell applications. The bonded interface is a metal-free n⁺GaAs/n⁺InP tunnel junction with highly conductive Ohmic contact suitable for solar cell applications overcoming the 4% lattice mismatch. The quantum efficiency spectrum for the bonded cell was quite similar to that for each of unbonded GaAs and InGaAs subcells. The bonded dual-junction cell open-circuit voltage was equal to the sum of the unbonded subcell open-circuit voltages, which indicates that the bonding process does not degrade the cell material quality since any generated crystal defects that act as recombination centers would reduce the open-circuit voltage. Also, the bonded interface has no significant carrier recombination rate to reduce the open circuit voltage.</p>
<p>Such a wafer bonding approach can also be applied to other photovoltaic heterojunctions where lattice mismatch accommodation is also a challenge, such as the InGaP/GaAs/InGaAsP/InGaAs four-junction tandem cell by bonding a GaAs-based lattice-matched InGaP/GaAs subcell to an InP-based lattice-matched InGaAsP/InGaAs subcell. Simple considerations suggest that for such a cell the currently-reported interfacial resistance of 0.12 Ohm-cm² would result in a negligible decrease in overall cell efficiency of ~0.02%, under 1-sun illumination.</p>
<p>Engineered substrates consisting of thin films of InP on Si handle substrates (InP/Si substrates or epitaxial templates) have the potential to significantly reduce the cost and weight of compound semiconductor solar cells relative to those fabricated on bulk InP substrates. InGaAs solar cells on InP have superior performance to Ge cells at photon energies greater than 0.7 eV and the current record efficiency cell for 1 sun illumination was achieved using an InGaP/GaAs/InGaAs triple junction cell design with an InGaAs bottom cell. Thermophotovoltaic (TPV) cells from the InGaAsP-family of III-V materials grown epitaxially on InP substrates would also benefit from such an InP/Si substrate. Additionally, a proposed four-junction solar cell fabricated by joining subcells of InGaAs and InGaAsP grown on InP with subcells of GaAs and AlInGaP grown on GaAs through a wafer-bonded interconnect would enable the independent selection of the subcell band gaps from well developed materials grown on lattice matched substrates. Substitution of InP/Si substrates for bulk InP in the fabrication of such a four-junction solar cell could significantly reduce the substrate cost since the current prices for commercial InP substrates are much higher than those for Si substrates by two orders of magnitude. Direct heteroepitaxial growth of InP thin films on Si substrates has not produced the low dislocation-density high quality layers required for active InGaAs/InP in optoelectronic devices due to the ~8% lattice mismatch between InP and Si.</p>
<p>We successfully fabricated InP/Si substrates by He implantation of InP prior to bonding to a thermally oxidized Si substrate and annealing to exfoliate an InP thin film. The thickness of the exfoliated InP films was only 900 nm, which means hundreds of the InP/Si substrates could be prepared from a single InP wafer in principle. The photovoltaic current-voltage characteristics of the In0.53Ga0.47As cells fabricated on the wafer-bonded InP/Si substrates were comparable to those synthesized on commercially available epi-ready InP substrates, and had a ~20% higher short-circuit current which we attribute to the high reflectivity of the InP/SiO²/Si bonding interface. This work provides an initial demonstration of wafer-bonded InP/Si substrates as an alternative to bulk InP substrates for solar cell applications.</p>
<p>Metallic nanostructures can manipulate light paths by surface plasmons and can dramatically increase the optical path length in thin active photovoltaic layers to enhance photon absorption. This effect has potential for cost and weight reduction with thinned layers and also for efficiency enhancement associated with increased carrier excitation level in the absorber layer.</p>
<p>We have observed photocurrent enhancements up to 260% at 900 nm for a GaAs cell with a dense array of Ag nanoparticles with 150 nm diameter and 20 nm height deposited through porous alumina membranes by thermal evaporation on top of the cell, relative to reference GaAs cells with no metal nanoparticle array. This dramatic photocurrent enhancement is attributed to the effect of metal nanoparticles to scatter the incident light into photovoltaic layers with a wide range of angles to increase the optical path length in the absorber layer.</p>
<p>GaAs solar cells with metallic structures at the bottom of the photovoltaic active layers, not only at the top, using semiconductor-metal direct bonding have been fabricated. These metallic back structures could incouple the incident light into surface plasmon mode propagating at the semiconductor/metal interface to increase the optical path, as well as simply act as back reflector, and we have observed significantly increased short-circuit current relative to reference cells without these metal components.</p>https://thesis.library.caltech.edu/id/eprint/2171A Bioinspired Computational Model of Cardiac Mechanics: Pathology and Development
https://resolver.caltech.edu/CaltechETD:etd-05292008-152117
Authors: {'items': [{'email': 'grosberg@uci.edu', 'id': 'Grosberg-Anna', 'name': {'family': 'Grosberg', 'given': 'Anna'}, 'orcid': '0000-0002-8878-0843', 'show_email': 'NO'}]}
Year: 2008
DOI: 10.7907/THMJ-C355
<p>In this work we study the function and development of the myocardium by creating models that have been stripped down to essentials. The model for the adult myocardium is based on the double helical band formation of the heart muscle fibers, observed in both histological studies and advanced DTMRI images. The muscle fibers in the embryonic myocardium are modeled as a helical band wound around a tubular chamber. We model the myocardium as an elastic body, utilizing the finite element method for the computations. We show that when the spiral band architecture is combined with spatial wave excitations the structure is twisted, thus driving the development of the embryonic heart into an adult heart. The double helical band model of the adult heart allows us to gain insight into the long standing paradox between the modest, by only 15 %, ability of muscle fibers to contract, and the large left ventricular volume ejection fraction of 60 %. We show that the double helical band structure is the essential factor behind such efficiency. Additionally, when the double helical band model is excited following the path of the Purkinje nerve network, physiological twist behavior is reproduced. As an additional validation, we show that when the stripped down double helical band is placed inside a sack of soft collagen-like tissue it is capable of producing physiologically high pressures.</p>
<p>We further develop the model to understand the different factors behind the loss of efficiency in heart with a common pathology such as dilated cardiomyopathy. Using the stripped down model we are able to show that the change to fiber angle is the much more important factor to heart function than the change in gross geometry. This finding has the potential to greatly impact the strategy used in certain surgical procedures.</p>https://thesis.library.caltech.edu/id/eprint/2263Constitutive models for polymers and soft biological tissues
https://resolver.caltech.edu/CaltechETD:etd-10242007-131150
Authors: {'items': [{'id': 'ElSayed-Tamer', 'name': {'family': 'El Sayed', 'given': 'Tamer'}, 'show_email': 'NO'}]}
Year: 2008
DOI: 10.7907/KH16-4S81
<p>Soft materials such as polymers and biological tissues have several engineering and biomechanical applications. These materials exhibit complex mechanical behavior, characterized by large strains, hysteresis, rate sensitivity, stress softening (Mullins effect), and deviatoric and volumetric plasticity. The need to accurately predict the behavior of such materials has been a tremendous challenge for scientists and engineers.</p>
<p>This thesis presents a seamless, fully variational constitutive model capable of capturing all of the above complex characteristics. Also, this work describes a fitting procedure based on the use of Genetic Algorithms, which proves to be necessary for the multi-modal, non-convex optimization required to identify fitting material parameters.</p>
<p>The capabilities of the presented model are demonstrated via several fits of experimental tests on a wide range of materials. These tests involve monotonic and cyclic loading of polyurea, high-density polyethylene, and brain tissue, and also involve cyclic hysteresis, softening, rate effects, shear, and cavitation plasticity.</p>
<p>Application to ballistic impact on a polyurea retrofitted DH36 steel plate is simulated and validated, utilizing the soft material model presented in this thesis for the polymer and a porous plasticity model for the metal. Localization elements are also included in this application to capture adiabatic shear bands. Moreover, computational capability for assessing the blast performance of metal/elastomer composite shells utilizing the soft material model for the elastomer is also presented.</p>
<p>Another implemented application is in the area of traumatic brain injuries under impact/acceleration loading. Clinically observed brain damage is reproduced utilizing the model presented in this work and a predictive capability of the distribution, intensity, and reversibility/irreversibility of brain tissue damage is demonstrated.</p>
https://thesis.library.caltech.edu/id/eprint/4238Characterization of Soft Polymers and Gels Using the Pressure-Bulge Technique
https://resolver.caltech.edu/CaltechETD:etd-05302008-161653
Authors: {'items': [{'email': 'winstonpj@gmail.com', 'id': 'Jackson-Winston-Paul', 'name': {'family': 'Jackson', 'given': 'Winston Paul'}, 'show_email': 'NO'}]}
Year: 2008
DOI: 10.7907/DMZ9-RE14
<p>A method to characterize the bulk hydrated properties of soft polymers and hydrogels, whose moduli are in the low MPa regime, using the pressure-bulge technique is presented. The pressure-bulge technique has been used extensively in the characterization of thin films, particularly for the case of metals. The extension of the plane-strain and circular bulge techniques to determine the Young's modulus and Poisson's ratio of bulk latex and silicone rubber sheets are shown here, in addition to the viscoelastic behavior of 5% agarose gels in the time domain using relaxation tests.</p>
<p>The membranes are clamped between two stainless steel plates that are connected to a liquid pressure chamber. A syringe connected to a linear actuator causes changes in the pressure and displacement, and a pressure sensor and confocal displacement sensor are used to monitor these changes in real time. The theory presented converts the measured pressure and displacement data into stress and stretch data, using a geometrically nonlinear analysis, and the elastic/viscoelastic properties are then determined from this data.</p>
<p>The results from the bulge tests are compared with data from uniaxial tension tests on hydrated specimens, and the data comparison with respect to each of the materials tested show good agreement between the two measurements. These results show promise regarding the use of pressure-displacement techniques to characterize other soft material systems, including biological polymers and tissues, as well as cell-to-matrix and cell-to-cell interactions under varying mechanical loading conditions of cell substrates.</p>
https://thesis.library.caltech.edu/id/eprint/2322A Constitutive Relation for Shape-Memory Alloys
https://resolver.caltech.edu/CaltechETD:etd-09292008-204618
Authors: {'items': [{'email': 'akelly@caltech.edu', 'id': 'Kelly-Alex', 'name': {'family': 'Kelly', 'given': 'Alex'}, 'show_email': 'NO'}]}
Year: 2009
DOI: 10.7907/YMT5-AX47
<p>The novel nonlinear thermoelastic behavior of shape-memory alloys (SMAs) makes them increasingly desirable as components in many advanced technological applications. In order to incorporate these materials into engineering designs, it is important to develop an understanding of their constitutive response. The purpose of this thesis is to develop a constitutive model of shape-memory polycrystals that is faithful to the underlying micromechanics while remaining simple enough for utility in engineering analysis and design.</p>
<p>We present a model in which the material microstructure is represented macroscopically as a recoverable transformation strain that is constrained by the texture of the polycrystal. The point of departure in this model is the recognition that the mechanics of the onset of martensitic transformation are fundamentally different from those of its saturation. Consequently, the constraint on the set of recoverable strains varies throughout the transformation process. The effects of constraint geometry on the constitutive response of SMAs are studied. Several well known properties of SMAs are demonstrated. Finally the model is simply implemented in a commercial finite-element package as a proof of the concept.</p>
https://thesis.library.caltech.edu/id/eprint/3823Wrinkling of Dielectric Elastomer Membranes
https://resolver.caltech.edu/CaltechETD:etd-09222008-161217
Authors: {'items': [{'email': 'lzheng@caltech.edu', 'id': 'Zheng-Ling', 'name': {'family': 'Zheng', 'given': 'Ling'}, 'show_email': 'NO'}]}
Year: 2009
DOI: 10.7907/RTAB-GX13
<p>Wrinkling of thin membranes due to different in-plane loading and boundary conditions has drawn attention of researchers in structural engineering since the development of thin webs for early aircraft structures. More recently, prestressed lightweight membrane structures have been proposed for future space missions, for example solar sails, the next generation space telescope sunshield and space-based radar systems. These structures are often partially wrinkled during operation. The formation of wrinkles alters the load paths and the structural stiffness of the membranes. More importantly its occurrence degrades the surface accuracy of these structures, which is a key design parameter.</p>
<p>This dissertation focuses on wrinkling of thin rectangular membranes subjected to uniaxial tension and investigates the onset and profiles of wrinkles using both experimental and numerical approaches.</p>
<p>An optical method, which integrates fringe projection method with four-frame phase-shifting technique, pre-conditioned conjugate gradient phase unwrapping algorithm and series-expansion carrier removal technique was developed in order to measure the full-field out-of-plane displacement of membranes, and an optical system was constructed including a uniaxial tension testbed, a LCD projector and a CCD camera. A series of uniaxial tensile tests were carried out on silicone rubber membranes of varying dimensions and aspect ratios in order to investigate the effect of geometric factors such as membrane dimension and aspect ratio on wrinkling onset; and a series of measurements were performed on each membrane at several desired strain levels to understand the evolution of the wrinkles, in particular wrinkle amplitude and wavelength.</p>
<p>A numerical study was carried out using the commercial finite element software ABAQUS to further understand the important characteristics of wrinkling of thin membranes observed in the physical model. Geometrically nonlinear finite element models of membrane structures were constructed with thin-shell elements. A series of simulations were carried out for different membrane dimensions. The critical buckling load and buckling modes was predicted for each dimension using a pre-buckling eigenvalue analysis. The desirable buckling mode was selected and introduced into the structure as a geometric imperfection. The formation and growth of wrinkles were simulated in the post-buckling analysis.</p>
<p>Finally, an idea of suppressing wrinkle instabilities of dielectric elastomer membranes using through-thickness electric field was proposed and verified in both experiment and numerical simulations.</p>https://thesis.library.caltech.edu/id/eprint/3701Active Oxide Nanophotonics
https://resolver.caltech.edu/CaltechETD:etd-05032009-154839
Authors: {'items': [{'email': 'mdicken@caltech.edu', 'id': 'Dicken-Matthew-James', 'name': {'family': 'Dicken', 'given': 'Matthew James'}, 'show_email': 'NO'}]}
Year: 2009
DOI: 10.7907/WPBT-C144
<p>Materials that can be manipulated electrically or mechanically to induce a change in their intrinsic properties are highly relevant when suitably integrated with current technologies. These "active" materials, such as oxide-based ferroelectrics or materials with easily accessible changes of phase, find extensive use as mechanical resonators, solid-state memories, and optical modulators. Barium titanate, a tetragonal ferroelectric at room temperature, is a prime example of a material both mechanically and optically active. This thesis deals primarily with the deposition of active, oxide-based materials and their integration into device structures where either the mechanical or optical properties are exploited.</p>
<p>The technologically interesting paradigms within which these active oxide materials have been investigated are microelectromechanical systems, plasmonics, and metamaterials. Microelectromechanical systems are devices that have been micromachined and rely on an applied voltage to induce a mechanical response. Mechanically active materials, such as piezoelectrics or ferroelectrics, can increase the response of these devices. Plasmonics deals with electromagnetic waves resonantly coupled into free electron oscillations at a metal-dielectric interface or metal nanoparticle. Coupling to these resonant modes allows surface plasmon polaritons to propagate along the metal with a nonlinear dispersion. Metamaterials are ordered, subwavelength, metal inclusions in a dielectric, which respond collectively to electromagnetic radiation. This response can yield a material permittivity or permeability not found in nature. The optical properties of metamaterials lead to effects such as negative index response and super lensing, and can be used to design optical cloaking structures. Here, devices utilizing these effects are investigated with an eye toward tuning or switching their resonant response using optically active oxide thin films.</p>
<p>This manuscript follows the evolution of active oxide thin films from deposition, through design of plasmonic devices and active metamaterials, finite difference modeling of these structures, and finally experimental validation. First, deposition and material integration techniques for oxide-based thin films will be discussed. The role of molecular beam epitaxy, pulsed laser deposition, and ion beam assisted deposition as material growth techniques are investigated. Development of a multitude of oxide materials using these techniques including barium titanate, strontium ruthenate, vanadium oxide, and magnesium oxide will be covered. The following two sections deal with the mechanical and optical properties of barium titanate thin films as they are studied and utilized to design and fabricate active devices. Films were characterized mechanically, using nanoindentation and piezoresponse force microscopy, and optically with variable angle spectroscopic ellipsometry. The subsequent section deals with the design, fabrication, and experimental validation of an active optical device based on surface plasmon polariton wavevector modulation via electrooptic modulation of a barium titanate thin film. Interferometers based on pairs of parallel slits fabricated in silver films on barium titanate are used to investigate optical modulation due to both domain switching and the electrooptic effect. Finally, active metamaterials are discussed through the investigation of a new material, vanadium oxide, as it is deposited and characterized, and the results used to design and fabricate active, split-ring resonator metamaterial structures.</p>
https://thesis.library.caltech.edu/id/eprint/5263A Critical Appraisal of Nanoindentation with Application to Elastic-Plastic Solids and Soft Materials
https://resolver.caltech.edu/CaltechETD:etd-09162008-023546
Authors: {'items': [{'email': 'bennyp@caltech.edu', 'id': 'Poon-Poh-Chieh-Benny', 'name': {'family': 'Poon', 'given': 'Poh Chieh Benny'}, 'show_email': 'NO'}]}
Year: 2009
DOI: 10.7907/J1WM-BW36
<p>This study examines the accuracy of the extracted elastic properties using nanoindentation. Since the conventional method to extract these properties utilizes Sneddon’s elastic solution, this study first considers indentations of linearly elastic solids for direct comparison. The study proposes a criterion for a converged specimen’s geometry and modifies Sneddon’s equation to account for the finite tip radius and specimen compressibility effects. A composite correction factor is derived to account for the violations of the underlying assumptions behind Sneddon’s derivation. This factor is a function of indentation depth, and a critical depth is derived beyond which the finite tip radius effect will be insignificant. Techniques to identify the radius of curvature of the indenter and to decouple the elastic constants for linear elastic materials are proposed. Experimental results on nanoindentation of natural latex are reported and discussed in light of the proposed modified relation and techniques.</p>
<p>The second part of the study examines the accuracy of the extracted material properties in elastic-plastic nanoindentations. The study establishes that the accurate determination of the projected area of contact, A, is crucial. However, the conventional method to determine A is largely limited to elastic materials, hence a new electrical resistance method is proposed to measure A for elastic-plastic materials. With an accurate A, the error associated with the extracted elastic material properties is reduced by more than 50% in some cases. This error remains to be a function of the material’s Poisson’s ratio, which is identified to influence the amount of residual stresses at the plastic imprint.</p>
<p>Finally, this study examines the accuracy of the extracted material properties in the nanoindentation of soft materials using an Atomic Force Microscope (AFM). The effects of cantilever stiffness, preload, and surface interaction forces are observed to influence the measurements. Three set of experiments were performed to decouple these effects. The effect of a preload resembles a shift of nanoindentation load-displacement curve, while the cantilever stiffness is observed to have significant influence on the measurement of the surface forces. Lastly, a novel technique to account for these effects is proposed, in order to accurately extract the material properties of interest.</p>https://thesis.library.caltech.edu/id/eprint/3567Three-Dimensional Elastodynamic Modeling of Frictional Sliding with Application to Intersonic Transition
https://resolver.caltech.edu/CaltechETD:etd-02142009-181805
Authors: {'items': [{'email': 'yil@caltech.edu', 'id': 'Liu-Yi', 'name': {'family': 'Liu', 'given': 'Yi'}, 'show_email': 'NO'}]}
Year: 2009
DOI: 10.7907/JWCV-8V74
<p>Spontaneous slip on frictional interfaces involves both short-lived inertially-driven events and long-term quasi-static sliding. An example of considerable practical importance is the response of faults in the Earth's crust to tectonic loading. The response combines earthquakes that cause destructive ground motions and aseismic slip. Numerical models are needed to study the physics and mechanics of such complex behavior. In part, the models can help understand the observed slip patterns and interpret them in terms of constitutive properties of rocks determined in the lab.</p>
<p>This thesis contains two main contributions. The first one is the development and implementation of a 3D methodology for simulations of spontaneous long-term interface slip punctuated by rapid inertially driven ruptures. Our approach is the first one to combine long-term deformation histories and the resulting stress redistribution on faults with full inclusion of inertial effects during simulated earthquakes in the context of 3D models. It reproduces all stages of earthquake cycles, from accelerating slip before dynamic instability, to rapid inertially driven propagation of earthquake rupture, to post-seismic slip, and to interseismic creep, including aseismic transients. The second main contribution is the discovery of the potentially dominating effect of favorable heterogeneity on intersonic transition in earthquakes, in both 2D models of single dynamic ruptures and 3D models of long-term fault slip. Studies of intersonic ruptures are practically important as they have the potential to cause strong ground motion farther from the fault than subsonic ruptures. Our conclusion that rheological boundaries promote transition to intersonic speeds in 3D rupture models is completely unexpected, as the neighboring stably slipping regions inhibit fast, inertially driven slip. The result could not be established in earlier studies, as it requires the computational methodology developed here that combines inertial effects, long-term slip histories, and 3D fault models. The thesis also develops test problems for dynamic rupture propagation and evaluates simplified quasi-dynamic approaches.</p>
<p>The obtained results emphasize that dynamic ruptures should be considered in the context of the entire slip history of the fault, as such approach allows dynamic ruptures to occur under stress conditions established by prior slip, which leads to characteristic stress distributions that are not considered in single-event simulations. The developed 3D methodology can be applied to a number of problems in earthquake physics and mechanics that involve interaction of seismic and aseismic slip.</p>
https://thesis.library.caltech.edu/id/eprint/638Active Metal-Insulator-Metal Plasmonic Devices
https://resolver.caltech.edu/CaltechETD:etd-09222009-133531
Authors: {'items': [{'email': 'diest@caltech.edu', 'id': 'Diest-Kenneth-Alexander', 'name': {'family': 'Diest', 'given': 'Kenneth Alexander'}, 'show_email': 'YES'}]}
Year: 2010
DOI: 10.7907/7J9Z-N927
<p>As the field of photonics constantly strives for ever smaller devices, the diffraction limit of light emerges as a fundamental limitation in this pursuit. A growing number of applications for optical "systems on a chip" have inspired new ways of circumventing this issue. One such solution to this problem is active plasmonics. Active plasmonics is an emerging field that enables light compression into nano-structures based on plasmon resonances at a metal-dielectric interface and active modulation of these plasmons with an applied external field. One area of active plasmonics has focused on replacing the dielectric layer in these waveguides with an electro-optic material and designing the resulting structures in such a way that the transmitted light can be modulated. These structures can be utilized to design a wide range of devices including optical logic gates, modulators, and filters.</p>
<p>This thesis focuses on replacing the dielectric layer within a metal-insulator-metal plasmonic waveguide with a range of electrically active materials. By applying an electric field between the metal layers, we take advantage of the electro-optic effect in lithium niobate, and modulating the carrier density distribution across the structure in n-type silicon and indium tin oxide.</p>
<p>The first part of this thesis looks at fabricating metal-insulator-metal waveguides with ion-implantation induced layer transferred lithium niobate. The process is analyzed from a thermodynamic standpoint and the ion-implantation conditions required for layer transfer are determined. The possible failure mechanisms that can occur during this process are analyzed from a thin-film mechanics standpoint, and a metal-bonding method to improve successful layer transfer is proposed and analyzed. Finally, these devices are shown to naturally filter white light into individual colors based on the interference of the different optical modes within the dielectric layer. Full-field electromagnetic simulations show that these devices can preferentially couple to any of the primary colors and can tune the output color of the device with an applied field.</p>
<p>The second part of this thesis looks at fabricating metal-insulator-metal waveguides with n-type silicon and indium tin oxide. With the silicon device, by tuning the thicknesses of the layers used in a metal-oxide semiconductor geometry, the device we call the "plasMOStor" can support plasmonic modes as well as exactly one photonic mode. With an applied field, this photonic mode is pushed into cutoff and modulation depths of 11.2 dB are achieved. With the indium tin oxide device, the doping density within the material is changed and as a result, the plasma frequency is shifted into the near-infrared and visible wavelengths. Using spectroscopic ellipsometry, the structure is characterized with and without an applied electric field, and measurements show that when an accumulation layer is formed within the structure, the index of refraction within that layer is significantly changed and as a result, will change the optical modes supported in such a structure.</p>
https://thesis.library.caltech.edu/id/eprint/5282Low Temperature Catalytic Ethanol Conversion Over Ceria-Supported Platinum, Rhodium, and Tin-Based Nanoparticle Systems
https://resolver.caltech.edu/CaltechTHESIS:06102010-171305208
Authors: {'items': [{'email': 'eugeneldmahmoud@yahoo.com', 'id': 'Mahmoud-Eugene-Leo-Draine', 'name': {'family': 'Mahmoud', 'given': 'Eugene Leo Draine'}, 'show_email': 'NO'}]}
Year: 2010
DOI: 10.7907/Q9W4-0356
<p>Due to the feasibility of ethanol production in the United States, ethanol has become more attractive as a fuel source and a possible energy carrier within the hydrogen economy. Ethanol can be stored easily in liquid form, and can be internally pre-formed prior to usage in low temperature (200C – 400C) solid acid and polymer electrolyte membrane fuel cells. However, complete electrochemical oxidation of ethanol remains a challenge. Prior research of ethanol reforming at high temperatures (> 400C) has identified several metallic and oxide-based catalyst systems that improve ethanol conversion, hydrogen production, and catalyst stability. In this study, ceria-supported platinum, rhodium, and tin-based nanoparticle catalyst systems will be developed and analyzed in their performance as low-temperature ethanol reforming catalysts for fuel cell applications.</p>
<p>Metallic nanoparticle alloys were synthesized with ceria supports to produce the catalyst systems studied. Gas phase byproducts of catalytic ethanol reforming were analyzed for temperature-dependent trends and chemical reaction kinetic parameters. Results of catalytic data indicate that catalyst composition plays a significant role in low-temperature ethanol conversion. Analysis of byproduct yields demonstrate how ethanol steam reforming over bimetallic catalyst systems (platinum-tin and rhodium-tin) results in higher hydrogen selectivity than was yielded over single-metal catalysts. Additionally, oxidative steam reforming results reveal a correlation between catalyst composition, byproduct yield, and ethanol conversion. By analyzing the role of temperature and reactant composition on byproduct yields from ethanol reforming, this study also proposes how these parameters may contribute to optimal catalytic ethanol reforming.</p>
https://thesis.library.caltech.edu/id/eprint/5947Mechanical Performance of Amorphous Metallic Cellular Structures
https://resolver.caltech.edu/CaltechTHESIS:01292010-170058619
Authors: {'items': [{'email': 'joseph.p.schramm@gmail.com', 'id': 'Schramm-Joseph-Paul', 'name': {'family': 'Schramm', 'given': 'Joseph Paul'}, 'show_email': 'NO'}]}
Year: 2010
DOI: 10.7907/H56A-SA70
Metallic glass and metallic glass matrix composites are excellent candidates for application in cellular structures because of their outstanding plastic yield strengths and their ability to deform plastically prior to fracture. The mechanical performance of metallic-glass and metallic-glass-matrix-composite honeycomb structures are discussed, and their strength and energy absorption capabilities examined in quasi-static compression tests for both in-plane and out-of-plane loading. These structures exhibit strengths and energy absorption that well exceed the performance of similar structures made from crystalline metals. The strength and energy absorption capabilities of amorphous metal foams produced by a powder metallurgy process are also examined, showing that foams produced by this method can be highly porous and are able to inherit the strength of the parent metallic glass and absorb large amounts of energy. The mechanical properties of a highly stochastic set of foams are examined at low and high strain rates. It is observed that upon a drastic increase in strain rate, the dominant mechanism of yielding for these foams undergoes a change from elastic buckling to plastic yielding. This mechanism change is thought to be the result of the rate of the mechanical test approaching or even eclipsing the speed of elastic waves in the material.https://thesis.library.caltech.edu/id/eprint/5543Shape Changing Transformations: Interactions with Plasticity and Electrochemical Processes
https://resolver.caltech.edu/CaltechTHESIS:05282010-141343271
Authors: {'items': [{'email': 'farshid_roumi@yahoo.com', 'id': 'Roumi-Farshid', 'name': {'family': 'Roumi', 'given': 'Farshid'}, 'show_email': 'NO'}]}
Year: 2010
DOI: 10.7907/P94H-4B23
<p>Solids undergo phase transformations where the crystal structure changes with temperature, chemical potential, stress, applied electric fields, or other external parameters. These occur by either long-range diffusion of atoms (diffusional phase transformation) or by some form of cooperative, homogeneous movement of many atoms that results in changes in crystal structure (displacive phase transformation). In the latter case, these movements are usually less than the interatomic distances, and the atoms maintain their coordination. The most common example of displacive phase transformations is martensitic transformation. The martensitic transformation in steel is economically very important and can result in very different behavior in the product. Other examples of martensitic transformations are shape memory alloys which are lightweight, solid-state alternatives to conventional actuators such as hydraulic, pneumatic, and motor-based systems.</p>
<p>The martensitic transformation usually only depends on temperature and stress and, in contrast to diffusion-based transformations, is not time dependent. In shape memory alloys the transformation is reversible. On the other hand in steel, the martensite formation from austenite by rapidly cooling carbon-steel is not reversible; so steel does not have shape memory properties.</p>
<p>In Chapters 2 and 3, we study the interesting yet very complicated behavior of martensitic transformation interactions with plastic deformations. A good example here is steel, which has been known for thousands of years but still is believed to be a very complicated material. Steel can show different behavior depending on its complex microstructure. Thus understanding the formation mechanisms is crucial for the interpretation and optimization of its properties. As an example, low alloyed steels with transformation induced plasticity (TRIP), metastable austenite steels, are known for strong hardening and excellent elongation and strength. It is suggested that the strain-induced transformation of small amounts of untransformed (retained) austenite into martensite during plastic deformation is a key to this excellent behavior.</p>
<p>In Chapters 4 and 5, we study the interactions of solid-solid phase transformations with electrochemical processes. It is suggested that electronic and ionic structures depends on lattice parameters, thus it is expected that structural transformations can lead to dramatic changes in material properties. These transformations can also change the energy barrier and hysteresis. It is known that compatible interfaces can reduce elastic energy and hysteresis, thus may extend the life of the system. Solid-solid transformations change the crystalline structure. These geometry changes can have long range effects and cause stresses in the whole material. The generated stress field itself changes the total free energy, due to the change in elastic energy, and thus, the electrochemical potential and processes are affected. An example is olivine phosphates which are candidates for cathode material in Li-ion batteries. These materials undergo an orthorhombic to orthorhombic phase transition. Experiments in the literature have suggested that elastic compatibility can affect rates of charge/discharge in the battery. Our theory provides some insight into this observation.</p>https://thesis.library.caltech.edu/id/eprint/5883Multiscale Modeling and Simulation of Damage by Void Nucleation and Growth
https://resolver.caltech.edu/CaltechTHESIS:11022010-080434454
Authors: {'items': [{'email': 'celiareinaromo@gmail.com', 'id': 'Reina-Romo-Celua', 'name': {'family': 'Reina Romo', 'given': 'Celia'}, 'show_email': 'YES'}]}
Year: 2011
DOI: 10.7907/WFYW-AS22
<p>Voids are observed to be generated under sufficient loading in many materials, ranging from polymers and metals to biological tissues. The presence of these voids can have drastic implications at the macroscopic level including strong material softening and more incipient fracture. Developing tools to appropriately account for these effects is therefore very desirable.</p>
<p>This thesis is concerned with both, the appearance of voids (nucleation process) and the modeling and simulation of materials in the presence of voids. A particular nucleation mechanism based on vacancy aggregation in high purity metallic single crystals is analyzed. A multiscale model is developed in order to obtain an approximate value of the time required for vacancies to form sufficiently large clusters for further growth by plastic deformation. It is based on quantum mechanical results, kinetic Monte Carlo methods and continuum mechanics estimates calibrated with quasi-continuum results. The ultimate goal of these simulations is to determine the feasibility of this nucleation mechanism under shock loading conditions, where the temperature and tensions are high and vacancy diffusion is promoted.</p>
<p>On the other hand, the effective behavior of materials with pre-existent voids is analyzed within the general framework of continuum mechanics and is therefore applicable to any material. The overall properties of the heterogeneous material are obtained through a two-level characterization: a representative volume element consisting of a hollow sphere is used to describe the "microscopic" fields, and an equivalent homogeneous material is used for the "macroscopic" behavior. A variational formulation of this two-scale model is presented. It provides a consistent definition of the macro-variables under general loading conditions, extending the well-known static averaging results so as to include microdynamic effects under finite deformations. This variational framework also provides a suitable starting point for time discretization and consistent definitions within discrete time. The spatial boundary value problem resulting from this multiscale model is solved with a particular spherical shell element specially developed for this problem. The approximation space is based on spherical harmonics, which respects the symmetries of the porous material and allows the representation of the fields on the sphere with very few degrees of freedom. Numerical tools, such as the exact representation of the boundary conditions and an exact quadrature rule, are also provided. The resulting numerical model is verified extensively, demonstrating good convergence results, and its applicability is shown through several material point calculations and a full two-scale finite element implementation.</p>https://thesis.library.caltech.edu/id/eprint/6165Electrochemical and Thermochemical Behavior of CeO₂-δ
https://resolver.caltech.edu/CaltechTHESIS:11042010-235339265
Authors: {'items': [{'email': 'willchueh@gmail.com', 'id': 'Chueh-William-C', 'name': {'family': 'Chueh', 'given': 'William C.'}, 'show_email': 'YES'}]}
Year: 2011
DOI: 10.7907/EBKT-ET32
The mixed-valent nature of nonstoichiometric ceria (CeO<sub>2</sub>-δ) gives rise to a wide range of intriguing properties, such as mixed ionic and electronic conduction and oxygen storage. Surface and transport behavior in rare-earth (samaria) doped and undoped ceria were investigated, with particular emphasis on applications in electrochemical and thermochemical energy conversion processes such as fuel cells and solar fuel production. The electrochemical responses of bulk- processed ceria with porous Pt and Au electrodes were analyzed using 1-D and 2-D transport models to decouple surface reactions, near-surface transport and bulk transport. Combined experimental and numerical results indicate that hydrogen electro-oxidation and hydrolysis near open-circuit conditions occur preferentially over the ceria | gas interface rather than over the ceria | gas | metal interface, with the rate-limiting step likely to be either surface reaction or transport through the surface oxygen vacancy depletion layer. In addition, epitaxial thin films of ceria were grown on zirconia substrates using pulsed-laser deposition to examine electrocatalysis over well-defined microstructures. Physical models were derived to analyze the electrochemical impedance response. By varying the film thickness, interfacial and chemical capacitance were decoupled, with the latter shown to be proportional to the small polaron densities. The geometry of microfabricated metal current collectors (metal = Pt, Ni) was also systematically varied to investigate the relative activity of the ceria | gas and the ceria | metal | gas interfaces. The data suggests that the electrochemical activity of the metal-ceria composite is only weakly dependent on the metal due to the relatively high activity of the ceria | gas interface. In addition to electrochemical experiments, thermochemical reduction-oxidation studies were performed on ceria. It was shown that thermally-reduced ceria, upon exposure to H<sub>2</sub>O and/or CO<sub>2</sub>, can be reoxidized to form H<sub>2</sub>, CO, and/or CH<sub>4</sub>. Analysis of gas evolution rates confirms that the kinetics of ceria oxidation by H<sub>2</sub>O and CO<sub>2</sub> are dominated by surface reactions, rather than by ambipolar oxygen diffusion. Temperature-programmed oxidation experiments revealed that, even under thermodynamically favored conditions, carbonaceous species do not form on the surface of neat ceria, thereby giving a high CO selectivity when dissociating CO<sub>2</sub>. A scaled-up ceria-based solar reactor was designed and tested to demonstrate the feasibility of solar fuel production via thermochemical cycling.https://thesis.library.caltech.edu/id/eprint/6170Multiscale Modeling of Microcrystalline Materials
https://resolver.caltech.edu/CaltechTHESIS:11222010-061455728
Authors: {'items': [{'email': 'dhurtado@caltech.edu', 'id': 'Hurtado-Sepulveda-Daniel-Esteban', 'name': {'family': 'Hurtado Sepulveda', 'given': 'Daniel Esteban'}, 'show_email': 'NO'}]}
Year: 2011
DOI: 10.7907/FHZT-3A33
<p>Materials with micrometer dimensions and their distinct mechanical properties have generated a great interest in the material science community over the last couple of decades. There is strong experimental evidence showing that microcrystalline materials are capable of achieving much higher yield and fracture strength values than bulk mesoscopic samples as they decrease in size. Several theories have been proposed to explain the size effect found in micromaterials, but a predictive physics-based model suitable for numerical simulations remains an open avenue of research. Since the successful design of micro-electro-mechanical systems (MEMS) and novel engineered materials hinges upon the mechanical properties at the micrometer scale, there is a compelling need for a quantitative and accurate characterization of the size effects exhibited by metallic micromaterials.</p>
<p>This work is concerned with the multiscale material modeling and simulation of strength in crystalline materials with micrometer dimensions. The elasto-viscoplastic response is modeled using a continuum crystal plasticity formulation suitable for large-deformation problems. Crystallographic dislocation motion is accounted for by stating the crystal kinematics within the framework of continuously distributed dislocation theory. The consideration of the dislocation self-energy and the step formation energy in the thermodynamic formulation of the constitutive relations renders the model non-local and introduces a length scale. Exploiting the concept of total variation we are able to recover an equivalent model that is local under a staggered approach, and therefore amenable to time integration using variational constitutive updates. Numerical simulations of compression tests in nickel micropillars using the proposed multiscale framework quantitatively capture the size dependence found in experimental results, showcasing the predictive capabilities of the model.</p>
https://thesis.library.caltech.edu/id/eprint/6187Coarse-Graining Kohn-Sham Density Functional Theory
https://resolver.caltech.edu/CaltechTHESIS:05292011-200916324
Authors: {'items': [{'email': 'phanish@caltech.edu', 'id': 'Suryanarayana-Phanish', 'name': {'family': 'Suryanarayana', 'given': 'Phanish'}, 'show_email': 'NO'}]}
Year: 2011
DOI: 10.7907/GCKH-EX20
<p>Defects, though present in relatively minute concentrations, play a significant role in determining macroscopic properties. Even vacancies, the simplest and most common type of defect, are fundamental to phenomena like creep, spall and radiation ageing. This necessitates an accurate characterization of defects at physically relevant concentrations, which is typically in parts per million. This represents a unique challenge since both the electronic structure of the defect core as well as the long range elastic field need to be resolved simultaneously. Unfortunately, accurate ab-initio electronic structure calculations are limited to a few hundred atoms, which is orders of magnitude smaller than that necessary for a complete description. Thus, defects represent a truly challenging multiscale problem.</p>
<p>Density functional theory developed by Hohenberg, Kohn and Sham (DFT) is a widely accepted, reliable ab-initio method for computing a wide range of material properties. We present a real-space, non-periodic, finite-element and max-ent formulation for DFT. We transform the original variational problem into a local saddle-point problem, and show its well-posedness by proving the existence of minimizers. Further, we prove the convergence of finite-element approximations including numerical quadratures. Based on domain decomposition, we develop parallel finite-element and max-ent implementations of this formulation capable of performing both all-electron and pseudopotential calculations. We assess the accuracy of the formulation through selected test cases and demonstrate good agreement with the literature.</p>
<p>Traditional implementations of DFT solve for the wavefunctions, a procedure which has cubic-scaling with respect to the number of atoms. This places serious limitations on the size of the system which can be studied. Further, they are not amenable to coarse-graining since the wavefunctions need to be orthonormal, a global constraint. To overcome this, we develop a linear-scaling method for DFT where the key idea is to directly evaluate the electron density without solving for the individual wavefunctions. Based on this linear-scaling method, we develop a numerical scheme to coarse-grain DFT derived solely based on approximation theory, without the introduction of any new equations and resultant spurious physics. This allows us to study defects at a fraction of the original computational cost, without any significant loss of accuracy. We demonstrate the efficiency and efficacy of the proposed methods through examples. This work enables the study of defects like vacancies, dislocations, interfaces and crack tips using DFT to be computationally viable.</p>https://thesis.library.caltech.edu/id/eprint/6473Mechanics of Thin Carbon Fiber Composites with a Silicone Matrix
https://resolver.caltech.edu/CaltechTHESIS:03152011-154253229
Authors: {'items': [{'email': 'fl@caltech.edu', 'id': 'Lopez-Jimenez-Francisco', 'name': {'family': 'Lopez Jimenez', 'given': 'Francisco'}, 'show_email': 'NO'}]}
Year: 2011
DOI: 10.7907/A773-KF92
<p>This thesis presents an experimental, numerical and analytical study of the behavior of thin fiber composites with a silicone matrix. The main difference with respect to traditional composites with epoxy matrix is the fact that the soft matrix allows the fibers to microbuckle without breaking. This process acts as a stress relief mechanism during folding, and allows the material to reach very high curvatures, which makes them particularly interesting as components of space deployable structures. The goal of this study is to characterize the behavior and understand the mechanics of this type of composite.</p>
<p>Experimental testing of the bending behavior of unidirectional composites with a silicone matrix shows a highly non-linear moment vs. curvature relationship, as well as strain softening under cyclic loading. These effects are not usually observed in composites with an epoxy matrix. In the case of tension in the direction transverse to the fibers, the behavior shows again non-linearity and strain softening, as well as an initial stiffness much higher than what would be expected based on the traditional estimates for fiber composites.</p>
<p>The micro mechanics of the material have been studied with a finite element model. It uses solid elements and a random fiber arrangement produced with a reconstruction process based on micrographs of the material cross section. The simulations capture the macroscopic non-linear response, as well as the fiber microbuckling, and show how microbuckling reduces the strain in the fibers. The model shows good agreement for the bending stiffness of specimens with low fiber volume fraction, but it overestimates the effect of the matrix for more densely packed fibers. This is due to the high matrix strain that derives from the assumption of perfect bonding between fiber and matrix. In the case of tension transverse to the fibers, the model shows a much better agreement with experiments than traditional composite theory, and shows that the reason for the observed high stiffness is the incompressibility of the matrix. In order to capture the strain softening due to fiber debonding, cohesive elements have been introduced between the fibers and the matrix. This allows the model to capture quantitatively the non-linear behavior in the case of loading transverse to the fibers, and the damage due to cyclic loading. A single set of parameters for the cohesive elements produce good agreement with the experimental results for very different values of the fiber volume fraction, and could also be used in the analysis of more complicated loading cases, such as bending or biaxial tension.</p>
<p>In addition to the simulations, a homogenized analytical model has also been created. It extends previous analysis of composites with a soft matrix to the case of very thin composites. It provides a good qualitative description of the material behavior, and it helps understand the mechanics that take place within the material, such as the equilibrium of energy terms leading to a finite wave length, as opposed to microbuckling under compression.</p>https://thesis.library.caltech.edu/id/eprint/6271Mechanics of Peeling: Cohesive Zone Law and Stability
https://resolver.caltech.edu/CaltechTHESIS:05262011-172059575
Authors: {'items': [{'email': 'ckovalchick@caltech.edu', 'id': 'Kovalchick-Christopher', 'name': {'family': 'Kovalchick', 'given': 'Christopher'}, 'show_email': 'YES'}]}
Year: 2011
DOI: 10.7907/W2KT-CY70
<p>The measurement of interface mechanical properties between an adhesive layer and a substrate is significant for optimization of a high-quality interface. A common method for measuring these properties is the peel test. While there are many interesting applications of peel in such areas as cell and gecko adhesion, the focus here is to obtain a better understanding of the fundamental mechanics underlying the problem.</p>
<p>The mechanics of the peel test is examined through experiments, finite element simulations, and theoretical analysis with the aim of developing governing relations to describe the role of fracture in the peel test for elastic adhesive tapes. An inverse formulation is developed to extract a cohesive zone law from a set of experimental peel tests using a theoretical framework based upon non-linear beam theory. Through extracting a cohesive zone law, the adhesion energy during a peel test is determined along with the force distribution in the process zone. This local method of determining the adhesion energy is compared to a global method used by Rivlin in the context of finite deformations, showing good agreement.</p>
<p>The effect of rate-dependency in the peel test is also examined experimentally, with the results used to derive a rate-dependent power-law for the adhesion energy in a peel test as a function of the peel rate. The effects of varying different geometrical parameters during the peel test and how they affect the force distribution and adhesion energy are also presented. Finally, a study of the stability in the peel test, including the role of compliance through several newly developed force-controlled experimental configurations is discussed. The stiffness of the system is varied by altering the magnitude and direction of the applied load during a test. This change in stiffness can be tuned in order to trigger or delay the onset of instability. Theoretical stability criteria are also presented to in order to develop insights of the role of parameters investigated experimentally.</p>https://thesis.library.caltech.edu/id/eprint/6458High Pressure Hugoniot Measurements in Solids Using Mach Reflections
https://resolver.caltech.edu/CaltechTHESIS:05242011-143955754
Authors: {'items': [{'email': 'jlbrown@caltech.edu', 'id': 'Brown-Justin-Lee', 'name': {'family': 'Brown', 'given': 'Justin Lee'}}]}
Year: 2011
DOI: 10.7907/SC1V-PK42
Shock compression experiments provide access to high pressures in a laboratory setting. Matter at extreme pressures is often studied by utilizing a well controlled planar impact between two flat plates to generate a one dimensional shock wave. While these experiments are a powerful tool in equation of state (EOS) development, they are inherently limited by the velocity of the impacting plate. In an effort to dramatically increase the range of pressures which can be studied with available impact velocities, a new experimental technique is examined. The target plate is replaced by a composite assembly consisting of two concentric cylinders and is designed such that the initial shock velocity in a well characterized outer cylinder is higher than in the inner cylinder material of interest. After impact, conically converging shocks are generated at the interface due to the impedance mismatch between the two materials and the axisymmetric geometry. Upon convergence, an irregular reflection occurs and the conical analog of a Mach reflection develops. This Mach reflection grows until it reaches a steady state, for which an extremely high pressure state is concentrated behind the Mach stem. The reflection is studied using a combination of analytical, numerical, and experimental techniques. Ideas from gas dynamics, such as shock polars, are connected to the classic treatment of one-dimensional shocks in solids to form a simple method for treating the oblique reflections in the Mach lens configuration. Numerical simulations provide detailed full-field solutions and illustrate a methodology for extracting EOS information. The technique is validated experimentally by studying the shock response of copper and iron. Two different confining materials, 6061-T6 aluminum and molybdenum, are used to drive the converging shock waves for which the high pressure state is measured through a combination of velocity interferometry and impedance matching techniques.https://thesis.library.caltech.edu/id/eprint/6427Electrocatalysis in Solid Acid Fuel Cells
https://resolver.caltech.edu/CaltechTHESIS:05232011-144137426
Authors: {'items': [{'email': 'mlouie@caltech.edu', 'id': 'Louie-Mary-W-C', 'name': {'family': 'Louie', 'given': 'Mary W. C.'}, 'show_email': 'NO'}]}
Year: 2011
DOI: 10.7907/1HK1-2M22
<p>Solid state electrochemical reactions play a crucial role in many energy conversion devices, yet the pathways of many reactions remain unknown. The elusiveness of the reaction mechanisms is due, in part, to the complexity of electrochemical reactions; because electrochemical reactions require the interaction of many species (e.g., ions, electrons, and adsorbates) across multiple phases (e.g., electrolyte, catalyst, and gas phases), elucidation of the reaction pathway can quickly become complicated. In this work, we develop and utilize model catalyst | electrolyte systems, that is, structures of reduced complexity, to study electrode reactions in solid acid fuel cells which operate at intermediate temperatures of ~ 250 ºC. We employ AC impedance spectroscopy to explore the reaction pathway for hydrogen electro-oxidation over Pt thin films sputter-deposited atop the proton-conducting solid acid electrolyte CsH<sub>2</sub>PO<sub>4</sub>. We observed that hydrogen electro-oxidation occurs by diffusion of hydrogen through Pt, taking advantage of the entire Pt | CsH<sub>2</sub>PO<sub>4</sub> interfacial area rather than being confined to the triple-phase sites. This insight opens up new avenues for developing high performance electrodes with low Pt loadings by eliminating the requirement that Pt-based electrodes be comprised of high triple-phase site densities long considered to be critical for Pt electrocatalysis. Indeed, even for flat, planar electrodes of very thin Pt films, we obtained a Pt utilization that is significantly higher than in typical composite electrodes. </p>
<p> We also demonstrate the efficacy of a new tool for probing the spatial heterogeneity of electrochemical reactions at the metal | electrolyte interface. We characterized oxygen electro-reduction kinetics at the nanoscale Pt | CsHSO<sub>4</sub> interface at ~ 150 ºC using conducting atomic force microscopy in conjunction with cyclic voltammetry and AC impedance spectroscopy. Not only did we find the electrochemical activity for oxygen electro-reduction to vary dramatically across the electrolyte surface but the current-voltage data, when analyzed in the Butler-Volmer framework, exhibited a strong counter-correlation between two key kinetic parameters, the exchange coefficient and exchange current. Specifically, the exchange current spanned five orders of magnitude while the exchange coefficient ranged between 0.1 and 0.6. Such a correlation has not been observed before and points to the power of atomic force microscopy for electrochemical characterization at electrolyte | metal | gas boundaries in general. </p>
<p>As reduction in microstructural complexity is a key advantage in model electrode | electrolyte systems, we also sought to understand the bulk properties of solid acid compounds, specifically, the relationship between microstructure and the superprotonic phase transition, the latter of which lends solid acid compounds their high proton conductivities at intermediate temperatures. We found a correlation between phase transformation hysteresis and crystallographic compatibility of the high- and low-temperature phases of the Cs<sub>1–x</sub>Rb<sub>x</sub>H<sub>2</sub>PO<sub>4</sub> solid solution series. Therefore, it is to be expected that hysteresis, and therefore microcrack formation, can be minimized during phase transformation via the principle of crystallographic compatibility. This is confirmed in single crystals of CsHSO<sub>4</sub>, which was found to have higher crystallographic compatibility, lower hysteresis, and significantly fewer microcracks formed during phase transition compared to CsH<sub>2</sub>PO<sub>4</sub>. The apparent applicability of the theory of crystallographic compatibility implies a new tool for identifying solid acid compounds with suitable microstructures for fuel cell application and for model electrode | electrolyte systems.
</p>
https://thesis.library.caltech.edu/id/eprint/6420Individual Particle Motion in Colloids: Microviscosity, Microdiffusivity, and Normal Stresses
https://resolver.caltech.edu/CaltechTHESIS:05262011-141745737
Authors: {'items': [{'email': 'roseannazee@yahoo.com', 'id': 'Zia-Roseanna-Nellie', 'name': {'family': 'Zia', 'given': 'Roseanna Nellie'}, 'show_email': 'NO'}]}
Year: 2011
DOI: 10.7907/2743-8W26
<p>Colloidal dispersions play an important role in nearly every aspect of life, from paint to biofuels to nano-therapeutics. In the study of these so-called complex ﬂuids, a connection is sought between macroscopic material properties and the micromechanics of the suspended particles. Such properties include viscosity, diffusivity, and the osmotic pressure, for example. But many such systems are themselves only microns in size overall; recent years have thus seen a dramatic growth in demand for exploring microscale systems at a much smaller length scale than can be probed with conventional macroscopic techniques. Microrheology is one approach to such microscale interrogation, in which a Brownian “probe” particle is driven through a complex ﬂuid, and its motion tracked in order to infer the mechanical properties of the embedding material. With no external forcing the probe and background particles form an equilibrium microstructure that ﬂuctuates thermally with the solvent. Probe motion through the dispersion distorts the microstructure; the character of this deformation, and hence its inﬂuence on probe motion, depends on the strength with which the probe is forced, F ext , compared to thermal forces, kT/b, defining a P´eclet number, P e = F ext /(kT /b), where kT is the thermal energy and b the bath-particle size. Both the mean and the ﬂuctuating motion of the probe are of interest. Recent studies showed that the reduction in mean probe speed gives the eﬀective material viscosity. But the velocity of the probe also ﬂuctuates due to collisions with the suspended particles, causing the probe to undergo a random walk process. It is shown that the long-time mean-square ﬂuctuational motion of the probe is diffusive and the effective diffusivity of the forced probe is determined for the full range of P´eclet number. At small Pe Brownian motion dominates and the diffusive behavior of the probe characteristic of passive microrheology is recovered, but with an incremental ﬂow-induced “micro-diffusivity” that scales as Dmicro ∼ Da P e 2 φb , where viii φb is the volume fraction of bath particles and Da is the self-diffusivity of an isolated probe. At the other extreme of high P´eclet number the fuctuational motion is still diffusive, and the diffusivity becomes primarily force-induced , scaling as (F ext /η)φb , where η is the viscosity of the solvent. The force-induced “microdiffusivity” is anisotropic, with diffusion longitudinal to the direction of forcing larger in both limits compared to transverse diffusion, but more strongly so in the high-P e limit.</p>
<p>Previous work in microrheology defined a scalar viscosity; however, a tensorial expression for the suspension stress in microrheology was still lacking. The notion that diffusive ﬂux is driven by gradients in particle-phase stress leads to the idea that the microdiffusivity can be related directly to the suspension stress. In consequence, the anisotropy of the diffusion tensor may reﬂect the presence of normal stress differences in non-linear microrheology. While the particle-phase stress tensor can be determined as the second moment of the deformed microstructure, in this study a connection is made between diffusion and stress gradients, and an analytical expression for particle-phase stress as a function of the microdiffusivity and microviscosity is obtained. The two approaches agree, suggesting that normal stresses and normal stress differences can be measured in active microrheological experiments if both the mean and mean-square motion of the probe are monitored. Owing to the axisymmetry of the motion about a spherical probe, the second normal stress difference is zero, while the ﬁrst normal stress difference is linear in P e for P e ≫ 1 and vanishes as P e 3 for P e ≪ 1. An additional important outcome is that the analytical expression obtained for stress-induced migration can be viewed as a generalized non-equilibrium Stokes-Einstein relation.</p>
<p>Studies of steady-state dispersion behavior reveal the hydrodynamic and microstructural mechanisms that underlie non-Newtonian behaviors (e.g. shear-thinning, shear-thickening, and normal stress differences). But an understanding of how the microstructures evolve from the equilibrium state, and how non-equilibrium properties develop in time is much less well understood. Transient suspension behavior in the near-equilibrium, linear response regime has been studied via its connection to low-amplitude oscillatory probe forcing and the complex modulus; at very weak forcing, the microstructural response that drives viscosity is indistinguishable from equilibrium ﬂuctuations. But important information about the basic physical aspects of structural development and relaxation ix in a medium are captured by start-up and cessation of the imposed deformation in the non-linear regime, where the structure is driven far from equilibrium. Here we study the evolution of stress and microstructure in a colloidal dispersion by tracking transient probe motion during start-up and cessation of a strong ﬂow. For large P e, steady state is reached when a boundary layer (in which advection balances diffusion) forms at particle contact on the timescale of the ﬂow, a/U , where a is the probe size and U its speed. On the other hand, relaxation following cessation occurs over several timescales corresponding to distinct physical processes. For very short times, the timescale for relaxation is set by the diffusion over the boundary-layer thickness. Nearly all stress relaxation occurs during this process, owing to the dependence of the bath-particle drag on the contact value of the microstructure. At longer times the collective diffusion of the bath particles acts to close the wake. In this long-time limit as structural isotropy is restored, the majority of the microstructural relaxation occurs with very little change in suspension stress. Theoretical results are presented and compared with Brownian dynamics simulation. Two regimes of probe motion are studied: an externally applied constant force and an imposed constant velocity. The microstructural evolution is qualitatively different for the two regimes, with a longer transient phase and a thinner boundary layer and longer wake at steady state in the latter case. The work is also compared to analogous results for sheared suspensions undergoing start-up and cessation.</p>
<p>The study moves next to investigations of dual-probe microrheology. Motivated by the phenomenon of equilibrium depletion interactions, we study the interaction between a pair of probe particles translating with equal velocity through a dispersion with their line of centers transverse to the external forcing. The character of the microstructure surrounding the probes is determined both by the distance R by which the two probes are separated and by the strength of the external forcing, P e = U a/Db , where U is the constant probe velocity and Db the diffusivity of the bath particles. Osmotic pressure gradients develop as the microstructure is deformed, giving rise to an interactive force between the probes. This force is studied for a range of P e and R. For all separations R > 2a, the probes attract when P e is small. As the strength of the forcing increases, a qualitative change in the interactive force occurs: the probes repel each other. The probe separation R at which the x attraction-to-repulsion transition occurs decreases as P e increases, because the entropic depletion attraction becomes weak compared to the force-induced osmotic repulsion. The non-equilibrium interactive force is strictly repulsive for two separated probes.</p>
<p>But non-linear microrheology provides far more than a microscale technique for interrogating complex ﬂuids. In 1906, Einstein published the famous thought experiment in which he proposed that if a liquid were indeed composed of atoms, then the motion of a small particle suspended in the ﬂuid would move with the same random trajectories as the solvent atoms. Combining the theories of kinetics, diffusion, and thermodynamics, he showed that the diffusive motion of a small particle is indeed evidence of the existence of the atom. Perrin conﬁrmed the theory with measurement in 1909. This is a profound conclusion, drawn by simply watching a particle move in a liquid. Here, we follow this example and watch a particle move in a complex ﬂuid—but now for a system that is not at equilibrium. In equilibrium systems, the relationship between ﬂuctuation and dissipation is fundamental to our understanding of colloid physics. By studying ﬂuctuations away from equilibrium, we have discovered an analogous non-equilibrium relation between ﬂuctuation and dissipation—and that the balance between the two is stored in the material stress. A ﬁnal connection can be made between this stress and energy storage.</p>https://thesis.library.caltech.edu/id/eprint/6455Non-Destructive Evaluation of Material System Using Highly Nonlinear Acoustic Waves
https://resolver.caltech.edu/CaltechTHESIS:05102012-091402754
Authors: {'items': [{'email': 'devvrathk@gmail.com', 'id': 'Khatri-Devvrath', 'name': {'family': 'Khatri', 'given': 'Devvrath'}, 'show_email': 'YES'}]}
Year: 2012
DOI: 10.7907/P3VR-Q582
<p>A chain of granular particles is one of the most studied examples of highly nonlinear systems deriving its response from the nonlinear Hertzian contact interaction between particles. Interest in these systems derives from their tunable dynamic response, encompassing linear, weakly nonlinear, and strongly nonlinear regimes, controlled by varying the static and dynamic load applied. In chains with a very weak (or zero) static precompression, the system supports the formation and propagation of highly nonlinear solitary waves (HNSWs). The dual-nonlinear interaction between particles (i.e., a power-law type contact potential in compression, and zero strength in tension) combined with discreteness of the system, makes the granular system highly tunable. The propagation properties of these waves, such as traveling pulse width, wave speed, number of separated pulses (single or train of pulses), etc., can be controlled by modifying one or many of the parameters, like the particle's dimension, material properties, static and dynamic force amplitude, the type and duration of the initial excitation applied to the system, and/or the periodicity of the chain. The ability to control the wave properties in such chains has been proposed for several different practical engineering applications.</p>
<p>The dynamic properties of these granular chains have been conventionally studied using discrete particle models (DPMs) which consider the particles in the chains as point masses connected by nonlinear Hertzian springs with the neighboring particles. Although, this is a good approximation under proper circumstances, it does not capture many features of the three dimensional elastic particles such as the elastic wave propagation within the particles, the local deformation of the particles in the vicinity of the contact point, the corresponding changes in the contact area, and the collective vibrations of the particles among others. This thesis focuses on the development of a nite element model (FEM)using the commercially available software Abaqus, which takes into account many of these characteristic features. The nite element model discretizes particles by considering them as three-dimensional deformable bodies of revolution and describes the nonlinear dynamic response of one-dimensional granular chains composed of particles with various geometries and orientations. We showed that particles' geometries and orientations provide additional design parameters for controlling the dynamic response of the system, compared to chains composed of spherical particles. We also showed that the tunable and compact nature of these waves can be used to tailor the properties of HNSWs for specfic application, such as information carriers for actuation and sensing of mechanical properties and boundary effects of adjoining media in Non-Destructive Evaluation (NDE) and Structural Health Monitoring (SHM). Using experiments and numerics, we characterized interface dynamics between granular media and adjoining linear elastic media, and found that the coupling produced temporary localization of the incident waves at the boundaries between the two media and their decomposition into reflected waves. We monitored the formation of reflected solitary waves propagating back from the interface and found that their properties are sensitive to the geometric and material properties of the adjoining media. The work done in this research enhances our understanding of the basic physics and tunability of nonlinear granular media, and further establishes a theoretical and numerical foundation
in the applications of HNSWs as information carriers.</p>https://thesis.library.caltech.edu/id/eprint/7022Clefted Equilibrium Shapes of Superpressure Balloon Structures
https://resolver.caltech.edu/CaltechTHESIS:06062012-202646378
Authors: {'items': [{'email': 'dengxw03@gmail.com', 'id': 'Deng-Xiaowei', 'name': {'family': 'Deng', 'given': 'Xiaowei'}}]}
Year: 2012
DOI: 10.7907/YYTP-2005
<p>This thesis presents a numerical and analytical study of the clefted equilibrium shape of superpressure balloon structures. Lobed superpressure balloons have shown a tendency to deploy into unexpected asymmetric shapes, hence their design has to strike a balance between the lower stresses achieved by increasing lobing and the risk of incomplete deployment. Extensive clefting is a regular feature of balloons that are incompletely inflated, and is regularly seen during launch and ascent. Our particular interest in the research is in clefts that remain once a balloon has reached its float altitude and is fully pressurized.</p>
<p>A simplified simulation technique for orthotropic viscoelastic membranes is presented in the thesis. Wrinkling is detected by a combined stress-strain criterion and an iterative scheme searches for the wrinkle angle using a pseudoelastic material stiffness matrix based on a nonlinear viscoelastic constitutive model. This simplified model has been implemented in ABAQUS/Explicit and is able to compute the behavior of a membrane structure by superposition of a small number of response increments. The model has been tested against a published solution for a time-independent isotropic membrane under simple shear and also against experimental results on StratoFilm 420 under simple shear.</p>
<p>A fully three-dimensional finite element model of balloon structures incorporating wrinkling and frictionless contact, able to simulate the shapes taken up by lobed superpressure balloons during the final stages of their ascent has been established. Two different methods have been considered to predict the clefts: (i) deflation and
inflation method and (ii) constraint shift method. In method (i), the starting configuration is obtained by deflating an initially symmetric balloon subject to uniform pressure. The deflation simulation is continued until the differential pressure at the bottom of the balloon has become negative, at which point the balloon is extensively clefted. The balloon is then inflated by increasing the bottom pressure while maintaining a uniform vertical ressure gradient, and the evolution of the shape and stress distribution of the balloon is studied. Two different designs of uperpressure balloons are investigated: a flat facet balloon and a ighly lobed balloon. It is found that the flat facet balloon follows essentially the same path during deflation and inflation, and hence will deploy into a unique, symmetric shape. For the lobed balloon it is found that it follows different paths during deflation and inflation, and deploys into an alternate, clefted equilibrium shape.</p>
<p>Compared to method (i), method (ii) is computationally a more efficient clefting test. The test consists in setting up the balloon in its symmetrically inflated configuration, then breaking the symmetry of this shape by artificially introducing a clefting imperfection, and finally determining the equilibrium shape of the balloon. The clefting imperfection is computed by shifting the constraint at the bottom of the balloon and removing the pressure in the bottom region, below the shifted constraint. The clefting test is applied successfully to three 27~m diameter superpressure balloons that have been tested indoors by NASA, of which one had remained clefted when it was inflated and the other two had deployed completely.</p>
<p>In addition to numerical simulations, formulation of a new cleft factor, employed as an indicator of tendency to S-cleft for superpressure balloons based on constant-stress design has been established through dimensional analysis. The cleft factor, defined as the ratio of clefted volume to cyclically symmetrical volume, is expressed in the form of power law relation of the dimensionless groups. An example illustrates how to calculate the coefficients of the analytical formula and analyze sensitivity of design parameters to clefting.</p>https://thesis.library.caltech.edu/id/eprint/7141Particle-Based Modeling of Ni-YSZ Anodes
https://resolver.caltech.edu/CaltechTHESIS:03302012-133547448
Authors: {'items': [{'email': 'vaughantel1@gmail.com', 'id': 'Thomas-Vaughan-Lamar', 'name': {'family': 'Thomas', 'given': 'Vaughan Lamar'}, 'show_email': 'YES'}]}
Year: 2012
DOI: 10.7907/JF8P-5495
<p>In this work we examine the performance of particle-based models with respect to the Ni-YSZ composite anode system. The conductivity and triple-phase boundary (tpb) of particle-based systems is estimated. The systems considered have mono-dispersed particle size distributions, bi-modal particle size distributions with a YSZ:Ni particle size ratio of 1:0.781, and particle size distributions based on experimental measurements. All three types of systems show qualitative behavioral agreement in terms of conductivity, with clear transition from non-conducting behavior to high conducting behavior over a small transition regime which varied from a nickel phase fraction of .22-.28 for the mono- dispersed cases, 0.19-.0.25 for the bimodal cases, and 0.19-0.30 for the experimentally based cases. Mono-dispersed and simple-polydispersed particle size distribution show very low variation from case to case, with σ/μ ≤ 0.04. Cases based on empirical particle size distribution data demonstrated significantly higher variances which varied over a very large range, 0.3 ≤ σ/μ ≤ 1.1. With respect to the calculations of the TPB length, we find that the same pattern of variance in the measure of the triple-phase boundary length. The TPB length for the mono-dispersed and simple poly-dispersed systems was in the range of 3 × 1012 –4 × 1013 m/m3 . For empirical particle size distribution data the TPB length density was in the range of 8×109–2×1011 m/m3. The variance of the TPB length density follows the same pattern as the conductivity measurements with very low variance for the mono-dispersed and simple poly-dispersed systems and much larger variance for the empirically-based systems. We also examine the association between the TPB length and the availability of conducting pathways for the participating particles xv of individual TPBs. The probability of a TPB having a conducting pathway in the gas phase is essentially 100% in all cases. The probability of an individual tpb section having conducting pathways in either of the solid phases is directly related to percolation condition of that phase.</p>
<p>We also considered a particle-based composite electrode realization based on a three- dimensional reconstruction of an actual Ni-YSZ composite electrode. For this model we used particles which vary in nominal size from 85–465 nm, with size increments of 42.5 nm. We paid particular attention to the coordination numbers between particles and the distribution of particle size interconnections. We found that homogeneous inter-particle connections were far more common than would occur using a random distribution of particles. In particular we found that for a random collection of particles of similar composition the likelihood Ni-Ni particle connections was between 0.18–0.30. For the reconstruction we found the likelihood of Ni-Ni particle connections to be greater than 0.56 in all cases. Similarly, the distribution of connections between particles, with respect to particle size of the participating particles, deviated from what would be expected using a random distribution of particles. Particles in the range of 85–169 nm showed the highest coordination with particles of the same size. Particles in the range of 211–338 nm have the highest coordination with particles of radius 169 nm with very similar distributions. Particles with radius greater than 338 nm represented only 7.2 × 10−3 % of the particles within the reconstruction, and showed the highest coordination with particles of radius of 211 nm, but the distributions vary widely.</p>
<p>In the final chapter, we build a model which can account for mass transfer, hetero- geneous chemistry, surface chemistry, and electrochemistry within a porous electrode. The electric potential is calculated on a particle basis using a network model; gas phase concentrations and surface coverages are calculated with a one-dimensional porous me- dia model. Properties of the porous media are calculated via a TPMC method. TPB electrochemistry is calculated at individual triple phase boundaries within the particle xvi model, based on local gas phase concentrations, surface coverages and particle poten- tials, and then added to the porous media model. Using this tool we are able to calculate the spatial distribution of the Faradaic current within the electrode, and variation in gas phase concentrations within the porous media.</p>https://thesis.library.caltech.edu/id/eprint/6881Hierarchical Structures of Aligned Carbon Nanotubes as Low-Density Energy-Dissipative Materials
https://resolver.caltech.edu/CaltechTHESIS:05072012-134317580
Authors: {'items': [{'email': 'jordanraney@gmail.com', 'id': 'Raney-Jordan-Robert', 'name': {'family': 'Raney', 'given': 'Jordan Robert'}, 'show_email': 'NO'}]}
Year: 2012
DOI: 10.7907/25R0-JT92
<p>Carbon nanotubes (CNTs) are known to have remarkable properties, such as a specific strength two orders of magnitude higher than that of steel. It has remained a challenge, however, to achieve useful bulk properties from CNTs. Toward that goal, here we develop low-density bulk materials (0.1-0.4 g cm<sup>-3</sup>) entirely or nearly entirely from CNTs. These consist of nominally-aligned arrays of CNTs that display a dissipative compressive response, with a notable stress-strain hysteresis. The compressive properties of CNT arrays are examined in detail. This analysis reveals interesting features in the mechanical response, such as strain localization (resulting from a gradient in physical properties along the height), recovery after compression, non-linear viscoelasticity, and behavior under repeated compression that depends on the strain of previous cycles (similar to the Mullins effect in rubbers). We observe that in compression the energy dissipation of these materials is more than 200 times that of polymeric foams of comparable density.</p>
<p>Next, materials based on CNT arrays are studied as exemplary of hierarchical materials (materials with distinct structure at multiple length scales). Hierarchical materials have pushed the limits of traditional material tradeoffs (e.g., the typical trend that increased strength requires increased weight). Techniques are developed to separately vary the structure of CNT arrays at nanometer, micrometer, and millimeter length scales, and the effects on the bulk material response are examined. Structure can be modified during CNT synthesis, such as by varying the composition of the flow gas or by manipulating the input rate of chemical precursors; it can also be modified post-synthesis, e.g., by the in situ synthesis of nanoparticles in the interstices of the CNT arrays or by the assembly of multilayer structures of multiple CNT arrays connected by polymeric or metallic interlayers.</p>
<p>Finally, a mathematical model is applied to capture the complexities of the mechanical response. This one-dimensional, multiscale, bistable spring model is able to match the global stress-strain response as well as local effects such as strain localization and Mullins-like behavior. A technique is developed to reliably discern the model's material parameters based on in situ optical data from the experiments.</p>https://thesis.library.caltech.edu/id/eprint/7009Phonon Anharmonicity of Ionic Compounds and Metals
https://resolver.caltech.edu/CaltechTHESIS:05012012-155623422
Authors: {'items': [{'email': 'chenwli@gmail.com', 'id': 'Li-Chen-W', 'name': {'family': 'Li', 'given': 'Chen W.'}, 'orcid': '0000-0002-0758-5334', 'show_email': 'YES'}]}
Year: 2012
DOI: 10.7907/7VS5-0F52
<p>Vibrational studies of materials at elevated temperatures are relatively rare, and most phonon work also has emphasized harmonic behavior. Non-harmonic effects are often unexplored. These non-harmonic effects can be important for many properties of the material, such as thermal transport and phase stability.</p>
<p>Phonon theory and computational methods are briefly reviewed, and the experimental techniques for phonon study, such as Raman spectroscopy and inelastic neutron scattering, are discussed. Several experiments on phonon anharmonicity were performed, and interpreted with these computational methods.</p>
<p>In Raman spectroscopy studies on the phonon dynamics of hafnia and zirconia, Raman line positions, and shapes of temperatures to 1000 K were measured and the types of modes that exhibit the most anharmonicity were characterized and correlated to the vibrational displacements of individual atoms in the unit cell. It was found that anharmonicity in these systems is rich in information and strongly mode dependent.</p>
<p>Using time-of-flight inelastic neutron scattering, we found purely quartic transverse modes with an anomalous mode stiffening with temperature, and related these modes to the enormous negative thermal expansion of the DO9 structure of scandium fluoride.</p>
<p>Using second-order perturbation theory, phonon linewidths from the third-order anharmonicity were calculated from first-principles density functional theory with the supercell finite-displacement method. For face-centered cubic aluminum, the good agreement between calculations and the phonon density of states up to 750 K indicates that the third-order phonon-phonon interactions calculated can account for the lifetime broadenings of phonons in aluminum to at least 80% of its melting temperature.</p>https://thesis.library.caltech.edu/id/eprint/6997Coupled Effects of Mechanics, Geometry, and Chemistry on Bio-Membrane Behavior
https://resolver.caltech.edu/CaltechTHESIS:06062013-102758695
Authors: {'items': [{'email': 'gianghak4@gmail.com', 'id': 'Giang-Ha-Thanh', 'name': {'family': 'Giang', 'given': 'Ha Thanh'}, 'show_email': 'NO'}]}
Year: 2013
DOI: 10.7907/BVSK-K782
<p>Lipid bilayer membranes are models for cell membranes--the structure that helps regulate cell function. Cell membranes are heterogeneous, and the coupling between composition and shape gives rise to complex behaviors that are important to regulation. This thesis seeks to systematically build and analyze complete models to understand the behavior of multi-component membranes.</p>
<p>We propose a model and use it to derive the equilibrium and stability conditions for a general class of closed multi-component biological membranes. Our analysis shows that the critical modes of these membranes have high frequencies, unlike single-component vesicles, and their stability depends on system size, unlike in systems undergoing spinodal decomposition in flat space. An important implication is that small perturbations may nucleate localized but very large deformations. We compare these results with experimental observations.</p>
<p>We also study open membranes to gain insight into long tubular membranes that arise for example in nerve cells. We derive a complete system of equations for open membranes by using the principle of virtual work. Our linear stability analysis predicts that the tubular membranes tend to have coiling shapes if the tension is small, cylindrical shapes if the tension is moderate, and beading shapes if the tension is large. This is consistent with experimental observations reported in the literature in nerve fibers. Further, we provide numerical solutions to the fully nonlinear equilibrium equations in some problems, and show that the observed mode shapes are consistent with those suggested by linear stability. Our work also proves that beadings of nerve fibers can appear purely as a mechanical response of the membrane. </p> https://thesis.library.caltech.edu/id/eprint/7851Proton Transfers at the Air-Water Interface
https://resolver.caltech.edu/CaltechTHESIS:05092013-220921048
Authors: {'items': [{'email': 'hmishra1983@gmail.com', 'id': 'Mishra-Himanshu', 'name': {'family': 'Mishra', 'given': 'Himanshu'}, 'show_email': 'YES'}]}
Year: 2013
DOI: 10.7907/A9HR-PN89
<p>Proton transfer reactions at the interface of water with hydrophobic media, such as air or lipids, are ubiquitous on our planet. These reactions orchestrate a host of vital phenomena in the environment including, for example, acidification of clouds, enzymatic catalysis, chemistries of aerosol and atmospheric gases, and bioenergetic transduction. Despite their importance, however, quantitative details underlying these interactions have remained unclear. Deeper insight into these interfacial reactions is also required in addressing challenges in green chemistry, improved water quality, self-assembly of materials, the next generation of micro-nanofluidics, adhesives, coatings, catalysts, and electrodes. This thesis describes experimental and theoretical investigation of proton transfer reactions at the air-water interface as a function of hydration gradients, electrochemical potential, and electrostatics. Since emerging insights hold at the lipid-water interface as well, this work is also expected to aid understanding of complex biological phenomena associated with proton migration across membranes.</p>
<p>Based on our current understanding, it is known that the physicochemical properties of the gas-phase water are drastically different from those of bulk water. For example, the gas-phase hydronium ion, H<sub>3</sub>O<sup>+</sup>(g), can protonate most (non-alkane) organic species, whereas H<sub>3</sub>O<sup>+</sup>(aq) can neutralize only relatively strong bases. Thus, to be able to understand and engineer water-hydrophobe interfaces, it is imperative to investigate this fluctuating region of molecular thickness wherein the ‘function’ of chemical species transitions from one phase to another via steep gradients in hydration, dielectric constant, and density. Aqueous interfaces are difficult to approach by current experimental techniques because designing experiments to specifically sample interfacial layers (< 1 nm thick) is an arduous task. While recent advances in surface-specific spectroscopies have provided valuable information regarding the structure of aqueous interfaces, but structure alone is inadequate to decipher the function. By similar analogy, theoretical predictions based on classical molecular dynamics have remained limited in their scope.</p>
<p>Recently, we have adapted an analytical electrospray ionization mass spectrometer (ESIMS) for probing reactions at the gas-liquid interface in real time. This technique is direct, surface-specific,and provides unambiguous mass-to-charge ratios of interfacial species. With this innovation, we have been able to investigate the following:</p>
<p>1. How do anions mediate proton transfers at the air-water interface?</p>
<p>2. What is the basis for the negative surface potential at the air-water interface?</p>
<p>3. What is the mechanism for catalysis ‘on-water’?</p>
<p>In addition to our experiments with the ESIMS, we applied quantum mechanics and molecular dynamics to simulate our experiments toward gaining insight at the molecular scale. Our results unambiguously demonstrated the role of electrostatic-reorganization of interfacial water during proton transfer events. With our experimental and theoretical results on the ‘superacidity’ of the surface of mildly acidic water, we also explored implications on atmospheric chemistry and green chemistry. Our most recent results explained the basis for the negative charge of the air-water interface and showed that the water-hydrophobe interface could serve as a site for enhanced autodissociation of water compared to the condensed phase.</p>https://thesis.library.caltech.edu/id/eprint/7693Superprotonic Solid Acids: Thermochemistry, Structure, and Conductivity
https://resolver.caltech.edu/CaltechTHESIS:09142012-115522353
Authors: {'items': [{'email': 'ikedashome@yahoo.co.jp', 'id': 'Ikeda-Ayako', 'name': {'family': 'Ikeda', 'given': 'Ayako'}, 'show_email': 'YES'}]}
Year: 2013
DOI: 10.7907/R1SG-VY83
<p>In this work, in order to investigate the thermochemistry and property of the superprotonic solid acid compounds, the measurement methods were established for <italic>in situ</italic> observation, because superprotonic phases are neither stable at room temperature nor freezable to room temperature. A humidity-controlled TG, DSC and AC impedance measurement system, and high temperature stage for XRD were built for thermal analysis and characterization of the solid acid compounds.</p>
<p>The thermodynamic and kinetics of the dehydration and hydration of CsH<sub>2</sub>PO<sub>4</sub> is investigated by TG, DSC, and XRD analysis. By making use of the enhanced kinetics afforded by SiO2, the phase boundary between CsH<sub>2</sub>PO<sub>4</sub>, CsPO<sub>3</sub>, and dehydrated liquid was precisely determined. The stability of CsH<sub>2</sub>PO<sub>4</sub> and the liquid dehydrate, CsH<sub>2(1-x)</sub>PO<sub>4-x</sub>(l), were confirmed by the complete reversal of dehydration to recover these phases in the appropriate temperature and water partial pressure ranges. Rehydration and conversion of CsPO<sub>3</sub>(s) to CsH<sub>2</sub>PO<sub>4</sub>(s) occurs over a period of several hours, depending on temperature, water partial pressure, and morphology of the metaphosphate. High and small particles favor rapid dehydration, whereas the temperature dependence of the rehydration kinetics is nonmonotonic, reaching its fastest rate in the vicinity of the superprotonic transition.</p>
<p>Doping Rb and K into CDP was examined and the stable region of Cs<sub>1-x</sub>RbxH<sub>2</sub>PO<sub>4</sub> and Cs<sub>1-x</sub>KxH<sub>2</sub>PO<sub>4</sub> are determined by in situ XRD and DSC measurement. Then the effects of doping to the structure and conductivity are discussed. It was found that Rb has whole-range solubility for both cubic and monoclinic CDP. Ts increases and Td decrease with Rb content. K has 27% solubility for cubic CDP, Ts and Td decrease with K content. The eutectic temperature is 208 ± 2°C. The lattice size of Rb- or K- doped CDP depends on the averaged cation size. Conductivity linearly decreases by dopant concentration. The impact of K doping is deeper than that of Rb for the equivalent averaged cation size.</p>
<p><italic>in situ</italic> XRD measurement was carried out using single-crystal CsH<sub>2</sub>PO<sub>4</sub> in order to study the phase transformation mechanism of this compound. A plate-like single crystal with (100) orientation was prepared, and the phase transition was observed by heating and cooling with ramp rate 0.2 K/min. From the obtained XRD profile — the after-first-phase transition (monoclinic-->cubic) — the distribution of the domain orientation was estimated. It was found that (100) is the preferential orientation after phase transition, however, the amount of the domains with other orientation is not ignorable. Therefore, it is considered that the phase transformation in CsH<sub>2</sub>PO<sub>4</sub> is not simple martensitic, but that some other event, such as recrystallization, happens during the transition process.</p>https://thesis.library.caltech.edu/id/eprint/7205Flight Dynamics in Drosophila Through a Dynamically-scaled Robotic Approach
https://resolver.caltech.edu/CaltechTHESIS:06072013-110839676
Authors: {'items': [{'email': 'michael.j.elzinga@gmail.com', 'id': 'Elzinga-Michael-John', 'name': {'family': 'Elzinga', 'given': 'Michael John'}, 'show_email': 'YES'}]}
Year: 2013
DOI: 10.7907/MSRS-JG88
<p>Flies are particularly adept at balancing the competing demands of delay tolerance, performance, and robustness during flight, which invites thoughtful examination of their multimodal feedback architecture. This dissertation examines stabilization requirements for inner-loop feedback strategies in the flapping flight of Drosophila, the fruit fly, against the backdrop of sensorimotor transformations present in the animal. Flies have evolved multiple specializations to reduce sensorimotor latency, but sensory delay during flight is still significant on the timescale of body dynamics. I explored the effect of sensor delay on flight stability and performance for yaw turns using a dynamically-scaled robot equipped with a real-time feedback system that performed active turns in response to measured yaw torque. The results show a fundamental tradeoff between sensor delay and permissible feedback gain, and suggest that fast mechanosensory feedback provides a source of active damping that compliments that contributed by passive effects. Presented in the context of these findings, a control architecture whereby a haltere-mediated inner-loop proportional controller provides damping for slower visually-mediated feedback is consistent with tethered-flight measurements, free-flight observations, and engineering design principles.</p>
<p>Additionally, I investigated how flies adjust stroke features to regulate and stabilize level forward flight. The results suggest that few changes to hovering kinematics are actually required to meet steady-state lift and thrust requirements at different flight speeds, and the primary driver of equilibrium velocity is the aerodynamic pitch moment. This finding is consistent with prior hypotheses and observations regarding the relationship between body pitch and flight speed in fruit flies. The results also show that the dynamics may be stabilized with additional pitch damping, but the magnitude of required damping increases with flight speed. I posit that differences in stroke deviation between the upstroke and downstroke might play a critical role in this stabilization. Fast mechanosensory feedback of the pitch rate could enable active damping, which would inherently exhibit gain scheduling with flight speed if pitch torque is regulated by adjusting stroke deviation. Such a control scheme would provide an elegant solution for flight stabilization across a wide range of flight speeds.</p>
https://thesis.library.caltech.edu/id/eprint/7864Phase Behavior of Complex Superprotonic Solid Acids
https://resolver.caltech.edu/CaltechTHESIS:05302013-183134007
Authors: {'items': [{'email': 'chatr.p@hotmail.com', 'id': 'Panithipongwut-Chatr', 'name': {'family': 'Panithipongwut', 'given': 'Chatr'}, 'show_email': 'YES'}]}
Year: 2013
DOI: 10.7907/NXG8-TY79
<p>Superprotonic phase transitions and thermal behaviors of three complex solid acid systems are presented, namely Rb<sub>3</sub>H(SO<sub>4</sub>)<sub>2</sub>-RbHSO<sub>4</sub> system, Rb<sub>3</sub>H(SeO<sub>4</sub>)<sub>2</sub>2-Cs<sub>3</sub>H(SeO<sub>4</sub>)<sub>2</sub> solid solution system, and Cs<sub>6</sub>(H<sub>2</sub>SO<sub>4</sub>)<sub>3</sub>(H<sub>1.5</sub>PO<sub>4</sub>)<sub>4</sub>. These material systems present a rich set of phase transition characteristics that set them apart from other, simpler solid acids. A.C. impedance spectroscopy, high-temperature X-ray powder diffraction, and thermal analysis, as well as other characterization techniques, were employed to investigate the phase behavior of these systems.</p>
<p>Rb<sub>3</sub>H(SO<sub>4</sub>)<sub>2</sub> is an atypical member of the M<sub>3</sub>H(XO<sub>4</sub>)<sub>2</sub> class of compounds (M = alkali metal or NH<sub>4</sub><sup>+</sup> and X = S or Se) in that a transition to a high-conductivity state involves disproportionation into two phases rather than a simple polymorphic transition [1]. In the present work, investigations of the Rb<sub>3</sub>H(SO<sub>4</sub>)<sub>2</sub>-RbHSO<sub>4</sub> system have revealed the disproportionation products to be Rb<sub>2</sub>SO<sub>4</sub> and the previously unknown compound Rb<sub>5</sub>H<sub>3</sub>(SO<sub>4</sub>)<sub>4</sub>. The new compound becomes stable at a temperature between 25 and 140 °C and is isostructural to a recently reported trigonal phase with space group P3̅m of Cs<sub>5</sub>H<sub>3</sub>(SO<sub>4</sub>)<sub>4</sub> [2]. At 185 °C the compound undergoes an apparently polymorphic transformation with a heat of transition of 23.8 kJ/mol and a slight additional increase in conductivity.</p>
<p>The compounds Rb<sub>3</sub>H(SeO<sub>4</sub>)<sub>2</sub> and Cs<sub>3</sub>H(SeO<sub>4</sub>)<sub>2</sub>, though not isomorphous at ambient temperatures, are quintessential examples of superprotonic materials. Both adopt monoclinic structures at ambient temperatures and ultimately transform to a trigonal (R3̅m) superprotonic structure at slightly elevated temperatures, 178 and 183 °C, respectively. The compounds are completely miscible above the superprotonic transition and show extensive solubility below it. Beyond a careful determination of the phase boundaries, we find a remarkable 40-fold increase in the superprotonic conductivity in intermediate compositions rich in Rb as compared to either end-member.</p>
<p>The compound Cs<sub>6</sub>(H<sub>2</sub>SO<sub>4</sub>)<sub>3</sub>(H<sub>1.5</sub>PO<sub>4</sub>)<sub>4</sub> is unusual amongst solid acid compounds in that it has a complex cubic structure at ambient temperature and apparently transforms to a simpler cubic structure of the CsCl-type (isostructural with CsH<sub>2</sub>PO<sub>4</sub>) at its transition temperature of 100-120 °C [3]. Here it is found that, depending on the level of humidification, the superprotonic transition of this material is superimposed with a decomposition reaction, which involves both exsolution of (liquid) acid and loss of H<sub>2</sub>O. This reaction can be suppressed by application of sufficiently high humidity, in which case Cs<sub>6</sub>(H<sub>2</sub>SO<sub>4</sub>)<sub>3</sub>(H<sub>1.5</sub>PO<sub>4</sub>)<sub>4</sub> undergoes a true superprotonic transition. It is proposed that, under conditions of low humidity, the decomposition/dehydration reaction transforms the compound to Cs<sub>6</sub>(H<sub>2-0.5x</sub>SO<sub>4</sub>)<sub>3</sub>(H<sub>1.5</sub>1.5PO<sub>4</sub>)<sub>4-x</sub>, also of the CsCl structure type at the temperatures of interest, but with a smaller unit cell. With increasing temperature, the decomposition/dehydration proceeds to greater and greater extent and unit cell of the solid phase decreases. This is identified to be the source of the apparent negative thermal expansion behavior.</p>
<p>References: <br />
[1] L.A. Cowan, R.M. Morcos, N. Hatada, A. Navrotsky, S.M. Haile, Solid State Ionics 179 (2008) (9-10) 305.<br />
[2] M. Sakashita, H. Fujihisa, K.I. Suzuki, S. Hayashi, K. Honda, Solid State Ionics 178 (2007) (21-22) 1262.<br />
[3] C.R.I. Chisholm, Superprotonic Phase Transitions in Solid Acids: Parameters affecting the presence and stability of superprotonic transitions in the MHnXO4 family of compounds (X=S, Se, P, As; M=Li, Na, K, NH4, Rb, Cs), Materials Science, California Institute of Technology, Pasadena, California (2003).</p>https://thesis.library.caltech.edu/id/eprint/7778Dynamics of Cell–Matrix Mechanical Interactions in Three Dimensions
https://resolver.caltech.edu/CaltechTHESIS:05312013-133431536
Authors: {'items': [{'email': 'jknotbohm@gmail.com', 'id': 'Notbohm-Jacob-K', 'name': {'family': 'Notbohm', 'given': 'Jacob K.'}, 'show_email': 'NO'}]}
Year: 2013
DOI: 10.7907/AXD0-2D10
<p>The forces cells apply to their surroundings control biological processes such as growth, adhesion, development, and migration. In the past 20 years, a number of experimental techniques have been developed to measure such cell tractions. These approaches have primarily measured the tractions applied by cells to synthetic two-dimensional substrates, which do not mimic in vivo conditions for most cell types. Many cell types live in a fibrous three-dimensional (3D) matrix environment. While studying cell behavior in such 3D matrices will provide valuable insights for the mechanobiology and tissue engineering communities, no experimental approaches have yet measured cell tractions in a fibrous 3D matrix.</p>
<p>This thesis describes the development and application of an experimental technique for quantifying cellular forces in a natural 3D matrix. Cells and their surrounding matrix are imaged in three dimensions with high speed confocal microscopy. The cell-induced matrix displacements are computed from the 3D image volumes using digital volume correlation. The strain tensor in the 3D matrix is computed by differentiating the displacements, and the stress tensor is computed by applying a constitutive law. Finally, tractions applied by the cells to the matrix are computed directly from the stress tensor.</p>
<p>The 3D traction measurement approach is used to investigate how cells mechanically interact with the matrix in biologically relevant processes such as division and invasion. During division, a single mother cell undergoes a drastic morphological change to split into two daughter cells. In a 3D matrix, dividing cells apply tensile force to the matrix through thin, persistent extensions that in turn direct the orientation and location of the daughter cells. Cell invasion into a 3D matrix is the first step required for cell migration in three dimensions. During invasion, cells initially apply minimal tractions to the matrix as they extend thin protrusions into the matrix fiber network. The invading cells anchor themselves to the matrix using these protrusions, and subsequently pull on the matrix to propel themselves forward.</p>
<p>Lastly, this thesis describes a constitutive model for the 3D fibrous matrix that uses a finite element (FE) approach. The FE model simulates the fibrous microstructure of the matrix and matches the cell-induced matrix displacements observed experimentally using digital volume correlation. The model is applied to predict how cells mechanically sense one another in a 3D matrix. It is found that cell-induced matrix displacements localize along linear paths. These linear paths propagate over a long range through the fibrous matrix, and provide a mechanism for cell-cell signaling and mechanosensing. The FE model developed here has the potential to reveal the effects of matrix density, inhomogeneity, and anisotropy in signaling cell behavior through mechanotransduction.</p>https://thesis.library.caltech.edu/id/eprint/7793Interplay of Martensitic Phase Transformation and Plastic Slip in Polycrystals
https://resolver.caltech.edu/CaltechTHESIS:06072013-023915252
Authors: {'items': [{'email': 'awrichar@gmail.com', 'id': 'Richards-Andrew-Walter', 'name': {'family': 'Richards', 'given': 'Andrew Walter'}, 'show_email': 'NO'}]}
Year: 2013
DOI: 10.7907/MM8X-BZ69
<p>Inspired by key experimental and analytical results regarding Shape Memory Alloys (SMAs), we propose a modelling framework to explore the interplay between martensitic phase transformations and plastic slip in polycrystalline materials, with an eye towards computational efficiency. The resulting framework uses a convexified potential for the internal energy density to capture the stored energy associated with transformation at the meso-scale, and introduces kinetic potentials to govern the evolution of transformation and plastic slip. The framework is novel in the way it treats plasticity on par with transformation.</p>
<p>We implement the framework in the setting of anti-plane shear, using a staggered implicit/explict update: we first use a Fast-Fourier Transform (FFT) solver based on an Augmented Lagrangian formulation to implicitly solve for the full-field displacements of a simulated polycrystal, then explicitly update the volume fraction of martensite and plastic slip using their respective stick-slip type kinetic laws. We observe that, even in this simple setting with an idealized material comprising four martensitic variants and four slip systems, the model recovers a rich variety of SMA type behaviors. We use this model to gain insight into the isothermal behavior of stress-stabilized martensite, looking at the effects of the relative plastic yield strength, the memory of deformation history under non-proportional loading, and several others.</p>
<p>We extend the framework to the generalized 3-D setting, for which the convexified potential is a lower bound on the actual internal energy, and show that the fully implicit discrete time formulation of the framework is governed by a variational principle for mechanical equilibrium. We further propose an extension of the method to finite deformations via an exponential mapping. We implement the generalized framework using an existing Optimal Transport Mesh-free (OTM) solver. We then model the $\alpha$--$\gamma$ and $\alpha$--$\varepsilon$ transformations in pure iron, with an initial attempt in the latter to account for twinning in the parent phase. We demonstrate the scalability of the framework to large scale computing by simulating Taylor impact experiments, observing nearly linear (ideal) speed-up through 256 MPI tasks. Finally, we present preliminary results of a simulated Split-Hopkinson Pressure Bar (SHPB) experiment using the $\alpha$--$\varepsilon$ model.</p>
https://thesis.library.caltech.edu/id/eprint/7859Fracture of Materials Undergoing Solid-Solid Phase Transformation
https://resolver.caltech.edu/CaltechTHESIS:05302013-233635296
Authors: {'items': [{'email': 'prasad.bharat@gmail.com', 'id': 'Penmecha-Bharat-Prasad', 'name': {'family': 'Penmecha', 'given': 'Bharat Prasad'}, 'show_email': 'YES'}]}
Year: 2013
DOI: 10.7907/FNTG-9T08
<p>A large number of technologically important materials undergo solid-solid phase transformations. Examples range from ferroelectrics (transducers and memory devices), zirconia (Thermal Barrier Coatings) to nickel superalloys and (lithium) iron phosphate (Li-ion batteries). These transformations involve a change in the crystal structure either through diffusion of species or local rearrangement of atoms. This change of crystal structure leads to a macroscopic change of shape or volume or both and results in internal stresses during the transformation. In certain situations this stress field gives rise to cracks (tin, iron phosphate etc.) which continue to propagate as the transformation front traverses the material. In other materials the transformation modifies the stress field around cracks and effects crack growth behavior (zirconia, ferroelectrics). These observations serve as our motivation to study cracks in solids undergoing phase transformations. Understanding these effects will help in improving the mechanical reliability of the devices employing these materials.</p>
<p>In this thesis we present work on two problems concerning the interplay between cracks and phase transformations. First, we consider the directional growth of a set of parallel edge cracks due to a solid-solid transformation. We conclude from our analysis that phase transformations can lead to formation of parallel edge cracks when the transformation strain satisfies certain conditions and the resulting cracks grow all the way till their tips cross over the phase boundary. Moreover the cracks continue to grow as the phase boundary traverses into the interior of the body at a uniform spacing without any instabilities. There exists an optimal value for the spacing between the cracks. We ascertain these conclusion by performing numerical simulations using finite elements.</p>
<p>Second, we model the effect of the semiconducting nature and dopants on cracks in ferroelectric perovskite materials, particularly barium titanate. Traditional approaches to model fracture in these materials have treated them as insulators. In reality, they are wide bandgap semiconductors with oxygen vacancies and trace impurities acting as dopants. We incorporate the space charge arising due the semiconducting effect and dopant ionization in a phase field model for the ferroelectric. We derive the governing equations by invoking the dissipation inequality over a ferroelectric domain containing a crack. This approach also yields the driving force acting on the crack. Our phase field simulations of polarization domain evolution around a crack show the accumulation of electronic charge on the crack surface making it more permeable than was previously believed so, as seen in recent experiments. We also discuss the effect the space charge has on domain formation and the crack driving force.</p>https://thesis.library.caltech.edu/id/eprint/7785Techniques for Strength Measurement at High Pressures and Strain-Rates using Transverse Waves
https://resolver.caltech.edu/CaltechTHESIS:01152014-115401299
Authors: {'items': [{'email': 'vstolyarfirst@gmail.com', 'id': 'Richmond-Victoria-Stolyar', 'name': {'family': 'Richmond', 'given': 'Victoria Stolyar'}, 'show_email': 'NO'}]}
Year: 2014
DOI: 10.7907/SH60-5659
<p>The study of the strength of a material is relevant to a variety of applications including automobile collisions, armor penetration and inertial confinement fusion. Although dynamic behavior of materials at high pressures and strain-rates has been studied extensively using plate impact experiments, the results provide measurements in one direction only. Material behavior that is dependent on strength is unaccounted for. The research in this study proposes two novel configurations to mitigate this problem.</p>
<p>The first configuration introduced is the oblique wedge experiment, which is comprised of a driver material, an angled target of interest and a backing material used to measure in-situ velocities. Upon impact, a shock wave is generated in the driver material. As the shock encounters the angled target, it is reflected back into the driver and transmitted into the target. Due to the angle of obliquity of the incident wave, a transverse wave is generated that allows the target to be subjected to shear while being compressed by the initial longitudinal shock such that the material does not slip. Using numerical simulations, this study shows that a variety of oblique wedge configurations can be used to study the shear response of materials and this can be extended to strength measurement as well. Experiments were performed on an oblique wedge setup with a copper impactor, polymethylmethacrylate driver, aluminum 6061-t6 target, and a lithium fluoride window. Particle velocities were measured using laser interferometry and results agree well with the simulations.</p>
<p>The second novel configuration is the y-cut quartz sandwich design, which uses the anisotropic properties of y-cut quartz to generate a shear wave that is transmitted into a thin sample. By using an anvil material to back the thin sample, particle velocities measured at the rear surface of the backing plate can be implemented to calculate the shear stress in the material and subsequently the strength. Numerical simulations were conducted to show that this configuration has the ability to measure the strength for a variety of materials.</p>
https://thesis.library.caltech.edu/id/eprint/8051Optimal Scaling in Ductile Fracture
https://resolver.caltech.edu/CaltechTHESIS:10162013-221817628
Authors: {'items': [{'email': 'turbolandry@yahoo.fr', 'id': 'Fokoua-Djodom-Landry', 'name': {'family': 'Fokoua Djodom', 'given': 'Landry'}, 'show_email': 'NO'}]}
Year: 2014
DOI: 10.7907/B1TW-2D81
This work is concerned with the derivation of optimal scaling laws, in the sense of matching lower and upper bounds on the energy, for a solid undergoing ductile fracture. The specific problem considered concerns a material sample in the form of an infinite slab of finite thickness subjected to prescribed opening displacements on its two surfaces. The solid is assumed to obey deformation-theory of plasticity and, in order to further simplify the analysis, we assume isotropic rigid-plastic deformations with zero plastic spin. When hardening exponents are given values consistent with observation, the energy is found to exhibit sublinear growth. We regularize the energy through the addition of nonlocal energy terms of the strain-gradient plasticity type. This nonlocal regularization has the effect of introducing an intrinsic length scale into the energy. We also put forth a physical argument that identifies the intrinsic length and suggests a linear growth of the nonlocal energy. Under these assumptions, ductile fracture emerges as the net result of two competing effects: whereas the sublinear growth of the local energy promotes localization of deformation to failure planes, the nonlocal regularization stabilizes this process, thus resulting in an orderly progression towards failure and a well-defined specific fracture energy. The optimal scaling laws derived here show that ductile fracture results from localization of deformations to void sheets, and that it requires a well-defined energy per unit fracture area. In particular, fractal modes of fracture are ruled out under the assumptions of the analysis. The optimal scaling laws additionally show that ductile fracture is cohesive in nature, i.e., it obeys a well-defined relation between tractions and opening displacements. Finally, the scaling laws supply a link between micromechanical properties and macroscopic fracture properties. In particular, they reveal the relative roles that surface energy and microplasticity play as contributors to the specific fracture energy of the material. Next, we present an experimental assessment of the optimal scaling laws. We show that when the specific fracture energy is renormalized in a manner suggested by the optimal scaling laws, the data falls within the bounds predicted by the analysis and, moreover, they ostensibly collapse---with allowances made for experimental scatter---on a master curve dependent on the hardening exponent, but otherwise material independent.https://thesis.library.caltech.edu/id/eprint/7993Design Strategies for Ultra-High Efficiency Photovoltaics
https://resolver.caltech.edu/CaltechTHESIS:06052014-163757869
Authors: {'items': [{'email': 'warmann@gmail.com', 'id': 'Warmann-Emily-Cathryn', 'name': {'family': 'Warmann', 'given': 'Emily Cathryn'}, 'show_email': 'NO'}]}
Year: 2014
DOI: 10.7907/0K8F-9871
<p>While concentrator photovoltaic cells have shown significant improvements in efficiency in the past ten years, once these cells are integrated into concentrating optics, connected to a power conditioning system and deployed in the field, the overall module efficiency drops to only 34 to 36%. This efficiency is impressive compared to conventional flat plate modules, but it is far short of the theoretical limits for solar energy conversion. Designing a system capable of achieving ultra high efficiency of 50% or greater cannot be achieved by refinement and iteration of current design approaches.</p>
<p>This thesis takes a systems approach to designing a photovoltaic system capable of 50% efficient performance using conventional diode-based solar cells. The effort began with an exploration of the limiting efficiency of spectrum splitting ensembles with 2 to 20 sub cells in different electrical configurations. Incorporating realistic non-ideal performance with the computationally simple detailed balance approach resulted in practical limits that are useful to identify specific cell performance requirements. This effort quantified the relative benefit of additional cells and concentration for system efficiency, which will help in designing practical optical systems.</p>
<p>Efforts to improve the quality of the solar cells themselves focused on the development of tunable lattice constant epitaxial templates. Initially intended to enable lattice matched multijunction solar cells, these templates would enable increased flexibility in band gap selection for spectrum splitting ensembles and enhanced radiative quality relative to metamorphic growth. The III-V material family is commonly used for multijunction solar cells both for its high radiative quality and for the ease of integrating multiple band gaps into one monolithic growth. The band gap flexibility is limited by the lattice constant of available growth templates. The virtual substrate consists of a thin III-V film with the desired lattice constant. The film is grown strained on an available wafer substrate, but the thickness is below the dislocation nucleation threshold. By removing the film from the growth substrate, allowing the strain to relax elastically, and bonding it to a supportive handle, a template with the desired lattice constant is formed. Experimental efforts towards this structure and initial proof of concept are presented.</p>
<p>Cells with high radiative quality present the opportunity to recover a large amount of their radiative losses if they are incorporated in an ensemble that couples emission from one cell to another. This effect is well known, but has been explored previously in the context of sub cells that independently operate at their maximum power point. This analysis explicitly accounts for the system interaction and identifies ways to enhance overall performance by operating some cells in an ensemble at voltages that reduce the power converted in the individual cell. Series connected multijunctions, which by their nature facilitate strong optical coupling between sub-cells, are reoptimized with substantial performance benefit.</p>
<p>Photovoltaic efficiency is usually measured relative to a standard incident spectrum to allow comparison between systems. Deployed in the field systems may differ in energy production due to sensitivity to changes in the spectrum. The series connection constraint in particular causes system efficiency to decrease as the incident spectrum deviates from the standard spectral composition. This thesis performs a case study comparing performance of systems over a year at a particular location to identify the energy production penalty caused by series connection relative to independent electrical connection.</p>
https://thesis.library.caltech.edu/id/eprint/8489Strength of Tantalum at High Pressures through Richtmyer-Meshkov Laser Compression Experiments and Simulations
https://resolver.caltech.edu/CaltechTHESIS:08092014-195153430
Authors: {'items': [{'email': 'kjohn@kistenet.com', 'id': 'John-Kristen-Kathleen', 'name': {'family': 'John', 'given': 'Kristen Kathleen'}, 'show_email': 'NO'}]}
Year: 2014
DOI: 10.7907/NE7Y-CK04
<p>Strength at extreme pressures (>1 Mbar or 100 GPa) and high strain rates (106-108 s-1) of materials is not well characterized. The goal of the research outlined in this thesis is to study the strength of tantalum (Ta) at these conditions. The Omega Laser in the Laboratory for Laser Energetics in Rochester, New York is used to create such extreme conditions. Targets are designed with ripples or waves on the surface, and these samples are subjected to high pressures using Omega’s high energy laser beams. In these experiments, the observational parameter is the Richtmyer-Meshkov (RM) instability in the form of ripple growth on single-mode ripples. The experimental platform used for these experiments is the “ride-along” laser compression recovery experiments, which provide a way to recover the specimens having been subjected to high pressures. Six different experiments are performed on the Omega laser using single-mode tantalum targets at different laser energies. The energy indicates the amount of laser energy that impinges the target. For each target, values for growth factor are obtained by comparing the profile of ripples before and after the experiment. With increasing energy, the growth factor increased. </p>
<p>Engineering simulations are used to interpret and correlate the measurements of growth factor to a measure of strength. In order to validate the engineering constitutive model for tantalum, a series of simulations are performed using the code Eureka, based on the Optimal Transportation Meshfree (OTM) method. Two different configurations are studied in the simulations: RM instabilities in single and multimode ripples. Six different simulations are performed for the single ripple configuration of the RM instability experiment, with drives corresponding to laser energies used in the experiments. Each successive simulation is performed at higher drive energy, and it is observed that with increasing energy, the growth factor increases. Overall, there is favorable agreement between the data from the simulations and the experiments. The peak growth factors from the simulations and the experiments are within 10% agreement. For the multimode simulations, the goal is to assist in the design of the laser driven experiments using the Omega laser. A series of three-mode and four-mode patterns are simulated at various energies and the resulting growth of the RM instability is computed. Based on the results of the simulations, a configuration is selected for the multimode experiments. These simulations also serve as validation for the constitutive model and the material parameters for tantalum that are used in the simulations.</p>
<p>By designing samples with initial perturbations in the form of single-mode and multimode ripples and subjecting these samples to high pressures, the Richtmyer-Meshkov instability is investigated in both laser compression experiments and simulations. By correlating the growth of these ripples to measures of strength, a better understanding of the strength of tantalum at high pressures is achieved.</p>
https://thesis.library.caltech.edu/id/eprint/8630Exploring the Kinetics of Domain Switching in Ferroelectrics for Structural Applications
https://resolver.caltech.edu/CaltechTHESIS:05302015-221358386
Authors: {'items': [{'email': 'cswojnar@gmail.com', 'id': 'Wojnar-Charles-Stanley', 'name': {'family': 'Wojnar', 'given': 'Charles Stanley'}, 'show_email': 'NO'}]}
Year: 2015
DOI: 10.7907/Z9HD7SM7
The complex domain structure in ferroelectrics gives rise to electromechanical coupling, and its evolution (via domain switching) results in a time-dependent (i.e. viscoelastic) response. Although ferroelectrics are used in many technological applications, most do not attempt to exploit the viscoelastic response of ferroelectrics, mainly due to a lack of understanding and accurate models for their description and prediction. Thus, the aim of this thesis research is to gain better understanding of the influence of domain evolution in ferroelectrics on their dynamic mechanical response.
There have been few studies on the viscoelastic properties of ferroelectrics, mainly due to a lack of experimental methods. Therefore, an apparatus and method called Broadband Electromechanical Spectroscopy (BES) was designed and built. BES allows for the simultaneous application of dynamic mechanical and electrical loading in a vacuum environment. Using BES, the dynamic stiffness and loss tangent in bending and torsion of a particular ferroelectric, viz. lead zirconate titanate (PZT), was characterized for different combinations of electrical and mechanical loading frequencies throughout the entire electric displacement hysteresis. Experimental results showed significant increases in loss tangent (by nearly an order of magnitude) and compliance during domain switching, which shows promise as a new approach to structural damping.
A continuum model of the viscoelasticity of ferroelectrics was developed, which incorporates microstructural evolution via internal variables and associated kinetic relations. For the first time, through a new linearization process, the incremental dynamic stiffness and loss tangent of materials were computed throughout the entire electric displacement hysteresis for different combinations of mechanical and electrical loading frequencies. The model accurately captured experimental results.
Using the understanding gained from the characterization and modeling of PZT, two applications of domain switching kinetics were explored by using Micro Fiber Composites (MFCs). Proofs of concept of set-and-hold actuation and structural damping using MFCs were demonstrated.https://thesis.library.caltech.edu/id/eprint/8947Shock Wave Behavior of Particulate Composites
https://resolver.caltech.edu/CaltechTHESIS:05292015-170754625
Authors: {'items': [{'email': 'mike.b.rauls@gmail.com', 'id': 'Rauls-Michael-Brian', 'name': {'family': 'Rauls', 'given': 'Michael Brian'}, 'show_email': 'NO'}]}
Year: 2015
DOI: 10.7907/Z98P5XHC
<p>Material heterogeneity at some scale is common in present engineering and structural materials as a means of strength improvement, weight reduction, and performance enhancement in a great many applications such as impact and blast protection, construction, and aerospace. While the benefits of transitioning toward composites in practical applications is obvious, the methods of measurement and optimization required to handle spatial heterogeneity and bridge length scale differences across multiple orders of magnitude are not. This is especially true as loading rates transition into the shock regime. Composite materials, such as concrete, have advantages afforded to them by their microstructure that allow them to dissipate and scatter impact energy. The mechanical mismatch between constituent phases in composites (mortar and cement paste in concrete, crystals and binder in polymer bonded explosives, ceramic powder and epoxy in potting materials, etc.) provides the interfaces required for shock wave reflection. The degree to which a shock is disrupted from its accepted form as a propagating discontinuity in stress and particle velocity is highly dependent upon the size, shape, and density of the interfaces present.</p>
<p>The experimental and computer aided simulations in this thesis seek to establish a scaling relationship between composite microstructure and shock front disruption in terms of particulate size and density through the use of multi-point heterodyne velocity interferometry. A model particulate composite has been developed to mimic the wave reflection properties of materials such as Ultra High Performace Composite (UHPC) concrete and polymer bonded explosives, while also being simple to source and manufacture repeatably. Polymethyl Methacrylate (PMMA), a thermoplastic polymer, and silica glass spheres satisfy the manufacturing constraints with a shock impedance mismatch of 4.1, when placed in-between the shock impedance of UHPC concretes (~ 10) and polymer bondedexplosives (~ 2). The flexibility afforded by the model composite allows for the use of mono-disperse bead particle diameter distributions centered at 5 discrete diameters centered in the range associated with high scattering effectiveness (5-50 times the shock thickness in the pure matrix material). Shock front disruption is measured at multiple points on the rear surface of a plate impact target to observe shock spreading and spatial heterogeneity in material response due to random particle placement.</p>
<p>Shock rise times are reported for composites of 30% and 40% glass spheres by volume, with glass spheres of 100, 300, 500, 700, and 1000 micron diameter. Composites with single mode as well as bi-modal bead diameter distributions are subjected to plate impact loading at an average pressure of 5 GPa. In single mode composites, a linear dependence of shock wave rise time on particle diameter is observed, with a constant of proportionality equal to the bulk shock speed in the material. Bi-modal bead diameter composites were fabricated in order to achieve higher volume fractions without composite degradation. The addition of a second phase to a base 30% glass by volume composite mix results in significant increases in shock wave rise time for base mixes of 500 micron beads, while a point of maximum scattering effectiveness is observed for base mixes
of 1000 micron diameter beads.</p>
<p>A comprehensive two dimensional series of CTH hydrocode simulations has been completed in tandem with experiments. An evaluation of the discrepancies in simulation and experimental results is presented. Shock disruption mechanisms and matrix/interface damage effects are discussed as possible sources of error and potential avenues for model improvement. The scaling arguments and model deficiency corrections made in this thesis have the potential to drive the development of new approaches of modeling shock waves in heterogeneous materials as well as optimization of microstructure for maximum shock front disruption.</p>https://thesis.library.caltech.edu/id/eprint/8936Rate and Microstructure Effects on the Dynamics of Carbon Nanotube Foams
https://resolver.caltech.edu/CaltechTHESIS:10162014-104834622
Authors: {'items': [{'email': 'thevamaranr@gmail.com', 'id': 'Thevamaran-Ramathasan', 'name': {'family': 'Thevamaran', 'given': 'Ramathasan'}, 'orcid': '0000-0001-5058-6167', 'show_email': 'NO'}]}
Year: 2015
DOI: 10.7907/Z9DB7ZRG
<p>Soft hierarchical materials often present unique functional properties that are sensitive to the geometry and organization of their micro- and nano-structural features across different lengthscales. Carbon Nanotube (CNT) foams are hierarchical materials with fibrous morphology that are known for their remarkable physical, chemical and electrical properties. Their complex microstructure has led them to exhibit intriguing mechanical responses at different length-scales and in different loading regimes. Even though these materials have been studied for mechanical behavior over the past few years, their response at high-rate finite deformations and the influence of their microstructure on bulk mechanical behavior and energy dissipative characteristics remain elusive.</p>
<p>In this dissertation, we study the response of aligned CNT foams at the high strain-rate regime of 10<sup>2</sup> - 10<sup>4</sup> s<sup>-1</sup>. We investigate their bulk dynamic response and the fundamental deformation mechanisms at different lengthscales, and correlate them to the microstructural characteristics of the foams. We develop an experimental platform, with which to study the mechanics of CNT foams in high-rate deformations, that includes direct measurements of the strain and transmitted forces, and allows for a full field visualization of the sample’s deformation through high-speed microscopy.</p>
<p>We synthesize various CNT foams (e.g., vertically aligned CNT (VACNT) foams, helical CNT foams, micro-architectured VACNT foams and VACNT foams with microscale heterogeneities) and show that the bulk functional properties of these materials are highly tunable either by tailoring their microstructure during synthesis or by designing micro-architectures that exploit the principles of structural mechanics. We also develop numerical models to describe the bulk dynamic response using multiscale mass-spring models and identify the mechanical properties at length scales that are smaller than the sample height.</p>
<p>The ability to control the geometry of microstructural features, and their local interactions, allows the creation of novel hierarchical materials with desired functional properties. The fundamental understanding provided by this work on the key structure-function relations that govern the bulk response of CNT foams can be extended to other fibrous, soft and hierarchical materials. The findings can be used to design materials with tailored properties for different engineering applications, like vibration damping, impact mitigation and packaging.</p>https://thesis.library.caltech.edu/id/eprint/8699Micromechanical Damage and Fracture in Elastomeric Polymers
https://resolver.caltech.edu/CaltechTHESIS:12202014-233824767
Authors: {'items': [{'email': 'stefanie.heyden@ruhr-uni-bochum.de', 'id': 'Heyden-Stefanie', 'name': {'family': 'Heyden', 'given': 'Stefanie'}, 'show_email': 'NO'}]}
Year: 2015
DOI: 10.7907/Z9HX19NS
<p>This thesis aims at a simple one-parameter macroscopic model of distributed damage and fracture of polymers that is amenable to a straightforward and efficient numerical implementation. The failure model is motivated by post-mortem fractographic observations of void nucleation, growth and coalescence in polyurea stretched to failure, and accounts for the specific fracture energy per unit area attendant to rupture of the material.</p>
<p>Furthermore, it is shown that the macroscopic model can be rigorously derived, in the sense of optimal scaling, from a micromechanical model of chain elasticity and failure regularized by means of fractional strain-gradient elasticity. Optimal scaling laws that supply a link between the single parameter of the macroscopic model, namely the critical energy-release rate of the material, and micromechanical parameters pertaining to the elasticity and strength of the polymer chains, and to the strain-gradient elasticity regularization, are derived. Based on optimal scaling laws, it is shown how the critical energy-release rate of specific materials can be determined from test data. In addition, the scope and fidelity of the model is demonstrated by means of an example of application, namely Taylor-impact experiments of polyurea rods. Hereby, optimal transportation meshfree approximation schemes using maximum-entropy interpolation functions are employed.</p>
<p>Finally, a different crazing model using full derivatives of the deformation gradient and a core cut-off is presented, along with a numerical non-local regularization model. The numerical model takes into account higher-order deformation gradients in a finite element framework. It is shown how the introduction of non-locality into the model stabilizes the effect of strain localization to small volumes in materials undergoing softening. From an investigation of craze formation in the limit of large deformations, convergence studies verifying scaling properties of both local- and non-local energy contributions are presented.</p>https://thesis.library.caltech.edu/id/eprint/8749A Variational Framework for Spectral Discretization of the Density Matrix in Kohn-Sham Density Functional Theory
https://resolver.caltech.edu/CaltechTHESIS:04132015-160812309
Authors: {'items': [{'email': 'xin.wang.cindy@gmail.com', 'id': 'Wang-Xin-C', 'name': {'family': 'Wang', 'given': 'Xin C.'}, 'orcid': '0000-0003-3854-4831', 'show_email': 'NO'}]}
Year: 2015
DOI: 10.7907/Z99021QK
Kohn-Sham density functional theory (KSDFT) is currently the main work-horse of quantum
mechanical calculations in physics, chemistry, and materials science. From a mechanical
engineering perspective, we are interested in studying the role of defects in the
mechanical properties in materials. In real materials, defects are typically found at
very small concentrations e.g., vacancies occur at parts per million,
dislocation density in metals ranges from $10^{10} m^{-2}$ to $10^{15} m^{-2}$,
and grain sizes vary from nanometers to micrometers in polycrystalline materials, etc. In order to model materials at
realistic defect concentrations using DFT, we would need
to work with system sizes beyond millions of atoms. Due to the cubic-scaling
computational cost with respect to the number of atoms in conventional DFT implementations, such system sizes are
unreachable. Since the early 1990s, there has been a huge interest in developing DFT
implementations that have linear-scaling computational cost. A promising
approach to achieving linear-scaling cost is to approximate the density matrix in
KSDFT. The focus of this
thesis is to provide a firm mathematical framework to study the convergence of
these approximations. We reformulate the Kohn-Sham density
functional theory as a nested variational problem in the density matrix,
the electrostatic potential, and a field dual to the electron density. The
corresponding functional is linear in the density matrix and thus amenable to
spectral representation. Based on this reformulation, we introduce a new
approximation scheme, called spectral binning, which does not require smoothing
of the occupancy function and thus applies at arbitrarily low temperatures. We
proof convergence of the approximate solutions with respect to spectral binning
and with respect to an additional spatial discretization of the domain. For a
standard one-dimensional benchmark problem, we present numerical experiments for
which spectral binning exhibits excellent convergence characteristics and
outperforms other linear-scaling methods. https://thesis.library.caltech.edu/id/eprint/8819Collective Behavior of Asperities as a Model for Friction and Adhesion
https://resolver.caltech.edu/CaltechTHESIS:05172015-152006825
Authors: {'items': [{'email': 'sriphy@gmail.com', 'id': 'Hulikal-Sampath-Kumaran-Srivatsan', 'name': {'family': 'Hulikal Sampath Kumaran', 'given': 'Srivatsan'}, 'show_email': 'NO'}]}
Year: 2015
DOI: 10.7907/Z94M92HM
<p>Understanding friction and adhesion in static and sliding contact of surfaces is important in numerous physical phenomena and technological applications. Most surfaces are rough at the microscale, and thus the real area of contact is only a fraction of the nominal area. The macroscopic frictional and adhesive response is determined by the collective behavior of the population of evolving and interacting microscopic contacts. This collective behavior can be very different from the behavior of individual contacts. It is thus important to understand how the macroscopic response emerges from the microscopic one.</p>
<p>In this thesis, we develop a theoretical and computational framework to study the collective behavior. Our philosophy is to assume a simple behavior of a single asperity and study the collective response of an ensemble. Our work bridges the existing well-developed studies of single asperities with phenomenological laws that describe macroscopic rate-and-state behavior of frictional interfaces. We find that many aspects of the macroscopic behavior are robust with respect to the microscopic response. This explains why qualitatively similar frictional features are seen for a diverse range of materials.</p>
<p>We first show that the collective response of an ensemble of one-dimensional independent viscoelastic elements interacting through a mean field reproduces many qualitative features of static and sliding friction evolution. The resulting macroscopic behavior is different from the microscopic one: for example, even if each contact is velocity-strengthening, the macroscopic behavior can be velocity-weakening. The framework is then extended to incorporate three-dimensional rough surfaces, long- range elastic interactions between contacts, and time-dependent material behaviors such as viscoelasticity and viscoplasticity. Interestingly, the mean field behavior dominates and the elastic interactions, though important from a quantitative perspective, do not change the qualitative macroscopic response. Finally, we examine the effect of adhesion on the frictional response as well as develop a force threshold model for adhesion and mode I interfacial cracks.</p>https://thesis.library.caltech.edu/id/eprint/8861A Model for Energy and Morphology of Crystalline Grain Boundaries with Arbitrary Geometric Character
https://resolver.caltech.edu/CaltechTHESIS:07082015-130125061
Authors: {'items': [{'email': 'brunnels@uccs.edu', 'id': 'Runnels-Brandon-Scott', 'name': {'family': 'Runnels', 'given': 'Brandon Scott'}, 'orcid': '0000-0003-3043-5227', 'show_email': 'YES'}]}
Year: 2016
DOI: 10.7907/Z9KS6PHP
<p>It has been well-established that interfaces in crystalline materials are key players in the mechanics of a variety of mesoscopic processes such as solidification, recrystallization, grain boundary migration, and severe plastic deformation. In particular, interfaces with complex morphologies have been observed to play a crucial role in many micromechanical phenomena such as grain boundary migration, stability, and twinning. Interfaces are a unique type of material defect in that they demonstrate a breadth of behavior and characteristics eluding simplified descriptions. Indeed, modeling the complex and diverse behavior of interfaces is still an active area of research, and to the author's knowledge there are as yet no predictive models for the energy and morphology of interfaces with arbitrary character. The aim of this thesis is to develop a novel model for interface energy and morphology that i) provides accurate results (especially regarding "energy cusp" locations) for interfaces with arbitrary character, ii) depends on a small set of material parameters, and iii) is fast enough to incorporate into large scale simulations.</p>
<p>In the first half of the work, a model for planar, immiscible grain boundary is formulated. By building on the assumption that anisotropic grain boundary energetics are dominated by geometry and crystallography, a construction on lattice density functions (referred to as "covariance") is introduced that provides a geometric measure of the order of an interface. Covariance forms the basis for a fully general model of the energy of a planar interface, and it is demonstrated by comparison with a wide selection of molecular dynamics energy data for FCC and BCC tilt and twist boundaries that the model accurately reproduces the energy landscape using only three material parameters. It is observed that the planar constraint on the model is, in some cases, over-restrictive; this motivates an extension of the model.</p>
<p>In the second half of the work, the theory of faceting in interfaces is developed and applied to the planar interface model for grain boundaries. Building on previous work in mathematics and materials science, an algorithm is formulated that returns the minimal possible energy attainable by relaxation and the corresponding relaxed morphology for a given planar energy model. It is shown that the relaxation significantly improves the energy results of the planar covariance model for FCC and BCC tilt and twist boundaries. The ability of the model to accurately predict faceting patterns is demonstrated by comparison to molecular dynamics energy data and experimental morphological observation for asymmetric tilt grain boundaries. It is also demonstrated that by varying the temperature in the planar covariance model, it is possible to reproduce a priori the experimentally observed effects of temperature on facet formation.</p>
<p>Finally, the range and scope of the covariance and relaxation models, having been demonstrated by means of extensive MD and experimental comparison, future applications and implementations of the model are explored.</p>https://thesis.library.caltech.edu/id/eprint/9053Earth-Abundant Zinc-IV-Nitride Semiconductors
https://resolver.caltech.edu/CaltechTHESIS:05252016-080726422
Authors: {'items': [{'email': 'naomi.coronel@gmail.com', 'id': 'Coronel-Naomi-Cristina', 'name': {'family': 'Coronel', 'given': 'Naomi Cristina'}, 'show_email': 'NO'}]}
Year: 2016
DOI: 10.7907/Z9CF9N28
This investigation is motivated by the need for new visible frequency direct bandgap semiconductor materials that are abundant and low-cost to meet the increasing demand for optoelectronic devices in applications such as solid state lighting and solar energy conversion. Proposed here is the utilization of zinc-IV-nitride materials, where group IV elements include silicon, germanium, and tin, as earth-abundant alternatives to the more common III-nitrides in optoelectronic devices. These compound semiconductors were synthesized under optimized conditions using reactive radio frequency magnetron sputter deposition. Single phase ZnSnN<sub>2</sub>, having limited experimental accounts in literature, is validated by identification of the wurtzite-derived crystalline structure predicted by theory through X-ray and electron diffraction studies. With the addition of germanium, bandgap tunability of ZnSn<sub>x</sub>Ge<sub>1-x</sub>N<sub>2</sub> alloys is demonstrated without observation of phase separation, giving these materials a distinct advantage over In<sub>x</sub>Ga<sub>1-x</sub>N alloys. The accessible bandgaps range from 1.8 to 3.1 eV, which spans the majority of the visible spectrum. Electron densities, measured using the Hall effect, were found to be as high as 10<sup>22</sup> cm<sup>−3</sup> and indicate that the compounds are unintentionally degenerately doped. Given these high carrier concentrations, a Burstein-Moss shift is likely affecting the optical bandgap measurements. The discoveries made in this thesis suggest that with some improvements in material quality, zinc-IV-nitrides have the potential to enable cost-effective and scalable optoelectronic devices.https://thesis.library.caltech.edu/id/eprint/9746Shock Wave Propagation in Composites and Electro-Thermomechanical Coupling of Ferroelectric Materials
https://resolver.caltech.edu/CaltechTHESIS:05272016-104209268
Authors: {'items': [{'email': 'vinamraagrawal786@gmail.com', 'id': 'Agrawal-Vinamra', 'name': {'family': 'Agrawal', 'given': 'Vinamra'}, 'orcid': '0000-0002-1698-1371', 'show_email': 'YES'}]}
Year: 2016
DOI: 10.7907/Z98G8HN8
<p>How is material behavior at the macro scale influenced by its properties and structure at the micro and meso-scales? How do heterogeneities influence the properties and the response of a material? How does nonlinear coupling of electro-thermo-mechanical properties influence the behavior of a ferroelectric material? How can design at the micro-scale be exploited to obtain selective response? These questions have been topics of significant interest in the materials and mechanics community. Recently, new materials like multifunctional composites and metamaterials have been developed, targeted at selective applications. These materials find applications in areas like energy harvesting, damage mitigation, biomedical devices, and various aerospace applications. The current thesis explores these questions with two major thrusts: (i) internal reflects of shocks in composite media and (ii) shocks in ferroelectric media.</p>
<p>Under the application of high-pressure, high strain rate loading, such as during high velocity impact, shock waves are generated in the material. They can cause the material to achieve very high stress states, and if transmitted without mitigation, can lead to failure of key components. An important question here is 'Can we design materials which can successfully mitigate damage due to shocks?' In a heterogeneous material, like a layered composite, the traveling waves undergo scattering due to internal reflections. In order to understand internal reflections, an idealized problem that focuses on nonlinear shocks and ignores less important elastic waves was formulated and studied in detail. The problem is studied by classifying all possible interactions in the material and then solving corresponding Riemann problems. Using dynamic programming tools, a new algorithm is designed that uses these solutions to generate a complete picture of the impact process. Different laminate designs are explored to study optimal design, by varying individual layer properties and their arrangement. Phenomena like spallation and delamination are also investigated.</p>
<p>Upon high strain rate loading, ferroelectric materials like lead zirconate titanate (PZT) undergo ferroelectric to anti-ferroelectric phase transition leading to large pulsed current output. These materials have thus found applications as pulsed power generators. The problem of shock induced depolarization and the associated electro-thermo-mechanical coupling of ferroelectric materials is studied in this thesis using theoretical and numerical methods. A large deformation dynamic analysis of such materials is conducted to study phase boundary propagation in the medium. The presence of high electrical fields can lead to formation of charges in the material, such as surface charge on the phase boundary. Using conservation laws and the second law of thermodynamics, a set of governing equations are formulated that dictate the phase boundary propagation in isothermal and adiabatic environments. Due to the possibility of surface charges on the phase boundary, the curvature of the phase boundary starts to play a role in the driving force acting on the phase boundary. The equations of motion and driving force see the contribution of nonlinear electro-thermomechanical coupling in the material. Using the equations derived, a canonical problem of impact on a ferroelectric material is studied. A new finite-volume, front-tracking method is developed to solve these equations. Finally, results from numerical simulations are compared to the experimental results.</p>https://thesis.library.caltech.edu/id/eprint/9783Force Chains, Friction, and Flow: Behavior of Granular Media across Length Scales
https://resolver.caltech.edu/CaltechTHESIS:09212015-105224808
Authors: {'items': [{'email': 'rchurley@gmail.com', 'id': 'Hurley-Ryan-Colt', 'name': {'family': 'Hurley', 'given': 'Ryan Colt'}, 'show_email': 'YES'}]}
Year: 2016
DOI: 10.7907/Z91Z429J
<p>We study the behavior of granular materials at three length scales. At the smallest length scale, the grain-scale, we study inter-particle forces and "force chains". Inter-particle forces are the natural building blocks of constitutive laws for granular materials. Force chains are a key signature of the heterogeneity of granular systems. Despite their fundamental importance for calibrating grain-scale numerical models and elucidating constitutive laws, inter-particle forces have not been fully quantified in natural granular materials. We present a numerical force inference technique for determining inter-particle forces from experimental data and apply the technique to two-dimensional and three-dimensional systems under quasi-static and dynamic load. These experiments validate the technique and provide insight into the quasi-static and dynamic behavior of granular materials.</p>
<p>At a larger length scale, the mesoscale, we study the emergent frictional behavior of a collection of grains. Properties of granular materials at this intermediate scale are crucial inputs for macro-scale continuum models. We derive friction laws for granular materials at the mesoscale by applying averaging techniques to grain-scale quantities. These laws portray the nature of steady-state frictional strength as a competition between steady-state dilation and grain-scale dissipation rates. The laws also directly link the rate of dilation to the non-steady-state frictional strength. </p>
<p>At the macro-scale, we investigate continuum modeling techniques capable of simulating the distinct solid-like, liquid-like, and gas-like behaviors exhibited by granular materials in a single computational domain. We propose a Smoothed Particle Hydrodynamics (SPH) approach for granular materials with a viscoplastic constitutive law. The constitutive law uses a rate-dependent and dilation-dependent friction law. We provide a theoretical basis for a dilation-dependent friction law using similar analysis to that performed at the mesoscale. We provide several qualitative and quantitative validations of the technique and discuss ongoing work aiming to couple the granular flow with gas and fluid flows.</p>https://thesis.library.caltech.edu/id/eprint/9162The Deformations of Thin Nematic Elastomer Sheets
https://resolver.caltech.edu/CaltechTHESIS:06022017-081925673
Authors: {'items': [{'email': 'plucinsp@gmail.com', 'id': 'Plucinsky-Paul-P', 'name': {'family': 'Plucinsky', 'given': 'Paul P.'}, 'orcid': '0000-0003-2060-8657', 'show_email': 'YES'}]}
Year: 2017
DOI: 10.7907/Z9765CCT
<p>Thin structures exhibit a broad range of mechanical responses as the competition between stretching and bending in these structures can result in buckling and localized deformations like folding and tension wrinkling. Active materials also exhibit a broad range of mechanical responses as features that manifest themselves at the microscale in these materials result in mechanical couplings at the engineering scale (thermal/electrical/dissipative) and novel function (e.g., the shape memory effect and piezoelectricity in select metal alloys and the immense fracture toughness of hydrogels). Given this richness in behaviors, my research broadly aims to address the following questions: What happens when active materials are incorporated into thin structures? Do phenomena inherent to these materials compete with or enhance those inherent to thin structures? Does this interplay result in entirely new and unexpected phenomena? And can all this be exploited to design new functions in engineering systems?</p>
<p>In this thesis, we explore these questions in the context of a theoretical study of thin sheets of nematic liquid crystal elastomer. These materials are active rubbery solids made of cross-linked polymer chains that have liquid crystals either incorporated into the main chain or pendent from them. Their structure enables a coupling between the mechanical elasticity of the polymer network and the ordering of the liquid crystals, and this in turn results in fairly complex mechanical behavior including large spontaneous distortion due to temperature change, soft-elasticity and fine-scale microstructure.</p>
<p>We study thin sheets of nematic elastomer. First, we show that thin of sheets of a particular class of nematic elastomer can resist wrinkling when stretched. Second, we show that thin sheets of another class of nematic elastomer can be actuated into a multitude of complex shapes. In order to obtain these results, we systematically develop two dimensional theories for thin sheets starting from a well-accepted first principles theory for nematic elastomers. These characterize (i) the mechanical response due to instabilities such as structural wrinkling and fine-scale material microstructure, and (ii) thermal actuation of heterogeneously patterned sheets. For the latter, we show that the theory, which comes in the form of a two dimensional metric constraint, admits two broad classes of designable actuation in nonisometric origami and lifted surface. For the former, we show that taut and appreciably stressed sheets of nematic elastomer are capable of suppressing wrinkling by modifying the expected state of stress through the formation of microstructure.</p>https://thesis.library.caltech.edu/id/eprint/10250Optimal Design of Materials for Energy Conversion
https://resolver.caltech.edu/CaltechTHESIS:06132017-164608976
Authors: {'items': [{'email': 'lincoln.n.collins@gmail.com', 'id': 'Collins-Lincoln-Nash', 'name': {'family': 'Collins', 'given': 'Lincoln Nash'}, 'show_email': 'NO'}]}
Year: 2017
DOI: 10.7907/Z9X928B7
<p>The efficiency of fuel cells, batteries and thermochemical energy conversion devices depends on inherent material characteristics that govern the complex chemistry and transport of multiple species as well as the spatial arrangement of the various materials. Therefore, optimization of the spatial arrangement is a recurrent theme in energy conversion devices. Traditional methods of synthesis offer limited control of the microstructure and there has been much work in advanced imaging for these uncontrolled microstructures and optimizing gross features. However, the growing ability for directed synthesis allows us to ask the question of what microgeometries are optimal for particular applications. Through this work, we study problems motivated by metal oxides used in solar-driven thermochemical conversion devices designed to split water or carbon dioxide into fuels. We seek to understand the arrangement of the solid and porous regions to maximize the transport given sources and sinks for the gaseous oxygen and vacancies. Three related problems are investigated with the common theme of understanding the role of microstructure design.</p>
<p>We derive the transport equations for electrons and oxygen vacancies through ceria under an externally-applied electric potential in an oxygen environment using various balance laws and constitutive equations. From this, we obtain various thermodynamic potentials that take into consideration the thermal, chemical, and mechanical state of the material. Accordingly, we obtain a system of partial differential equations describing ambipolar diffusion. We present the applicability of strain-engineering as a way to design systems to improve the behavior of thermochemical conversion devices. We look at an idealized thin film of mixed conductor attached to an inert substrate with a thermal mismatch as a way to induce strain into the film. The resulting impact on equilibrium non-stoichiometry is analyzed using data describing non-stoichiometry in ceria as a function of oxygen pressure and temperature.</p>
<p>The optimal design of material microstructure for thermochemical conversion is addressed from two standpoints: the mathematical homogenization of associated transport models, and from topology optimization. We present the homogenization of coupled transport through porous media consisting of linearized Stokes flow, convective diffusion, and diffusion in the solid phase with interface reaction. Depending on the strength of the interface chemistry, different forms of effective behavior are described at the macroscale, and we gain insight into the impact cell-design and pore shape has on the behavior.</p>
<p>The topology optimization of a model energy-conversion reactor is then presented. We express the problem of optimal design of the material arrangement as a saddle point problem and obtain an effective functional which shows that regions with very fine phase mixtures of the material arise naturally. To explore this further, we introduce a phase-field formulation of the optimal design problem, and numerically study selected examples. We find that zig-zag interfaces develop to balance mass transport and interface exchange. </p> https://thesis.library.caltech.edu/id/eprint/10336Determining Strength of Materials Under Dynamic Loading Conditions Using Hydrodynamic Instabilities
https://resolver.caltech.edu/CaltechTHESIS:05182017-095600418
Authors: {'items': [{'email': 'zsternberger@gmail.com', 'id': 'Sternberger-Zachary-Martin-Murphy', 'name': {'family': 'Sternberger', 'given': 'Zachary Martin Murphy'}, 'orcid': '0000-0002-7612-673X', 'show_email': 'NO'}]}
Year: 2017
DOI: 10.7907/Z9N877T5
<p>Hydrodynamic instability experiments allow access to material properties at extreme conditions where the pressure exceeds 100 GPa and the strain rate exceeds 10<sup>6</sup> 1/s. Laser ablation dynamically loads a sample, causing a manufactured initial perturbation to grow due to hydrodynamic instability. The instability growth rate depends on the strength of the sample. Material strength can then be inferred from a measurement of the instability growth. Past experiments relied on in-flight diagnostics to measure the amplitude growth, which are not available at all facilities.</p>
<p>Recovery instability experiments, where the initial and final amplitude of the instability are measured before and after the sample is dynamically loaded, obviate the need for in-flight diagnostics. Recovery targets containing copper and tantalum samples coined with 2D (hill and valley) and 3D (eggcrate) initial perturbations were dynamically loaded using the Janus laser at the Jupiter Laser Facility, Lawrence Livermore National Laboratory. The energy of the laser pulse was varied to cover a range of conditions in the dynamically compressed sample with pressures in the range 10 GPa to 150 GPa and strain rates in the range 10<sup>5</sup> 1/s to 10<sup>8</sup> 1/s.</p>
<p>The coupling of laser energy into a loading wave was studied with a combination of laser-matter interaction simulations (Hyades) and velocity interferometry data (VISAR). Laser ablation of the recovery targets generated a blast wave, loading the coined initial perturbations with a shock wave followed by a release wave. Different ablator materials and variations in the amount of laser energy deposited in the ablator lead to variations in the loading wave and consequently variations in instability growth.</p>
<p>The growth of the initial perturbation amplitude from initial to final conditions was studied with hydrocode simulations (CTH). During dynamic loading of the sample, the shock wave caused amplitude growth due to hydrodynamic instability. The release wave accelerated the perturbed interface and slowed amplitude growth, in some cases reversing growth.</p>
<p>The sensitivity of the instability growth to coarse changes in the strength model was demonstrated. However, uncertainty in modeling the laser ablation loading prevented a definitive comparison between simulation and experiment.</p>https://thesis.library.caltech.edu/id/eprint/10182Effective Toughness of Heterogeneous Materials
https://resolver.caltech.edu/CaltechTHESIS:06042017-165228124
Authors: {'items': [{'email': 'renhsueh@gmail.com', 'id': 'Hsueh-Chun-Jen', 'name': {'family': 'Hsueh', 'given': 'Chun-Jen'}, 'orcid': '0000-0001-6522-4505', 'show_email': 'YES'}]}
Year: 2017
DOI: 10.7907/Z9HH6H49
<p>Composite materials are widely used because of their extraordinary performance. It is understood that the heterogeneity / microstructure can dramatically affect the effective behavior of materials. Although there is a well-developed theory for this relation in elasticity, there is no similar theory in fracture mechanics. Therefore, we use theoretical, numerical, and experimental approaches to study the relationship between heterogeneity / microstructure and the effective fracture behavior in this thesis.</p>
<p>We use the surfing boundary condition, a boundary condition that ensures the macroscopic steady crack growth, and then define the effective toughness of heterogeneous materials as the peak energy release rate during crack propagation. We also use the homogenization theory to prove that the effective J-integral in heterogeneous materials is well defined, and that it can be calculated by the homogenized stress and strain field.</p>
<p>In order to study the relationship between heterogeneities and effective toughness, we first use the semi-analytical method under the assumption of small elastic contrast to study selected examples. For strong heterogeneities, we use the phase field fracture method to study the crack propagation numerically. We then optimize the microstructure with respect to effective stiffness and effective toughness in a certain class of microgeometries. We show that it is possible to significantly enhance toughness without significant loss of stiffness. We also design materials with asymmetric toughness.</p>
<p>We develop a new experimental configuration that can measure the effective toughness of specimens with arbitrary heterogeneities. We confirm through preliminary tests that the heterogeneities can enhance the effective toughness.</p>
<p>Besides study the effective toughness of heterogeneous materials, we also study a model problem of peeling a thin sheet from a heterogeneous substrate. We develop a methodology to systematically optimize microstructure.</p>https://thesis.library.caltech.edu/id/eprint/10266The Fully Nonlocal, Finite-Temperature, Adaptive 3D Quasicontinuum Method for Bridging Across Scales
https://resolver.caltech.edu/CaltechTHESIS:04222018-122438253
Authors: {'items': [{'email': 'ishan.tembhekar@gmail.com', 'id': 'Tembhekar-Ishan', 'name': {'family': 'Tembhekar', 'given': 'Ishan'}, 'orcid': '0000-0001-5123-1958', 'show_email': 'YES'}]}
Year: 2018
DOI: 10.7907/RF27-NA04
<p>Computational modeling of metallic materials across various length and time scales has been on the rise since the advent of efficient, fast computing machines. From atomistic methods like molecular statics and dynamics at the nanoscale to continuum mechanics modeled by finite element methods at the macroscale, various techniques have been established that describe and predict the mechanics of materials. Many recent technologies, however, fall into a gap between length scales (referred to as mesoscales), with microstructural features on the order of nanometers (thereby requiring full atomistic resolution) but large representative volumes on the order of micrometers (beyond the scope of molecular dynamics). There is an urgent need to predict material behavior using scale-bridging techniques that build up from the atomic level and reach larger length and time scales. To this end, there is extensive ongoing research in building hierarchical and concurrent scale-bridging techniques to master the gap between atomistics and the continuum, but robust, adaptive schemes with finite-temperature modeling at realistic length and time scales are still missing.</p>
<p>In this thesis, we use the quasicontinuum (QC) method, a concurrent scale-bridging technique that extends atomistic accuracy to significantly larger length scales by reducing the full atomic ensemble to a small set of representative atoms, and using interpolation to recover the motion of all lattice sites where full atomistic resolution is not necessary. We develop automatic model adaptivity by adding mesh refinement and adaptive neighborhood updates to the new fully nonlocal energy-based 3D QC framework, which allows for automatic resolution to full atomistics around regions of interest such as nanovoids and moving lattice defects. By comparison to molecular dynamics (MD), we show that these additions allow for a successful and computationally efficient coarse graining of atomistic ensembles while maintaining the same atomistic accuracy.</p>
<p>We further extend the fully nonlocal QC formulation to finite temperature (termed hotQC) using the principle of maximum entropy in statistical mechanics and averaging the thermal motion of atoms to obtain a temperature-dependent free energy using numerical quadrature. This hotQC formulation implements recently developed optimal summation rules and successfully captures temperature-dependent elastic constants and thermal expansion. We report for the first time the influence of temperature on force artifacts and conclude that our novel finite-temperature adaptive nonlocal QC shows minimal force artifacts and outperforms existing formulations. We also highlight the influence of quadrature in phase space on simulation outcomes.</p>
<p>We study 3D grain boundaries in the nonlocal hotQC framework (previously limited to single-crystals) by modeling coarse-grained symmetric-tilt grain boundaries in coincidence site lattice (CSL) based bicrystals. We predict relaxed energy states of various Σ-boundaries with reasonable accuracy by comparing grain boundary energies to MD simulations and outline a framework to model polycrystalline materials that surpasses both spatial and temporal limitations of traditional MD.</p>https://thesis.library.caltech.edu/id/eprint/10826The Avatar Paradigm in Granular Materials
https://resolver.caltech.edu/CaltechTHESIS:06072018-230955387
Authors: {'items': [{'email': 'rekawamo@gmail.com', 'id': 'Kawamoto-Reid-Yoshio', 'name': {'family': 'Kawamoto', 'given': 'Reid Yoshio'}, 'orcid': '0000-0002-4936-5321', 'show_email': 'NO'}]}
Year: 2018
DOI: 10.7907/4fr8-bn91
Granular materials are ubiquitous in both everyday life and various engineering and industrial applications, ranging from breakfast cereal to sand to rice to medical pills. However, despite the familiarity of granular materials, their behavior is complex and efforts to characterize them are currently broad research areas in physics and engineering. Research of granular materials, as is the case with the research of other engineering materials such as rocks and metals, is beset with two gaps: the gap between reconciling macroscopic behavior with microscale (particle-scale, in the case of granular materials) behavior, and the gap between reconciling experimental and computational results. In this dissertation, we bridge these gaps through the "avatar paradigm." The avatar paradigm is a two-step process that numerically characterizes (from experimental images) and simulates the shapes and behavior of individual particles, which we call avatars. First, we validate that our avatars are indeed capable of faithfully capturing particle kinematics and interparticle contact, then apply the characterization process, level set imaging (LS-imaging), to two experimental specimens to compute particle kinematics and contact statistics. We then detail a computational method, the level set discrete element method (LS-DEM), that is able to simulate the behavior of avatars, and apply it (and LS-imaging) to two other experimental specimens, calibrating the model to one specimen and using the results to predict the behavior of the other, thus providing some reconciliation between experimental and computational results. Finally, we use the avatar process to characterize and simulate yet another experimental specimen, this time analyzing the results at length scales ranging from particle behavior to local behavior to macroscopic behavior, further validating the ability of the avatar paradigm to bridge experiments and computations and showing its power to reconcile different length scales.https://thesis.library.caltech.edu/id/eprint/11042Proliferation of Twinning in Metals: Application to Magnesium Alloys
https://resolver.caltech.edu/CaltechTHESIS:08042017-190200194
Authors: {'items': [{'email': 'dingyi_sun@brown.edu', 'id': 'Sun-Dingyi', 'name': {'family': 'Sun', 'given': 'Dingyi'}, 'orcid': '0000-0003-2109-7123', 'show_email': 'YES'}]}
Year: 2018
DOI: 10.7907/Z93B5XB4
<p>In the search for new alloys with a great strength-to-weight ratio, magnesium has emerged at the forefront. With a strength rivaling that of steel and aluminum alloys --- materials which are deployed widely in real world applications today --- but only a fraction of the density, magnesium holds great promise in a variety of next-generation applications. Unfortunately, the widespread adoption of magnesium is hindered by the fact that it fails in a brittle fashion, which is undesirable when it comes to plastic deformation mechanisms. Consequently, one must design magnesium alloys to navigate around this shortcoming and fail in a more ductile fashion.</p>
<p>However, such designs are not possible without a thorough understanding of the underlying mechanisms of deformation in magnesium, which is somewhat contested at the moment. In addition to slip, which is one of the dominant mechanisms in metallic alloys, a mechanism known as twinning is also present, especially in hexagonal close-packed (HCP) materials such as magnesium. Twinning involves the reorientation of the material lattice about a planar discontinuity and has been shown as one of the preferred mechanisms by which magnesium accommodates out-of-plane deformation. Unfortunately, twinning is not particularly well-understood in magnesium, and needs to be addressed before progress can be made in materials design. In particular, though two specific modes of twinning have been acknowledged, various works in the literature have identified a host of additional modes, many of which have been cast aside as "anomalous" observations.</p>
<p>To this end, we introduce a new framework for predicting the modes by which a material can twin, for any given material. Focusing on magnesium, we begin our investigation by introducing a kinematic framework that predicts novel twin configurations, cataloging these twins modes by their planar normal and twinning shear. We then subject the predicted twin modes to a series of atomistic simulations, primarily in molecular statics but with supplementary calculations using density functional theory, giving us insight on both the energy of the twin interface and barriers to formation. We then perform a stress analysis and identify the twin modes which are most likely to be activated, thus finding the ones most likely to affect the yield surface of magnesium.</p>
<p>Over the course of our investigation, we show that many different modes actually participate on the yield surface of magnesium; the two classical modes which are accepted by the community are confirmed, but many additional modes --- some of which are close to modes which have been previously regarded as anomalies --- are also observed. We also perform some extensional work, showing the flexibility of our framework in predicting twins in other materials and in other environments and highlighting the complicated nature of twinning, especially in HCP materials.</p> https://thesis.library.caltech.edu/id/eprint/10365Laboratory Studies of Granular Materials Under Shear: From Avalanches to Force Chains
https://resolver.caltech.edu/CaltechTHESIS:05142018-133453405
Authors: {'items': [{'email': 'elmarteau@gmail.com', 'id': 'Marteau-Eloïse-Sophie-Hélène', 'name': {'family': 'Marteau', 'given': 'Eloïse Sophie Hélène'}, 'orcid': '0000-0001-7696-6264', 'show_email': 'NO'}]}
Year: 2018
DOI: 10.7907/FKM0-P754
<p>Granular materials reveal their complexity and some of their unique features when subjected to shear deformation. They can dilate, behave like a solid or a fluid, and are known to carry external forces preferentially as force chains. In this dissertation, we employ laboratory experiments to study the complex behavior of granular materials under shear. We introduce a multiscale approach in which the underlying grain-scale mechanics are experimentally measured and homogenized to obtain enriched macroscopic quantities. First, we investigate granular avalanches spontaneously generated by a rotating drum. Measurements of grain kinematics are directly incorporated into a rate-dependent plasticity model that explains and reproduces the life cycle of laboratory avalanches. The results presented here feature dilatancy as the key material parameter governing the triggering of an avalanche. Second, we report a set of experiments performed on a custom-built mechanical device that allows a specimen composed of a two-dimensional analogue granular assembly to be subjected to quasi-static shear conditions. A numerical force inference technique, the Granular Element Method (GEM), provides direct observation and quantitative characterization of force chain structures in assemblies made of realistic grains. Equipped with a complete description of the grain-scale mechanics, we show that shear deformation creates geometrical (fabric) and mechanical (force) anisotropy. Finally, the influence of grain shape on grain-scale processes is studied. We find that grain interlocking is a prominent deformation mechanism for non-circular grains that ultimately promotes a significant increase in macroscopic shear strength. By seamlessly connecting grain-scale information to continuum scale experiments, this dissertation sheds light on the multiscale mechanical behavior of granular assemblies under shear.</p>https://thesis.library.caltech.edu/id/eprint/10879On the Kinetics of Materials of Geophysical Interest
https://resolver.caltech.edu/CaltechTHESIS:08282017-105838669
Authors: {'items': [{'email': 'matthew.g.newman@gmail.com', 'id': 'Newman-Matthew-Gregory', 'name': {'family': 'Newman', 'given': 'Matthew Gregory'}, 'orcid': '0000-0003-2752-0121', 'show_email': 'YES'}]}
Year: 2018
DOI: 10.7907/Z9319T35
Knowledge of the equation of state and phase diagram of magnesium silicates and light iron alloys is important for understanding the thermal evolution and interior structure of terrestrial planets. Dynamic compression techniques are the primary viable methods to create the temperature and pressure conditions that are relevant to Earth and super-Earth (1-10 Earth mass) sized planets. However, due to the kinetic constraints imposed by the timescale of dynamic compression experiments, the nature of the state within the dynamically compressed sample (whether equilibrium or metastable) is uncertain. Here, we present the results of a series of dynamic compression experiments performed on both laser driven compression and plate impact facilities to study the nanosecond to microsecond response of forsterite and iron silicide. In situ x-ray diffraction measurements are used to probe the crystal structure of solid phases and test for the presence of melt, from which we investigate the decomposition of forsterite and iron silicide into compositionally distinct phases at high pressure. For forsterite, we do not observe chemical segregation in the solid phase, however the presence of melt speeds up the kinetics and allows chemical segregation to occur on nanosecond timescales. For iron silicide, our results show a textured solid phase upon shock compression to pressures ranging from 166(14) to 282(24) GPa consistent with cubic and hcp structures in coexistence. Above 313(29) GPa, the intense and textured solid diffraction peaks give way to a diffuse scattering feature and loss of texture, consistent with melting along the Hugoniot.https://thesis.library.caltech.edu/id/eprint/10393Observations of Failure Phenomena in Periodic Media
https://resolver.caltech.edu/CaltechTHESIS:05282018-024934056
Authors: {'items': [{'email': 'ltavellar@gmail.com', 'id': 'Avellar-Louisa-Taylor', 'name': {'family': 'Avellar', 'given': 'Louisa Taylor'}, 'orcid': '0000-0003-1299-5343', 'show_email': 'NO'}]}
Year: 2018
DOI: 10.7907/8N81-MV74
<p>New manufacturing techniques, such as 3D printing, allow for greater control over material properties and can be used to create custom heterogeneous materials. Heterogeneities can be leveraged to increase fracture toughness by redistributing the stresses, such as due to an elastic heterogeneity, or by impeding crack propagation, such as the renucleation at a material interface or edge of a void. The goal of this research is to study the mechanisms by which heterogeneities work to make composite materials more resistant to fracture than either of the individual base materials.</p>
<p>The influence of heterogeneities on the deformation and fracture of 3D printed fracture specimens is investigated. Brick-like heterogeneities are studied in compact tension and plate specimens with soft, stiff, and void heterogeneities. Horizontally layered heterogeneities are studied in compact tension specimens. The specimens are manufactured using a printer capable of printing multiple materials. The specimens are loaded until failure, and full-field displacement and strain data are collected using digital image correlation. The evolution of resistance to fracture is quantified by the energy release rate and fracture toughness values calculated using load, load-point displacement measurements, and crack extension data determined from images of the specimen. Both in soft specimens with stiff heterogeneities and in stiff specimens with soft heterogeneities, stresses are observed to be higher in the stiffer material. Fracture toughness is observed to increase in the presence of stiff inclusions and voids, although in the case of voids this is due to the crack terminating at the edge of the void and renucleating at the other edge.</p>
<p>The effects of interfaces on crack propagation in periodic media are experimentally studied. Comparative experiments on two proposed heterogeneity architectures aim to separate the effects of elastic deformation caused by heterogeneous inclusions in a composite from the effects of passing through an interface during crack propagation. The first, 'stripe' specimens, alternate equal width stripes perpendicular to the plane of the crack. The second, 'cross' specimens, have the same stripe pattern but with a narrow strip of one of the constituent materials in the plane of crack propagation. The 'cross' is wide enough to contain the crack to an area without material interfaces but thin enough that its overall effect on elastic deformation is minimal. Specimens are manufactured from two polymers using polyjet 3D printing. Energy release rate for fracture is calculated from load and displacement measurements. Digital image correlation is used to study strain and stress fields during crack propagation. While the stress fields during crack propagation appear similar, the fracture toughness in the 'stripe' specimens was found to be higher than that of the 'cross' specimens, indicating that fracture toughness is enhanced by renucleation at the interfaces. Additionally, the amount of enhancement was observed to depend on the width of the heterogeneous layers.</p>
<p>The interaction between the cohesive zone and elastic stiffness heterogeneity in the peeling of an adhesive tape from a rigid substrate is examined experimentally and with finite element simulations. It is understood that elastic stiffness heterogeneities can greatly enhance the adhesion of a tape without changing the properties of the interface. However, in peeling experiments performed on pressure sensitive adhesive tapes with both an elastic stiffness heterogeneity and a substantial cohesive zone, muted adhesion enhancement was observed. It is proposed that the cohesive zone acts to smooth out the effect of the discontinuity at the edge of the elastic stiffness heterogeneities, suppressing their effect on peel force enhancement. The results of numerical simulations show that the peel force enhancement depends on the strength of the adhesive and the size of the cohesive zone.</p>https://thesis.library.caltech.edu/id/eprint/10952Polycrystalline Perovskite Ferroelectrics: Microstructural Origins of the Macroscale Electromechanical Response
https://resolver.caltech.edu/CaltechTHESIS:06082019-133053987
Authors: {'items': [{'email': 'weilin.jade.tan@gmail.com', 'id': 'Tan-Wei-Lin', 'name': {'family': 'Tan', 'given': 'Wei Lin'}, 'orcid': '0000-0001-6855-8340', 'show_email': 'YES'}]}
Year: 2019
DOI: 10.7907/J2W5-XA95
<p>Ferroelectrics are a class of electromechanically coupled materials which possess an electric dipole polarization that can be permanently reoriented by applied electric and mechanical stress fields. Their reorientable polarization results in complex, nano- to micrometer scale domain structures whose evolution under electric and mechanical stress fields alters the material's overall time-dependent electrical and viscoelastic properties. To understand domain structure evolution, in-situ microscopy of domain switching processes in ferroelectric thin films, single crystals and nanoparticles have been well-studied in the past. However, domain evolution in bulk polycrystals is less well understood as their local stress and electric field environment differs from thin specimens.</p>
<p>This work seeks to understand ferroelectric domain evolution in bulk ferroelectric perovskite polycrystals using a combination of a recently-developed electromechanical characterization technique, Broadband Electromechanical Spectroscopy (BES), and theoretical-computational predictions. A constitutive material model for polycrystalline ferroelectrics is first developed and applied to simulate barium titanate single crystals and polycrystals. Simulated polarization, strain and energy dissipation hysteresis curves show good qualitative agreement to experimental data and demonstrate that macroscale properties can be efficiently predicted from microscale physics to some extent.</p>
<p>The microstructural origins of fatigue behavior in bulk polycrystalline lead zirconate titanate (PZT) are investigated using a combination of macroscale electrical and viscoelastic property characterization via BES, and scanning electron microscopy (SEM) imaging of microstructure. The evolution of electrical and viscoelastic properties during bipolar electrical fatigue show differences in the effects of electrical vs. mechanical fatigue processes, and the latter is verified through SEM imaging and measurement of microcracks.</p>
<p>Finally, the same electromechanical BES characterizations are performed on specimens of bulk polycrystalline barium titanate (BT). Results reveal stark qualitative differences in electrical and viscoelastic responses from PZT despite both materials being perovskite ferroelectrics. A growth vs. nucleation hypothesis is proposed to explain the observed results, guided by preliminary imaging of domain microstructure.</p>
<p>In summary, the BES is a powerful tool to elucidate domain switching processes within bulk ferroelectric specimens, while a computational method which bridges the micro- and macroscale further adds to the diagnostic toolbox of understanding bulk ferroelectric domain switching mechanisms. This opens the pathway to designing future applications which make use of the unique electrical and viscoelastic properties of ferroelectric switching.</p>https://thesis.library.caltech.edu/id/eprint/11727Predicting Microstructural Pattern Formation Using Stabilized Spectral Homogenization
https://resolver.caltech.edu/CaltechTHESIS:03272019-170619076
Authors: {'items': [{'email': 'vidyasagar.ananthan@gmail.com', 'id': 'Vidyasagar-A', 'name': {'family': 'Vidyasagar', 'given': 'A.'}, 'orcid': '0000-0003-0262-5429', 'show_email': 'YES'}]}
Year: 2019
DOI: 10.7907/F1VN-1X80
<p>Instability-induced patterns are ubiquitous in nature, from phase transformations and ferroelectric switching to spinodal decomposition and cellular organization. While the mathematical basis for pattern formation has been well-established, autonomous numerical prediction of complex pattern formation has remained an open challenge. This work aims to simulate realistic pattern evolution in material systems exhibiting non-(quasi)convex energy landscapes. These simulations are performed using fast Fourier spectral techniques, developed for high-resolution numerical homogenization. In a departure from previous efforts, compositions of standard FFT-based spectral techniques with finite-difference schemes are used to overcome ringing artifacts while adding grid-dependent implicit regularization.</p>
<p>The resulting spectral homogenization strategies are first validated using benchmark energy minimization examples involving non-convex energy landscapes. The first investigation involves the St. Venant-Kirchhoff model, and is followed by a novel phase transformation model and finally a finite-strain single-slip crystal plasticity model. In all these examples, numerical approximations of energy envelopes, computed through homogenization, are compared to laminate constructions and, where available, analytical quasiconvex hulls.</p>
<p>Subsequently, as an extension of single-slip plasticity, a finite-strain viscoplastic formulation for hexagonal-closed-packed magnesium is presented. Microscale intragranular inelastic behavior is captured through high-fidelity simulations, providing insight into the micromechanical deformation and failure mechanisms in magnesium. Studies of numerical homogenization in polycrystals, with varying numbers of grains and textures, are also performed to quantify convergence statistics for the macroscopic viscoplastic response.</p>
<p>In order to simulate the kinetics of pattern evolution, stabilized spectral techniques are utilized to solve phase-field equations. As an example of conservative gradient-flow kinetics, phase separation by anisotropic spinodal decomposition is shown to result in cellular structures with tunable elastic properties and promise for metamaterial design. Finally, as an example of nonconservative kinetics, the study of domain wall motion in polycrystalline ferroelectric ceramics predicts electromechanical hysteresis behavior under large bias fields. A first-principles approach using DFT-informed model constants is outlined for lead zirconate titanate, producing results showing convincing qualitative agreement with in-house experiments. Overall, these examples demonstrate the promise of the stabilized spectral scheme in predicting pattern evolution as well as effective homogenized response in systems with non-quasiconvex energy landscapes.</p>https://thesis.library.caltech.edu/id/eprint/11432Stochastic Multiscale Modeling of Dynamic Recrystallization
https://resolver.caltech.edu/CaltechTHESIS:05242019-144233476
Authors: {'items': [{'email': 'abbas.tutcuoglu@gmail.com', 'id': 'Tutcuoglu-Abbas-Davud', 'name': {'family': 'Tutcuoglu', 'given': 'Abbas Davud'}, 'orcid': '0000-0003-2360-706X', 'show_email': 'NO'}]}
Year: 2019
DOI: 10.7907/1VVP-T060
<p><i>Materials by design</i> is a core driver in enhancing sustainability and improving efficiency in a broad spectrum of industries. To this end, thermo-mechanical processes and many of the underlying phenomena were studied extensively in the context of specific cases. The goal of this thesis is threefold: First, we aim to establish a novel numerical model on the micro- and mesoscale that captures dynamic recrystallization in a generalized framework. Based on the inheritance of the idea of state switches, we term this scheme <i>Field-Monte-Carlo Potts method</i>. We employ a finite deformation framework in conjunction with a continuum-scale crystal plasticity formulation and extend the idea of state switches to cover both grain migration and nucleation. We introduce physically-motivated state-switch rules, based on which we achieve a natural marriage between the deterministic nature of crystal plasticity and the stochastic nature of dynamic recrystallization. Using a novel approach to undertake the states-switches in a transient manner, the new scheme benefits from enhanced stability and can, therefore, handle arbitrary levels of anisotropy. We demonstrate this functionality at the example of pure Mg at room temperature, which experiences strong anisotropy through the different hardening behavior on the 〈c+a〉-pyramidal and prismatic slip systems as opposed to the basal slip systems as well as through the presence of twinning as an alternative strain accommodating mechanisms. Building on this generalized approach, we demonstrate spatial convergence of the scheme along with the ability to capture the transformation from single- to multi-peak stress-strain behavior.</p>
<p>Second, motivated by the lack of transparency concerning the benefits of high-fidelity approaches in the modeling of dynamic recrystallization, we present two derivative models of the Field-Monte-Carlo Potts method, both of which afford reduced computational expense. One model preserves the spatial interpretation of grains, but imposes a Taylor assumption regarding the distribution of strain; the other reduces the spatial notion of a grain to a volume fraction in the idea of a <i>Taylor model</i>. In order to concentrate on the differences in accuracy between the various approaches, we fit all three schemes to experimental data for pure copper, which allows us to employ a well-understood crystal plasticity-based constitutive model and to simultaneously provide sufficient data for the analysis of the texture, stress and grain-size evolution. Owing to the large strains attained in these simulations, using the FFT-based scheme, we achieve capturing a precursor of <i>continuous dynamic recrystallization</i>. For low temperatures, the Taylor model fails to replicate the nucleation-dominated recrystallization process, whereas, at high temperatures, it shows compelling agreement with experiments and the two higher-fidelity models both in terms of the homogenized stress-evolution and the microstructural evolution.</p>
<p>Finally, we present a novel multiscale analysis of thermo-mechanical processes through coupling of the computationally efficient Taylor model for modeling dynamic recrystallization on the mesoscale to a <i>max-ent based meshfree approach</i> on the macroscale in the idea of <i>vertical homogenization</i>. We analyze the severe plastic deformation-based process of <i>equal channel angular extrusion</i>, which is intriguing from a numerical perspective due to the heavily localized zone of extensive shear deformation. By employing novel tools on the microscale regarding the stable update of internal variables as well as a careful interpretation of macroscale boundary conditions, we present the first multiscale analysis of a severe plastic deformation process informing simultaneously about the evolution of stress, texture and grain refinement. We attain convincing qualitative agreements for the evolution of the plunger force and texture. As an outlook on future investigations, we analyze multiple passes of the same billet in the form of route C with emphasis on the texture evolution after the second pass.</p>https://thesis.library.caltech.edu/id/eprint/11542Controlling the Buckling Behavior of Bilayered Systems
https://resolver.caltech.edu/CaltechTHESIS:09272018-211547049
Authors: {'items': [{'email': 'paul.mazur@gadz.org', 'id': 'Mazur-Paul-Antoine-Benoit', 'name': {'family': 'Mazur', 'given': 'Paul Antoine Benoit'}, 'orcid': '0000-0002-2837-9716', 'show_email': 'NO'}]}
Year: 2019
DOI: 10.7907/C70B-K221
<p>A bilayered system is an assembly of two different materials and has the form of flat and thin layers. The two materials are attached to each other at the surface. The attachment method varies depending on the materials properties. Bilayered systems made of materials with different dimensions and stiffness have been widely studied and used for different applications. The characteristic scale of this kind of system can go from hundreds of km in the case of geological layers on the Earth surface to some µm in the case of very small electronic systems or microlenses.</p>
<p>The behavior of a bilayered system, when submitted to a stimulus, is characterized by the conflict between the preferred response of each material and the constraint that one imposes on the other. As a result, the deformation of the bilayered system will be different from that which could be obtained when the materials are taken separately. Of particular interest is the buckling of such systems: when submitted to a particular stress distribution, one material will expand significantly more than the other, but as the two materials are attached at the interface surface, the material displacements must be continuous through this interface. The conflict between the continuity of displacement and the need to expand differently may result in nonlinear patterns at this interface. Those unstable situations can be used to define a limit of constraint for the materials or can be used as actuators for a desired surface pattern. Many studies have focused on characterizing homogeneous buckling within an entire surface due to homogeneous strain distribution within the top surface. This characterization was performed theoretically, numerically, and experimentally. But, some studies have shown different possibilities of evolution of the buckling patterns known today. As a consequence, we can pose two questions: 1) Is there a possibility to modify non-linear patterns regardless of what is imposed by mechanical properties and dimensions? 2) What happens in the case of a non-uniform state of constraints within the bilayered system?</p>
<p>This thesis explores those questions for the case of a thin stiff film attached to a compliant thick substrate. The first part of this thesis serves to describe the initial buckling theory in the case of uniform strain and explains how to define the loading threshold resulting in uniform buckling at the surface characterized by a finite number of spatial frequencies. The second part of the thesis studies the consequences of a non-uniform loading within the surface. A numerical method based on the theory of the first part is implemented to show the emergence of new frequencies due to the discontinuous loading distribution. The third part focuses on the possibility of tuning a uniform buckling by including an electromechanical coupling into the bilayered system. This coupling makes the materials sensitive to electric fields, thus creating a new energy term to interfere with the mechanical energy of deformation, thereby modifying the resulting spatial frequency of the buckling. This study is done theoretically and numerically by finite element modeling.</p>https://thesis.library.caltech.edu/id/eprint/11207Dynamic Strength of Silica Glasses at High Pressures and Strain Rates
https://resolver.caltech.edu/CaltechTHESIS:02202019-104738145
Authors: {'items': [{'email': 'chr.kettenbeil@gmail.com', 'id': 'Kettenbeil-Christian', 'name': {'family': 'Kettenbeil', 'given': 'Christian'}, 'orcid': '0000-0003-0301-3678', 'show_email': 'NO'}]}
Year: 2019
DOI: 10.7907/RZJW-MX30
<p>Understanding the behavior of silica glasses at high pressures and strain rates is of great importance for geological processes and highly relevant to many technological applications including high-powered laser-matter interactions in optical elements and impact/blast damage in defense systems. Materials typically experience large inelastic deformations at high pressures, which are strongly affected by strength-related phenomena such as work hardening, damage and thermal softening. The pressure-shear plate impact experiment (PSPI) provides detailed information on the pressure and strain rate dependent strength properties of materials subjected to uniaxial compression. However, its range of attainable pressures has so far been limited and the assumptions required for its analysis become invalid at pressures beyond the Hugoniot elastic limit of the anvil materials. In this dissertation, a high-pressure PSPI (HP-PSPI) technique is developed that greatly extends the range of attainable experimental conditions by achieving higher terminal projectile velocities in a powder gun setup. A novel fiber-optic heterodyne transverse velocimeter (HTV) is developed to enable the use of robust frequency-based data reduction techniques, which reduce the effect of signal noise and light coupling losses. A forward analysis method, based on finite element simulations, is employed to match the experimentally observed material response during HP-PSPI experiments on soda-lime glass samples while considering the inelastic deformation of the utilized tungsten carbide anvils. Symmetric HP-PSPI experiments on tungsten carbide revealed a loss of strength at normal stresses exceeding 25 GPa, which hint at active damage or softening mechanisms under nominally uniaxial strain compression. A pressure-dependent strain softening model transitions soda-lime glass from an intact strength of 2.8 GPa, below strains of 10-30%, to a failed granular state following extensive inelastic shear deformation, which accurately predicts the measured response over a wide range of stresses (9-21 GPa) and strain rates (3•10<sup>5</sup>-2•10<sup>7</sup>s<sup>-1</sup>). Extending the range of previously attainable pressures and strain rates in PSPI experiments, combined with more robust diagnostics and analysis tools, will greatly benefit our understanding of material strength in extreme environments and enables the investigation of material behavior in a currently unexplored range of pressures and strain rates.</p>https://thesis.library.caltech.edu/id/eprint/11404Fast Adaptive Augmented Lagrangian Digital Image Correlation
https://resolver.caltech.edu/CaltechTHESIS:10162018-093212227
Authors: {'items': [{'email': 'yangjin2009010843@gmail.com', 'id': 'Yang-Jin', 'name': {'family': 'Yang', 'given': 'Jin'}, 'orcid': '0000-0002-5967-980X', 'show_email': 'YES'}]}
Year: 2019
DOI: 10.7907/MZ5G-PS98
<p>Digital image correlation (DIC) is a powerful experimental technique for measuring full-field displacement and strain. The basic idea of the method is to compare images of an object decorated with a speckle pattern before and after deformation in order to compute the displacement and strain fields. Local Subset DIC and finite element-based Global DIC are two widely used image matching methods; however there are some drawbacks to these methods. In Local Subset DIC, the computed displacement field may not satisfy compatibility, and the deformation gradient may be noisy, especially when the subset size is small. Global DIC incorporates displacement compatibility, but can be computationally expensive. In this thesis, we propose a new method, the augmented-Lagrangian digital image correlation (ALDIC), that combines the advantages of both the local (fast and in parallel) and global (compatible) methods. We demonstrate that ALDIC has higher accuracy and behaves more robustly compared to both Local Subset DIC and Global DIC.</p>
<p>DIC requires a large number of high resolution images, which imposes significant needs on data storage and transmission. We combined DIC algorithms with image compression techniques and show that it is possible to obtain accurate displace- ment and strain fields with only 5 % of the original image size. We studied two compression techniques – discrete cosine transform (DCT) and wavelet transform, and three DIC algorithms – Local Subset DIC, Global DIC and our newly proposed augmented Lagrangian DIC (ALDIC). We found the Local Subset DIC leads to the largest errors and ALDIC to the smallest when compressed images are used. We also found wavelet-based image compression introduces less error compared to DCT image compression.</p>
<p>To further speed up and improve the accuracy of DIC algorithms, especially in the study of complex heterogeneous strain fields at various length scales, we apply an adaptive finite element mesh to DIC methods. We develop a new h-adaptive technique and apply it to ALDIC. We show that this adaptive mesh ALDIC algorithm significantly decreases computation time with no loss (and some gain) in accuracy.</p>https://thesis.library.caltech.edu/id/eprint/11233An Enhanced Maximum-Entropy Based Meshfree Method: Theory and Applications
https://resolver.caltech.edu/CaltechTHESIS:05062019-043913897
Authors: {'items': [{'email': 'siddhantk41@gmail.com', 'id': 'Kumar-Siddhant', 'name': {'family': 'Kumar', 'given': 'Siddhant'}, 'orcid': '0000-0003-1602-8641', 'show_email': 'NO'}]}
Year: 2019
DOI: 10.7907/0AP6-5F94
<p>This thesis develops an enhanced meshfree method based on the local maximum-entropy (max-ent) approximation and explores its applications. The proposed method offers an adaptive approximation that addresses the tensile instability which arises in updated-Lagrangian meshfree methods during severe, finite deformations. The proposed method achieves robust stability in the updated-Lagrangian setting and fully realizes the potential of meshfree methods in simulating large-deformation mechanics, as shown for benchmark problems of severe elastic and elastoplastic deformations. The improved local maximum-entropy approximation method is of a general construct and has a wide variety of applications. This thesis presents an extensive study of two applications - the modeling of equal-channel angular extrusion (ECAE) based on high-fidelity plasticity models, and the numerical relaxation of nonconvex energy potentials. In ECAE, the aforementioned enhanced maximum-entropy scheme allows the stable simulation of large deformations at the macroscale. This scheme is especially suitable for ECAE as the latter falls into the category of severe plastic deformation processes where simulations using mesh-based methods (e.g. the finite element method (FEM)) are limited due to severe mesh distortions. In the second application, the aforementioned max-ent meshfree method outperforms FEM and FFT-based schemes in numerical relaxation of nonconvex energy potentials, which is essential in discovering the effective response and associated energy-minimizing microstructures and patterns. The results from both of these applications show that the proposed method brings new possibilities to the subject of computational solid mechanics that are not within the reach of traditional mesh-based and meshfree methods.</p>
https://thesis.library.caltech.edu/id/eprint/11498A Line-Free Method of Monopoles for 3D Dislocation Dynamics
https://resolver.caltech.edu/CaltechTHESIS:08042018-083338014
Authors: {'items': [{'email': 'adeffonde@gmail.com', 'id': 'Deffo-Nde-Arnold-Durel', 'name': {'family': 'Deffo Nde', 'given': 'Arnold Durel'}, 'orcid': '0000-0001-9077-8315', 'show_email': 'YES'}]}
Year: 2019
DOI: 10.7907/23YV-3312
<p>Despite the emergence of architected materials for various applications, metals still play a key role in engineering in general and aeronautics in particular. Turbine blades in jets engines for instance are made from single-crystal Nickel superalloys. As a result, studying the failure mechanism of these crystalline materials would help understand the limits of their applications. At the core of this mechanism are line defects called <i>dislocations</i>. Indeed, the plastic deformation of metals is governed by the motion of dislocation ensembles inside the crystal. In this thesis, we propose a novel approach to dislocation dynamics through the <i>method of monopoles</i>. In this approach, we discretize the dislocation line as a collection of points (or <i>monopoles</i>), each of which carries a Burgers "charge" and an element of line. The fundamental difference between our method and current methods for dislocation dynamics lies in the fact that the latter discretize the dislocation as a collection of line segments from which spans a need to keep track of the connectivity of the nodes. In our approach, we propose a "line-free" discretization where a linear connectivity or sequence between monopoles need not be defined. This attribute of the formulation offers significant computational advantages in terms of simplicity and efficiency. Through verification examples, we show that our method is consistent with existing results for simple configurations. We then build on this success to investigate increasingly complex examples, this with the ultimate goal of simulating the plastic deformation of a BCC grain in an elastic matrix.</p>https://thesis.library.caltech.edu/id/eprint/11142Shock Compression of Molybdenum Single Crystals to High Stresses
https://resolver.caltech.edu/CaltechTHESIS:02192020-135417079
Authors: {'items': [{'email': 'o.tomo.oni@gmail.com', 'id': 'Oniyama-Tomoyuki', 'name': {'family': 'Oniyama', 'given': 'Tomoyuki'}, 'orcid': '0000-0001-6097-9917', 'show_email': 'NO'}]}
Year: 2020
DOI: 10.7907/YWPJ-5379
<p>To investigate the role of crystal anisotropy and the impact stress on the shock induced elastic-plastic deformation of BCC single crystals at high stresses, molybdenum single crystals were shock compressed along [100], [111], and [110] orientations. A series of plate impact experiments were conducted with various impact stresses (23 - 190 GPa) along each orientation. Along the [100] and [111] orientations, two-wave structure - an elastic shock wave trailed by a plastic shock wave - was observed to 110 GPa. Along the [110] orientation, the two-wave structure was observed only up to 90 GPa.</p>
<p>Based on the measured quantities, in-material quantities at the elastic limit and at the peak state were calculated. The elastic wave amplitudes were analyzed to determine the crystal anisotropy effects, the impact stress dependence, and the activated slip systems on the elastic limit. The elastic wave amplitude increased linearly with
increasing impact stress, and that was significantly larger along the [111] orientation compared to the other orientations. The difference between calculated maximum resolved shear stresses at the elastic limit and corresponding Peierls stress suggested the activation of {110}<111> slip systems.</p>
<p>At the peak state, the Hugoniot relations were calculated along each orientation and compared with polycrystalline molybdenum Hugoniot relations. The Hugoniot relations along three orientations were in agreement within experimental uncertainties, even though the elastic limit showed considerable anisotropy. Also, they agreed reasonably well with the polycrystalline molybdenum data. This implied that the in-material quantities at the peak state do not depend on crystal orientation or the presence of grain boundaries.</p>
<p>In addition to the plate impact experiments, finite element simulations of shock compressed molybdenum single crystals were conducted using Abaqus Explicit in order to gain insight into deformation mechanisms activated during the elasticplastic
deformation. Shear strains on slip systems were explicitly considered by the crystal plasticity model implemented using Abaqus VUMAT subroutine. The results of FEM simulations indicated that {110}<111> systems were likely to be operating at the elastic limit. This observation was consistent with the experimental results from the present study.</p>https://thesis.library.caltech.edu/id/eprint/13641Fracture and Toughening of Brittle Structures with Designed Anisotropy
https://resolver.caltech.edu/CaltechTHESIS:11122019-171331857
Authors: {'items': [{'email': 'nealbrodnik@gmail.com', 'id': 'Brodnik-Neal-Ryan', 'name': {'family': 'Brodnik', 'given': 'Neal Ryan'}, 'orcid': '0000-0002-4426-5997', 'show_email': 'NO'}]}
Year: 2020
DOI: 10.7907/ET0C-MK61
<p>Despite good thermal and chemical properties, the use of ceramic materials in structural applications is limited by their inherently brittle nature. Efforts have been made to improve the toughness of ceramics through composite design, but recent developments in net shape processing such as additive manufacturing have significantly expanded this design space. Where composite topologies and morphologies were previously limited by material composition and thermodynamics, tools like 3D printing now allow for the design of composite structures of nearly any shape or arrangement.</p>
<p>This work seeks to understand how these processing advances might be utilized to improve the toughness of brittle composites by exploring how previously inaccessible anisotropic inclusion structures might influence fracture behavior. The study begins with the evaluation of printed photopolymer structures as model brittle materials. First, printed structures are used to explore how elastic contrast between inclusions and matrix can affect crack propagation and improve toughness. Here, anisotropy presents an opportunity to achieve similar toughness to isotropic structures at smaller volume fractions by virtue of topologies that only exhibit toughening only in a singular direction, but require significantly less material to do so. Next, the effect of anisotropic voids is explored as a means of controlling crack nucleation and growth. With consideration of both compliance and directional propagation, a "fracture diode" that exhibits controlled, predictable fracture 100% of the time can be realized.</p>
<p>After exploring brittle polymers, ceramics systems with similar toughness and higher stiffness are considered. First, a model layered system of mica is explored, where wedge splitting can be used achieve stable crack growth. This allows for the evaluation of how changes in compliance can improve the interlayer toughness without directly interacting with the crack. Finally, this study extends further into ceramics by exploring silicon oxycarbide (SiOC) truss structures and truss elements produced from 3D printed preceramic polymers. In addition to considering the material itself, changes in truss structure are explored as a means of changing deformation mode, and by consequence, failure strength. These model experiments suggest that if trusses are compatible, they can be interchanged to control failure of the bulk structure.</p>
<p>This study demonstrates how designed heterogeneities with anisotropic structure can be used to both enhance the toughness of brittle composites as well achieve a greater degree of control over both crack nucleation and propagation in brittle systems where predicting failure is otherwise difficult. Looking forward, new processing tools like additive manufacturing present major opportunities for expanding the design space of brittle composites to achieve higher toughness and better fracture control than previously available. These new techniques may be able to expand the mechanical viability of ceramics, and make them better suited to mechanically demanding applications in the future.</p>https://thesis.library.caltech.edu/id/eprint/13574Topology Optimization and Failure Analysis of Deployable Thin Shells with Cutouts
https://resolver.caltech.edu/CaltechTHESIS:02032020-164711057
Authors: {'items': [{'email': 'serena1.ferraro@gmail.com', 'id': 'Ferraro-Serena', 'name': {'family': 'Ferraro', 'given': 'Serena'}, 'orcid': '0000-0002-6038-7863', 'show_email': 'NO'}]}
Year: 2020
DOI: 10.7907/9VZ4-3E71
<p>Shell structures with cutouts are widely used in architectural and engineering applications. For thin, lightweight, and deployable space structures, cutouts are cleverly positioned to fold and store the structure in a small volume. To maintain shape accuracy, these structures must fold without becoming damaged and must be stiff in their deployed configurations. Intuitive designs often fail to satisfy these two requirements. This research proposes solutions to the topology optimization of composite, thin shell structures with cutouts.</p>
<p>A novel optimization algorithm was developed that makes no assumptions on the initial number, shape, and location of cutouts on deployable thin shells. The algorithm uses a density-based approach, which distributes the material within the structure by assigning a density parameter to discretized locations. This parametrization of the design domain allows for the finding of new features and the connectivity of the domain, thus providing a completely general formulation to the optimization problem. The goal is to study the effects of volume and stress constraints imposed in a deformed configuration of thin shell structures. While classical topology optimization studies focus on finding solutions to linear problems, this method is applicable to geometrically nonlinear problems and implements stress constraints in the deformed, and hence most stressed, configuration of these shells. A mathematical formulation of the optimization problem and interpolation schemes for stiffness tensor, volume, and stress are presented. A sensitivity analysis of objective function, volume, and stress constraints is provided. Finally, solutions for a thin plate and a tape spring are proposed.</p>
<p>Density-based methods are computationally expensive when applied to large structures and complex shapes because of the large number of design variables. To address these challenges, two optimization methods that provide more specific solutions to the problem of composite, deployable shells are proposed. The first method uses level sets to parametrize the cutouts, thereby restricting the design space and simultaneously limiting the number of design variables. This greatly reduces the computational cost. Using this approach, successful solutions are found for stiff, composite, thin shells with complex shapes that can fold without becoming damaged. The second method uses a spline representation of the contour of a single cutout on the shell, thus performing fine tuning of the shape of the cutout. Modeling techniques that simulate localized strain and experimental methods for studying the quasi-static folding of these composite shells are developed. A laminate failure criterion suitable for thin, plain-weave composites is used in simulations to predict the onset of failure in folded shells. Numerical results are validated with folding experiments that demonstrated good agreement with numerical solutions.</p>
<p>Lastly, it was discovered that many of the best performing solutions have multiple closely spaced cutouts, as opposed to current designs for deployable space structures that have fewer large cutouts. This leads to the formation of small strips of material between cutouts. Hence, the behavior of thin, plain-weave composite material was characterized and the first study on size-scaling effects at small length scales (≤ 15 mm) in this type of material was performed. Size-scaling effects on stiffness and strength shown in this study were introduced in numerical simulations of deployable thin shells. The study demonstrates that the prediction of the onset of failure in folded shells strongly depends on these size effects. Numerical predictions are corroborated by an experimental investigation of localized damage in thin strips of material forming between cutouts. Deployable shells resulting from the optimization studies are built and tested and localized damage is measured via digital volume correlation techniques.</p>https://thesis.library.caltech.edu/id/eprint/13632Mechanics of Ultra-Thin Composite Coilable Structures
https://resolver.caltech.edu/CaltechTHESIS:01232020-134850757
Authors: {'items': [{'email': 'christophe.leclerc@outlook.com', 'id': 'Leclerc-Christophe', 'name': {'family': 'Leclerc', 'given': 'Christophe'}, 'orcid': '0000-0003-1999-4757', 'show_email': 'NO'}]}
Year: 2020
DOI: 10.7907/X60S-BR30
<p>Coilable structures are thin-shell structures that can be coiled around a hub by flattening their cross-section. They are attractive for multiple space applications as they allow efficient packaging and deployment of large planar structures. Reducing the shell thickness enables smaller coiling radius and more efficient packaging.</p>
<p>This thesis investigates TRAC structures, a type of coilable structure, made of ultra-thin composite materials. A design using a laminate made of glass fiber plainweave fabric and carbon fiber unidirectional tape is proposed, leading to a shell thickness of 0.08 mm. An in-autoclave, two-cure manufacturing process is presented, and a shape measurement method is used to mitigate post-cure shape changes due to residual stresses.</p>
<p>A study of the structure behavior in its deployed configuration is performed. First, the behavior when subjected to pure bending is investigated experimentally for structures with a length of 575 mm. Two regimes are observed, with a pre-buckling phase transitioning to a stable post-buckling phase after an initial buckling event. The ultimate buckling moment following the stable post-buckling regime can be as high as four times the initial buckling moment. A finite element model is developed and is able to reproduce all the features observed experimentally, except the ultimate buckling. This simulation model is used to study the effect of varying the structure length from 300 mm to 5000 mm on the initial buckling moment. Results show that nonlinearities in the pre-buckling deformations of the flanges under compression lead to a constant wavelength lateral-torsional buckling mode for which the critical moment is mostly constant across the range of length. The torsional behavior of the TRAC structure is also investigated. Good agreement is obtained between experiments and numerical simulations, and initial twist in the structure is shown to have little effect on the overall behavior due to the small torsional stiffness in the underformed configuration.</p>
<p>An analytical method to predict the buckling load of a TRAC structure under pure bending is presented. It is achieved by considering only one flange of the structure and solving the problem of a cylindrical shell panel with a longitudinal free edge under non-uniform axial compression. Partially uncoupled stability equations for a balanced laminate are derived and are used in conjunction with the Rayleigh-Ritz method to approximate the buckling load. This method overestimates the buckling load by 44% in the case of a 500 mm TRAC structure made with ultra-thin composite materials.</p>
<p>A study of the coiling behavior is also presented. High localized curvature in the transition region between the coiled and deployed regions is observed in experiments, leading to material failure for a structure made only of carbon fiber unidirectional tape. A numerical framework is developed and reproduces the localized curvature observed in experiments, predicting stress concentration at this location. The study shows that changing the laminate to a a single ply of carbon fiber unidirectional tape sandwiched between plies of glass fiber plainweave fabrics reduces significantly the maximum stress in the transition region, to the extent that the highest stress is now in the fully coiled region and can be accurately predicted using simple equations based on the change of curvatures due to the coiling process.</p>https://thesis.library.caltech.edu/id/eprint/13629Variational and Multiscale Modeling of Amorphous Silica Glass
https://resolver.caltech.edu/CaltechTHESIS:07202019-135213721
Authors: {'items': [{'email': 'will.schill@gmail.com', 'id': 'Schill-William-Joseph', 'name': {'family': 'Schill', 'given': 'William Joseph'}, 'orcid': '0000-0003-0950-7433', 'show_email': 'NO'}]}
Year: 2020
DOI: 10.7907/B2A9-RQ38
<p>We develop a critical-state model of fused silica plasticity on the basis of data mined from molecular dynamics (MD) calculations. The MD data is suggestive of an irreversible densification transition in volumetric compression resulting in permanent, or plastic, densification upon unloading. Moreover, this data exhibits dependence on temperature and the rate of deformation. We show that these characteristic behaviors are well-captured by a critical state model of plasticity, where the densification law for glass takes the place of the classical consolidation law of granular media and the locus of constant volume states denotes the critical-state line. A salient feature of the critical-state line of fused silica, as identified from the MD data, that renders its yield behavior anomalous is that it is strongly non-convex, owing to the existence of two well-differentiated phases at low and high pressures. We argue that this strong non-convexity of yield explains the patterning that is observed in molecular dynamics calculations of amorphous solids deforming in shear. We employ an explicit and exact rank-2 envelope construction to upscale the microscopic critical-state model to the macroscale. Remarkably, owing to the equilibrium constraint the resulting effective macroscopic behavior is still characterized by a non-convex critical-state line. Despite this lack of convexity, the effective macroscopic model is stable against microstructure formation and defines well-posed boundary-value problems. We present examples of ballistic impact of silica glass rods by way of the optimal transport meshfree method. We extend the study of the inelastic behavior of silica glass to include the effect of many different temperatures, pressures, and strain rates using MD and maximum entropy atomistics (MXE) calculations. Owing to the temperature dependence of the model, the macroscopic model becomes unstable against adiabatic shear localization. Thus, the material adopts small inter-facial regions where the shear strain is extremely high. We characterize the shear band size, thereby predicting a yield knockdown factor at the macroscale, and compare the results to behavior reported in flyer plate impact experiments.</p>https://thesis.library.caltech.edu/id/eprint/11744Thermal Conduction in Amorphous Materials and the Role of Collective Excitations
https://resolver.caltech.edu/CaltechTHESIS:01162020-015608435
Authors: {'items': [{'email': 'jaeyun.moon91@gmail.com', 'id': 'Moon-Jaeyun', 'name': {'family': 'Moon', 'given': 'Jaeyun'}, 'orcid': '0000-0001-8199-5588', 'show_email': 'NO'}]}
Year: 2020
DOI: 10.7907/Z23D-Z566
<p>The atomic vibrations and thermal properties of amorphous dielectric solids are of fundamental and practical interest. For applications, amorphous solids are widely used as thermal insulators in thermopile and other detectors where low thermal conductivity directly sets the sensitivity of the detector. Amorphous solids are of fundamental interest themselves because the lack of atomic periodicity complicates theoretical development. As a result, the lower limits of thermal conductivity in solids as well as the nature of the vibrational excitations that carry heat remain active topics of research.</p>
<p>In this thesis, we use numerical and experimental methods to investigate the thermal conduction in amorphous dielectrics. We begin by using molecular dynamics to investigate the thermal conductivity of amorphous nanocomposites. We find that mismatching the vibrational density of states of constituent materials in the composite is an effective route to achieve exceptionally low thermal conductivity in fully dense solids.</p>
<p>We then transition to examining the properties of the atomic vibrations transporting heat in amorphous solids. For decades, normal mode methods have been used extensively to study thermal transport in amorphous solids. These methods naturally assume that normal modes are the fundamental vibrational excitations transporting heat. We examine the predictions from normal mode analysis that are now able to be tested against experiments, and we find that the predictions from these methods do not agree with experimental observations. For instance, normal mode methods predict that the low frequency normal modes are scattered by anharmonic interactions as in single crystalline solids. However, temperature dependent thermal conductivity measurements demonstrate a typical glassy temperature dependence inconsistent with normal modes scattering through anharmonic interactions. These discrepancies suggest that normal modes are not the fundamental heat carriers in amorphous dielectrics.</p>
<p>To identify the actual heat carriers, we draw on fundamental concepts from many- body physics and inelastic scattering theory that dictate that the excitation energies of a many-body interacting system are given by the poles of the single-particle Green's function. The imaginary part of this function is proportional to the dynamic structure factor that is directly measured in inelastic scattering experiments. Collective excitations of a given energy and wavevector can thus be identified from peaks in the dynamic structure factor; their damping is given by the broadening of the peak. Using these concepts from many-body physics, the physical picture that emerges is that heat is carried in large part by a gas of weakly interacting collective excitations with a cutoff frequency that depends on the atomic structure and composition of the glass.</p>
<p>We test this picture using numerical and experimental inelastic scattering measurements on amorphous silicon, a commonly studied amorphous solid. We observe collective excitations up to 10 THz, well into the thermal spectrum, and far higher than previous inelastic scattering measurements on other glasses. Our numerical and experimental evidence also confirms that the collective excitations are damped by structural disorder rather than anharmonic interactions and that they dominate the thermal conduction in amorphous silicon. Subsequent analysis shows that these high frequency acoustic excitations are supported in amorphous silicon due to a large sound velocity and monatomic composition, suggesting that other monatomic amorphous solids with large sound velocities may also support these thermal excitations.</p>
<p>Overall, our results provide strong evidence that the heat carriers in amorphous dielectrics are collective excitations rather than normal modes. This change in physical picture advances our understanding of atomic dynamics in glasses and also provides a foundation for realizing dielectric solids with ultralow thermal conductivity.</p>https://thesis.library.caltech.edu/id/eprint/13625Linking Micro-Structure to Macro-Behavior of Granular Matter: From Flowing Heterogeneously to Morphing Adaptively
https://resolver.caltech.edu/CaltechTHESIS:04232020-202440477
Authors: {'items': [{'email': 'llc99210@gmail.com', 'id': 'Li-Liuchi', 'name': {'family': 'Li', 'given': 'Liuchi'}, 'orcid': '0000-0002-1360-4757', 'show_email': 'YES'}]}
Year: 2020
DOI: 10.7907/pbec-dk61
<p>From concrete gravels unloaded from trucks to wheat seeds discharged through funnels, from polymeric beads filled in shoe cushions to metallic pellets packed in robotic grippers, granular matter is becoming increasingly relevant in coping with our evolvingly sophisticated societal needs in many respects (e.g. expanding urbanization, growing population and advancing manufacturing). This increasing relevance urges developing micro-structural understandings of granular matter regarding its two basic macro-scale behaviors: flowing heterogeneously and morphing adaptively. However, findings in this regard so far suffered from a disconnection in length-scale - some adopting a top-down perspective lacking predictability due to few insights taken from underpinning micro-scale details (e.g. particle shape), while others adopting a bottom-up perspective lacking practicality due to few specificities incorporated from overlaying macro-scale conditions (e.g. heterogeneities).</p>
<p>In this dissertation, via Discrete Element Method (DEM) simulations, we bridge the divide between length-scales in this regard by revealing the fundamental role of microstructures. To begin with, we evaluate and verify the robustness of DEM in capturing granular microstructures, by systematically comparing simulation results with experimental measurements on quasi-statically sheared granular assemblies. Then, we first numerically study spatial phase transitions in heterogeneous granular flows from a top-down perspective. We start by calibrating and validating a DEM model using experiments we perform on fluidizing spherical particle pile formed in a rotating drum. We next take the validated model to produce flows with different microstructures by systematically varying boundary condition and loading rate, and lastly we study their correlations with phase transitions ranging from gas-like layers near the free surface, to underneath liquid-like layers, and to solid-like layers deep in the bulk. We propose a micro-scale parameter quantifying the level of structural anisotropy, that can for the first time elucidate the spatial phase transitions between these layers independent of imposed boundary conditions and loading rates. Further, we find that, in solid-like layers, this micro-structural quantity correlates to bulk effective friction, an integral macro-scale quantity in constitutive modeling. Next, we numerically study bending modulus adaptations in shape-morphing granular sheets from a bottom-up perspective. We start by calibrating and validating a DEM model using experiments we perform on bending 3D printed granular sheets enclosed in a flexible membrane. We next take the validated model to construct granular sheets with different microstructures by varying constituent particle shape, initial configuration and confining pressure. Lastly we study the correlation between microstructure variations and modulus adaptations. We discover a universal power-law correlation between bending modulus (a macro-scale quantity) and coordination number (a micro-scale quantity) in reminiscence of the canonical power-law scaling for packings of frictionless sphere near jamming. We also find larger coordination number favors interlocked particles over non-interlocked ones, leading to significantly better shape-morphing performance of chain-like sheets over discrete assemblies.</p>https://thesis.library.caltech.edu/id/eprint/13681Multi-Functional Metamaterials
https://resolver.caltech.edu/CaltechTHESIS:05062021-023201965
Authors: {'items': [{'email': 'ssharaninjeti@gmail.com', 'id': 'Injeti-Sai-Sharan', 'name': {'family': 'Injeti', 'given': 'Sai Sharan'}, 'orcid': '0000-0003-1941-9752', 'show_email': 'YES'}]}
Year: 2021
DOI: 10.7907/3rfm-1x78
<p>Optimally designing interdependent mechanical properties in a structure allows for it to be used in application where an arbitrary combination of properties is desired. Architected materials have proven to be an effective way of attaining mechanical behaviors that are unattainable using their constituent materials alone, such as unusual static mechanical properties, unusual wave propagation behavior, and shape morphing. The advent of 3-D printing has allowed for fabricating metamaterials with complex topologies that display engineered mechanics. However, much of the current efforts have focused on optimally designing simple mechanical behaviors such as designing for stiffness and weight, particular frequency bandgaps, or bi-stability. In this work, we study two metamaterial systems where we control and optimize a wide set of static and dynamic properties, and one complex multi-stable structure.</p>
<p>Most studies on the optimal design of static properties have focused on engineering stiffness and weight, and much remains unknown about ways to decouple the critical load to failure from stiffness and weight. This is the focus of the first part of our work. We show that the addition of local internal pre-stress in selected regions of architected materials enables the design of materials where the critical load to failure can be optimized independently from the density and/or quasistatic stiffness. We propose a method to optimize the specific load to failure and specific stiffness using sensitivity analysis, and derive the maximum bounds on the attainable properties. We demonstrate the method in a 2-D triangular lattice and a 3-D octahedral truss, showing excellent agreement between experimental and theoretical results. The method can be used to design materials with predetermined fracture load, failure location and fracture paths.</p>
<p>For the second part of our work, we focus on designing acoustically transparent structures, by engineering the acoustic impedance -- a combination of wave speed and density, to match that of the surroundings. Owing to the strong correlation between acoustic wave speed and static stiffness, it is challenging to design acoustically transparent materials in a fluid, while maintaining their high structural rigidity. We provide a sensitivity analysis to optimize these properties with respect to design parameters of the structure, that include localized masses at specific positions. We demonstrate the method on five different periodic, three dimensional lattices, to calculate bounds on the longitudinal wave speed as a function of their density and stiffness. We then perform experiments on 3-D printed structures, to validate our numerical simulations. Further, using the sensitivity analysis together with a data-driven approach, we design and demonstrate a mode demultiplexer, that is capable of splitting arbitrarily mixed modes. The tools developed in this work allow for designing structures in a plethora of applications, including ultrasound imaging, wave filtering, and waveguiding.</p>
<p>Finally, most multi-stable structures are limited by bi-stability either at the macroscopic or the unit cell level owing to the difficulty in engineering a highly non-linear energy landscape using just elements that display convex energy landscapes. We demonstrate a method to design arbitrarily complex multi-stable shape morphing structures, by introducing rigid kinematic constraints together with disengaging energy storing elements. We present the idea on a kagome lattice configuration, producing a quadri-stable unit cell and complex stable topologies with larger tessellations, validated by demonstrations on 3-D printed structures. Most designs that use passive actuation address one-way shape morphing along the direction of least resistance. We demonstrate reversible, thermally actuated shape morphing between stable open and closed topologies using shape memory springs. The designs can be extended to non-planar structures and fabricated at vastly different length scales.</p>https://thesis.library.caltech.edu/id/eprint/14134Multiscale Mechanical Characterization of Subcellular Structures in Living Walled Cells
https://resolver.caltech.edu/CaltechTHESIS:03262021-224805539
Authors: {'items': [{'email': 'leah.m.ginsberg@gmail.com', 'id': 'Ginsberg-Leah-Morgan', 'name': {'family': 'Ginsberg', 'given': 'Leah Morgan'}, 'orcid': '0000-0001-9685-7014', 'show_email': 'YES'}]}
Year: 2021
DOI: 10.7907/avj4-ve78
<p>The physiology of walled cells is dramatically different from that of human cells, but the biomechanics of walled cells are far less studied. Most bacterial, fungal, and plant cells have a strong cell wall (CW), which allows them to withstand large hydrostatic pressures in the cytoplasm, called turgor. Turgor pressure conflates the mechanics of subcellular components and complicates the characterization of the cell. In this dissertation, new models are introduced and explored for single cells to investigate the multiscale mechanics of plant and bacterial cells using micro- and nano-indentation experiments.</p>
<p>A multi-scale biomechanical assay is used to study the mechanical properties of plant cells. The plant CW is typically around 5% of the width of the entire cell, and is thought to carry most of the mechanical load. Large-scale indentations using a micro-indentation system probe the behavior of the overall cell structure, and atomic-force microscopy (AFM) nano-scale indentations are used to isolate the CW response. To determine the effect of external osmotic pressure, indentations are performed on cells in different osmotic conditions: hypotonic, isotonic, and hypertonic. The cell is idealized as two springs acting in series, one to represent the CW and one to represent the cytoplasm. The model uses the experimentally determined initial stiffnesses as input to the model to determine the relative stiffness contributions of the CW and the cytoplasm.</p>
<p>The first type of walled cells investigated is the xylem vessel element of <i>Arabidopsis thaliana</i>. The xylem is responsible for transporting water through the stem of any vascular plant (more commonly known as a land plant), and hence it must maintain structural integrity against high internal pressures while transporting water from the roots to the leaves. For extra structural support, xylem vessel elements develop secondary cell walls (SCWs), which are known to be a key component for mediating mechanical strength and stiffness in vascular plants. The structure and biomechanics of cultured plant cells are investigated during the cellular developmental stages associated with SCW formation using the multi-scale biomechanical assay described above. To determine the effect of morphological changes during differentiation, micro- and nano-indentations are performed on cells in different observed stages of the differentiation process.Prior to triggering differentiation, cells in hypotonic pressure conditions are significantly stiffer than cells in isotonic or hypertonic conditions, highlighting the dominant role of turgor pressure. Plasmolyzed cells with a SCW reach similar levels of stiffness as cells with maximum turgor pressure. Analysis using the two-spring model shows that the stiffness of the primary CW in all of these conditions is lower than the stiffness of the fully-formed SCW. These results provide the first experimental characterization of the mechanics of SCW formation at the single-cell level in plant cells.</p>
<p>Next, the mechanical response of individual <i>Nicotiana tabacum</i> cells from a suspension culture is studied using the same multi-scale biomechanical assay. The role played by the microtubules (MTs) and actin filaments (AFs) is determined through the use of drug treatments which selectively remove MTs and AFs. A generative statistical model is added to the two-spring model to quantify the stiffnesses of the CW, cytoplasm, turgor pressure, MTs, and AFs. Analysis of the initial stiffness and energy dissipation calculated from micro-indentation experiments indicates that the MTs and AFs contribute significantly to the mechanical response of a cell under compression. Micro- and nano-indentation tests confirm that turgor pressure is the most significant contributor to the stiffness response of turgid cells in compression. Finally, the results reveal that turgor pressure exerts stress on the CW, which leads to a measurable stiffening of the CW.</p>
<p>The studies described above focused on developing a discrete model to describe the mechanics of a cell in indentation experiments. However, the most common type of model used to evaluate the mechanics of a cell are continuum models. Continuum models are also necessary to decouple the material properties of subcellular components from their structure. In the final section, AFM indentations are simulated on a gram-negative bacterium, <i>Escherichia coli</i>, and a sensitivity study and inverse analysis are performed to solve for the CW elastic modulus and turgor pressure simultaneously. Sensitivity study results reveal that uncertainty in turgor pressure and CW elasticity indeed contribute the most to variability in force spectra from AFM measurements. The parameter space of possible values for CW elastic modulus and turgor pressure is discretized using triangular elements. "Simulated experiments" are tested throughout the parameter space, and correlations between the CW elastic modulus and turgor pressure, which depend on the type of objective function, are investigated. Two unique objective functions are tested in the inverse analysis, and a third objective function, which is a weighted sum of the first two, is found to reduce errors in estimated CW elastic modulus and turgor pressure by 20% and 11%, respectively. The use of this type of inverse analysis has the potential to elucidate the material properties of CWs using a single indentation measurement and reliably decouple these properties from the high turgor pressures inside walled cells.</p>https://thesis.library.caltech.edu/id/eprint/141123D Architected Battery Electrodes for Exploring Battery Kinetics from Nano to Millimeter
https://resolver.caltech.edu/CaltechTHESIS:05012021-183915976
Authors: {'items': [{'email': 'kai.y.narita@gmail.com', 'id': 'Narita-Kai', 'name': {'family': 'Narita', 'given': 'Kai'}, 'orcid': '0000-0002-3867-8234', 'show_email': 'YES'}]}
Year: 2021
DOI: 10.7907/dr3b-2d27
<p>The ability to design a particular geometry of porous electrodes at multiple length scales in a lithium-ion battery can significantly and positively influence battery performance because it enables control over kinetics and trajectories of ion and electron transport. None of the existing methods of engineering electrode structure is capable of creating 3D architected electrodes designed with independent and flexible form-factors at multiscale that are also resilient against cell packaging pressure. In addition, battery kinetics coupled at multiscale from ion transport in an electrolyte to solid electrolyte interphase (SEI) growth has only been studied by numerical simulations, but has never been experimentally explored.</p>
<p>In this thesis, we demonstrate an additive manufacturing technique to engineer porous electrode structure in 3D and explore battery kinetics at multiscale. First, we develop 3D architected carbon electrodes, whose structural factors are independently controlled and whose dimensions span microns to centimeters, using digital light processing and pyrolysis.
These free-standing lattice electrodes are disordered graphitic carbon composed of several stacked graphitic layers that are mechanically robust. Galvanostatic cycling using these architected carbon electrodes showed sloping capacity, typically observed in pyrolyzed carbon electrodes. We discuss the modified rate performance of the 3D architected carbon electrodes in the framework of ion transport kinetics in the electrode vs. electrolyte and overpotential, enabled by controlling structural factors of battery electrodes, including porosity, surface morphology, electrode thickness, and beam diameter, whose length scales range from nano to millimeter.</p>
<p>We then explore battery kinetics associated with SEI using deterministic, mechanically resilient, and thick 3D architected carbon electrodes, which allow us to study the formation, structure-resistance relationship, and position-dependent growth of SEI by combining the newly developed in operando DC-based technique and post-characterization using secondary ion mass spectroscopy. The amount of Li in SEI agrees with capacity losses, and the amount of F in SEI showed a strong linear correlation with SEI resistance evolutions. The position-dependent SEI growth was experimentally explored; the Li amount in SEI along the electrode thickness agrees with the simulation results in prior work, but the F amount in SEI showed the opposite tendency, suggesting modeling of multilayer SEI is necessary to predict precisely battery aging especially for thick electrodes. Our work demonstrates the use of 3D architected electrodes as a model system to explore multiscale kinetics in Li-ion batteries.</p>https://thesis.library.caltech.edu/id/eprint/14131Theoretical, Computational, and Experimental Characterization of Nematic Elastomers
https://resolver.caltech.edu/CaltechTHESIS:06042021-213808812
Authors: {'items': [{'email': 'victoriajlee2@gmail.com', 'id': 'Lee-Victoria-Jin-Young', 'name': {'family': 'Lee', 'given': 'Victoria Jin-Young'}, 'orcid': '0000-0002-2748-0089', 'show_email': 'YES'}]}
Year: 2021
DOI: 10.7907/f2hp-qe09
<p>Nematic elastomers are programmable soft materials that display large, reversible, and predictable deformation under an external stimulus such as a change in temperature or light. They are composed of a lightly crosslinked polymer network with stiff, rod-like liquid crystal molecules incorporated within the polymer chains. In thermotropic nematic elastomers, the liquid crystals undergo a continuous and reversible phase transition between the randomly oriented isotropic state and the highly oriented nematic state. Further, there is a direct thermo-mechanical coupling between the underlying temperature-responsive orientational order of the liquid crystal molecules and the macroscopic shape change of the surrounding elastomer chains. Finally, these materials display an unusually soft behavior. These remarkable properties make them promising materials for applications in aerospace as deployable structures and skins, in biomedical engineering as a soft pump, and in communications as the actuation mechanism in a reconfigurable antenna. Motivated by these applications, this thesis discusses the theoretical, computational, and experimental characterization of nematic elastomers.</p>
<p>We begin by investigating an example of actuation that takes advantage of the programmable, soft nature of these materials as well as instabilities associated with large deformation. We outline the multi-stable equilibrium solutions to a cylindrical balloon subjected to internal inflation, the material's microstructure formation due to this deformation, and its use as a soft pump with large ejection fraction, which involves a snap-through instability. Then we extend the Agostiniani-DeSimone-Dolzmann relaxed energy to a generalized Mooney-Rivlin constitutive relation and study four examples of Ericksen's universal deformations -- the inflation of cylindrical and spherical balloons, the cavitation of a disk, and the bending of a block.</p>
<p>We then move beyond the modeling of ideal materials and present a new constitutive relation for isotropic-genesis polydomain nematic elastomers. It is based on internal variables that describe the fine-scale domain patterns and evolve according to a kinetic process with dissipation. We discuss the model's implementation in the commercial finite-element software, ABAQUS, and study the problem of torsion of a cylinder. We identify an interesting instability at large torsional strains as a result of the Poynting effect. Finally, we present the design of a thermo-mechanical tensile setup and the experimental results for strain-rate dependence and temperature-dependence of samples that we synthesize in-house.</p>https://thesis.library.caltech.edu/id/eprint/14243Microstructure-Enabled Plasticity in Nano-to-Microscale Materials
https://resolver.caltech.edu/CaltechTHESIS:02232021-081136982
Authors: {'items': [{'email': 'janehlzhang@gmail.com', 'id': 'Zhang-Haolu-Jane', 'name': {'family': 'Zhang', 'given': 'Haolu Jane'}, 'orcid': '0000-0002-2871-5169', 'show_email': 'NO'}]}
Year: 2021
DOI: 10.7907/0zvc-tc14
<p>Microstructure-governed damage resistance in materials enables a variety of functional applications, such as durable biomedical implants and robust product packaging. For example, the refined phase compatibility qualifies NiTi for artery stents, while carbon fiber reinforced polymers improve structural strength in aerospace engineering. As the overall size of industrial applications continue to decrease, it has become increasingly apparent that when a material's external structural size and internal microstructural size become comparable, its mechanical behavior starts to deviate from that of bulk, such as the smaller-is-stronger size-effect in metals. This elucidation necessitates the characterization of materials at lengthscales relevant to their internal microstructure to guarantee accuracy in the design of real-world applications.</p>
<p>This thesis aims at deciphering the microstructure-mechanics relationship for materials at lengthscales bridging the gap between 1nm and 1µm, with shape memory ceramics, scorpion shells, and jellyfish biogel as sample systems. We use electron and x-ray diffraction to characterize microstructures such as twinning, defects, and fiber organization, while revealing strength, toughness, and other deformation mechanisms through <i>in-situ</i> nanomechanical experiments. We show improved shape recovery in an otherwise brittle ceramic by tuning its phase compatibility at the nanoscale and reveal unprecedented smaller-is-stronger size-dependence for its twinning-induced plasticity. We then unveil competing fiber orientations in Scorpion shells that follow fiber-mechanics principles and demonstrate a combined poroelasticity/viscoelasticity constitutive relation in jellyfish that explains their self-healing behavior. The correlation between microstructure and mechanical behavior unveils unique damage mitigation and energy dissipation techniques in both brittle ceramics and natural biomaterials at each order of lengthscale, paving the road to designing macroscopic materials with hierarchical mechanical behavior and improved plasticity.</p>https://thesis.library.caltech.edu/id/eprint/14093A Shock Compression Investigation of Failure Waves and Phase Transition in Soda-Lime Glass
https://resolver.caltech.edu/CaltechTHESIS:05282021-233441075
Authors: {'items': [{'email': 'akshay.joshikc@gmail.com', 'id': 'Joshi-Akshay', 'name': {'family': 'Joshi', 'given': 'Akshay'}, 'orcid': '0000-0001-8347-8357', 'show_email': 'NO'}]}
Year: 2021
DOI: 10.7907/b8xs-8r91
<p>Soda-lime glass (SLG) and other silica glasses find use in many technological applications involving high pressures and strain rates, such as systems with laser-matter interactions, transparent armor, etc. An experimentally validated constitutive model for these glasses is required for modeling their mechanical behavior at high pressures and strain rates. Also, due to the abundance of silica in the earth's crust, understanding the behavior of these glasses at high pressures can provide significant insights into many geophysical processes. To this end, shock compression experiments are carried out on SLG to study the material's behavior under impact stresses of 5-10 GPa. These experiments are accompanied by numerical simulations and constitutive modeling of SLG to gain further insights into the reported failure-wave phenomenon and phase transitions associated with the material.</p>
<p>The significant findings of this study in relation to the failure-wave phenomenon were the sudden densification/compaction of SLG associated with the failure-wave and the disappearance of the failure-wave phenomenon for impact stresses above 10 GPa. When viewed in the context of the findings from past experiments, these results seem to suggest that localized densification/compaction of SLG causes nucleation of cracks and subsequent comminution in the material under shock compression. These results and observations offer a potential explanation of the mechanism underlying the failure-wave phenomenon.</p>
<p>Further, the shock compression and release experiments performed in this work provided significant insights into the onset of possible phase-transition in SLG under shock compression. A loading-unloading hysteresis is observed in the material’s stress-strain curve for impact stresses higher than 5.8 GPa, with the permanent/residual strain increasing with impact stress. Further analysis of these results strongly indicates that the hysteresis is more likely due to a gradual, irreversible phase transition of SLG than due to regular inelastic behavior. Thus, the results suggest that the SLG undergoes a gradual phase transition to a stiffer phase, although other properties of this phase remain unclear. It can also be noted that this phase transition is postulated to start occurring under shock compression of SLG to stresses above 5 GPa, which is also the threshold stress for the onset of the failure-wave phenomenon. It is, therefore, possible that the two phenomena are interrelated. The experimental results from this study are further used to construct a constitutive model to capture the unloading behavior of SLG.</p>https://thesis.library.caltech.edu/id/eprint/14198Understanding Imperfections and Instabilities in Crystals via Physics-Based and Data-Driven Models
https://resolver.caltech.edu/CaltechTHESIS:04202021-184720643
Authors: {'items': [{'email': 'yingshi.teh@gmail.com', 'id': 'Ying-Shi-Teh', 'name': {'family': 'Teh', 'given': 'Ying Shi'}, 'orcid': '0000-0003-1743-4158', 'show_email': 'NO'}]}
Year: 2021
DOI: 10.7907/kd3n-eq78
<p>In crystals, atoms are arranged in a periodic manner in space. However in reality, imperfections and instabilities exist and this repeated arrangement is never perfect. The coupling between crystal defects, lattice instabilities, other defects like domain walls and domain patterns, and material properties generates interesting phenomena that can be leveraged on for future materials design. Nevertheless, the coupling of different scales and processes also makes the modeling and understanding of these materials an open challenge. This thesis examines these various aspects of crystalline solids through the development of both physics-based and data-driven computational models at the appropriate length scales.</p>
<p>Above-bandgap photovoltaic (PV) effect has been observed experimentally in multi-domain ferroelectric perovskites, but the underlying working mechanisms are not well understood. The first part of the thesis presents a device model to study the role of ferroelectric domain walls in the observed PV effect. The model accounts for the intricate interplay between ferroelectric polarization, space charges, photo-generation, and electronic transport. When applied to bismuth ferrite, results show a significant electric potential step across both 71° and 109° domain walls, which in turn contributes to the PV effect. The domain-wall-driven PV effect is further shown to be additive in nature, allowing for the possibility of generating the above-bandgap voltage.</p>
<p>In the second part, we present a lattice model incorporating random fields and long-range interactions where a frustrated state emerges at a specific composition, but is suppressed elsewhere. The model is motivated by perovskite solid solutions, and explains the phase diagram in such materials including the morphotropic phase boundary (MPB) that plays a critical role in applications for its enhanced dielectric, piezoelectric, and optical properties. Further, the model also suggests the possibility of entirely new phenomena by exploiting MPBs.</p>
<p>The final part of the thesis focuses on constructing data-driven models from first principles calculations, particularly density functional theory (DFT) for studying crystalline materials. Specifically we propose an approach that exploits machine learning to approximate electronic fields in crystalline solids subjected to deformation. When demonstrated on magnesium---a promising light weight structural material---our model predicts the energy and electronic fields to the level of chemical accuracy, and it even captures lattice instabilities. This DFT-based machine learning approach can be very useful in methods that require repeated DFT calculations of unit cell subjected to strain, especially multi-resolution studies of crystal defects and strain engineering that is emerging as a widely used method for tuning material properties.</p>https://thesis.library.caltech.edu/id/eprint/14125Modeling and Programming Shape-Morphing Structured Media
https://resolver.caltech.edu/CaltechTHESIS:09282021-231505066
Authors: {'items': [{'email': 'connorgmcmahan@gmail.com', 'id': 'McMahan-Connor-Glenn', 'name': {'family': 'McMahan', 'given': 'Connor Glenn'}, 'orcid': '0000-0001-5024-6138', 'show_email': 'NO'}]}
Year: 2022
DOI: 10.7907/rcw1-r139
<p>Shape-morphing and self-propelled locomotion are examples of mechanical behaviors that can be "programmed" in structured media by designing geometric features at micro- and mesostructural length scales. This programmability is possible because the small-scale geometry often imposes local kinematic modes that are strongly favored over other deformations. In turn, global behaviors are influenced by local kinematic preferences over the extent of the structured medium and by the kinematic compatibility (or incompatibility) between neighboring regions of the domain. This considerably expands the design space for effective mechanical properties, since objects made of the same bulk material but with different internal geometry will generally display very different behaviors. This motivates pursuing a mechanistic understanding of the connection between small-scale geometry and global kinematic behaviors. This thesis addresses challenges pertaining to the modeling and design of structured media that undergo large deformations.</p>
<p>The first part of the thesis focuses on the relation between micro- or mesoscale patterning and energetically favored modes of deformation. This is first discussed within the context of twisted bulk metallic glass ribbons whose edges display periodic undulations. The undulations cause twist concentrations in the narrower regions of the structural element, delaying the onset of material failure and permitting the design of structures whose deployment and compaction emerge from the ribbons' chirality. Following this discussion of a periodic system, we study sheets with non-uniform cut patterns that buckle out-of-plane. Motivated by computational challenges associated with the presence of geometric features at disparate length scales, we construct an effective continuum model for these non-periodic systems, allowing us to simulate their post-buckling behavior efficiently and with good accuracy.</p>
<p>The second part of the thesis discusses ways to leverage the connection between micro/mesoscale geometry and energetically favorable local kinematics to create "programmable matter" that undergo prescribed shape changes or self-propelled locomotion when exposed to an environmental stimulus. We first demonstrate the capabilities of an inverse design method that automates the design of structured plates that morph into target 3D geometries over time-dependent actuation paths. Finally, we present devices made of 3D-printed liquid crystal elastomer (LCE) hinges that change shape and self-propel when heated.</p>https://thesis.library.caltech.edu/id/eprint/14376Geometry Synthesis and Multi-Configuration Rigidity of Reconfigurable Structures
https://resolver.caltech.edu/CaltechTHESIS:09182021-045958776
Authors: {'items': [{'email': 'charlesjdorn@gmail.com', 'id': 'Dorn-Charles-Jacob', 'name': {'family': 'Dorn', 'given': 'Charles Jacob'}, 'orcid': '0000-0001-6516-2586', 'show_email': 'YES'}]}
Year: 2022
DOI: 10.7907/ph2w-9a34
<p>Reconfigurable structures are structures that can change their shapes to change their functionalities. Origami-inspired folding offers a path to achieving shape changes that enables multi-functional structures in electronics, robotics, architecture and beyond. Folding structures with many kinematic degrees of freedom are appealing because they are capable of achieving drastic shape changes, but are consequently highly flexible and therefore challenging to implement as load-bearing engineering structures. This thesis presents two contributions with the aim of enabling folding structures with many degrees of freedom to be load-bearing engineering structures.</p>
<p>The first contribution is the synthesis of kirigami patterns capable of achieving multiple target surfaces. The inverse design problem of generating origami or kirigami patterns to achieve a single target shape has been extensively studied. However, the problem of designing a single fold pattern capable of achieving multiple target surfaces has received little attention. In this work, a constrained optimization framework is presented to generate kirigami fold patterns that can transform between several target surfaces with varying Gaussian curvature. The resulting fold patterns have many kinematic degrees of freedom to achieve these drastic geometric changes, complicating their use in the design of practical load-bearing structures.</p>
<p>To address this challenge, the second part of this thesis introduces the concept of multi-configuration rigidity as a means of achieving load-bearing capabilities in structures with multiple degrees of freedom. By embedding springs and unilateral constraints, multiple configurations are rigidly held due to the prestress between the springs and unilateral constraints. This results in a structure capable of rigidly supporting finite loads in multiple configurations so long as the loads do not exceed some threshold magnitude. A theoretical framework for rigidity due to embedded springs and unilateral constraints is developed, followed by a systematic method for designing springs to maximize the load-bearing capacity in a set of target configurations. An experimental study then validates theoretical predictions for a linkage structure. Together, the application of geometry synthesis and multi-configuration rigidity constitute a path towards engineering reconfigurable load-bearing structures.</p>https://thesis.library.caltech.edu/id/eprint/14367Shape-Changing Phased Arrays
https://resolver.caltech.edu/CaltechTHESIS:03312022-192034489
Authors: {'items': [{'email': 'david.elliott.williams@gmail.com', 'id': 'Williams-David-Elliott', 'name': {'family': 'Williams', 'given': 'David Elliott'}, 'orcid': '0000-0002-6213-4712', 'show_email': 'YES'}]}
Year: 2022
DOI: 10.7907/r6f1-zq65
<p>Historically, increasing the degrees of freedom in electromagnetic structures has revolutionized the capabilities of wireless systems and introduced new applications. While research on phased arrays has explored everything from antenna drive settings to the element placement, the array geometry is assumed to be a fixed parameter. This thesis summarizes the author's work developing shape-changing phased arrays. It demonstrates the fundamental trade-off between gain and steering range for a given geometry. Measurements of the first shape-changing phased array both verify this theory and demonstrate the ability to break this trade-off using geometric reconfiguration. In addition, the mathematical consequences of shape-change and their impact on the arrays electromagnetic properties are discussed. Programmable passive switching networks on flexible sheets embedded in the array are proposed to address these challenges. The ability of these structures to enhance array performance is demonstrated by <i>in-situ</i> optimization experiments on a demonstration array. The associated optimization problem is characterized with a statistical analysis on a simulated array. Finally, avenues for further research are proposed.</p>https://thesis.library.caltech.edu/id/eprint/14536Machine Learning and Scientific Computing
https://resolver.caltech.edu/CaltechTHESIS:05252022-180406320
Authors: {'items': [{'email': 'kovachki93@gmail.com', 'id': 'Kovachki-Nikola-Borislavov', 'name': {'family': 'Kovachki', 'given': 'Nikola Borislavov'}, 'orcid': '0000-0002-3650-2972', 'show_email': 'NO'}]}
Year: 2022
DOI: 10.7907/8nc5-cc67
<p>The remarkable success of machine learning methods for tacking problems in computer vision and natural language processing has made them auspicious tools for applications to scientific computing tasks. The present work advances both machine learning techniques by using ideas from numerical analysis, inverse problems, and data assimilation and introduces new machine learning based tools for accurate and computationally efficient scientific computing. Chapters 2 and 3 introduce new methods and analyze existing methods for the optimization of deep neural networks. Chapters 4 and 5 formulate approximation architectures acting between infinite dimensional functions spaces for applications to parametric PDE problems. Chapter 6 demonstrates how to re-formulate GAN(s) so they can condition on continuous data and exhibits applications to Bayesian inverse problems. In Chapter 7, we present a novel regression-clustering method and apply it to the problem of predicting molecular activation energies.</p>https://thesis.library.caltech.edu/id/eprint/14621Slip Patterns on Heterogeneous Frictional Interfaces
https://resolver.caltech.edu/CaltechTHESIS:02232022-193800084
Authors: {'items': [{'email': 'kavya.sudhir.017@gmail.com', 'id': 'Sudhir-Kavya', 'name': {'family': 'Sudhir', 'given': 'Kavya'}, 'orcid': '0000-0001-6673-0979', 'show_email': 'YES'}]}
Year: 2022
DOI: 10.7907/xkbp-ks08
<p>Understanding the implications of heterogeneity on frictional interfaces for the resulting slip patterns is a challenging, highly nonlinear, and dynamic problem with special relevance to earthquake source processes. Natural fault surfaces are rarely homogeneous and host a spectrum of slip behaviors in response to slow tectonic loading where slow steady slip and earthquake ruptures are just the end members. Understanding how heterogeneous frictional properties translate into different slip patterns would enable us to constrain the heterogeneity of natural faults and get an insight into processes that are difficult to observe in the field such as earthquake nucleation, with important implications for the assessment of seismic hazard.</p>
<p>In this thesis, we advance our understanding of fault heterogeneity and its effects by conducting numerical simulations of long-term slip histories on heterogeneous frictional interfaces. We first focus on how irregular fault geometry affects the variability in repeating sequences by investigating a specific example of the SF-LA repeaters in the Parkfield segment of the San Andreas Fault (SAF) in California. We then investigate the effect of increasing heterogeneity in the effective normal stress on earthquake nucleation processes, complexity of earthquake sequences, and features of larger-scale ruptures. In both cases, we incorporate the heterogeneity in physical properties into 2D planar faults governed by rate-and-state friction and embedded into 3D homogeneous elastic bulk. Fully dynamic simulations are used to numerically solve the resulting elastodynamic problems with friction as a nonlinear boundary condition.</p>
<p>Our models reproduce many observations about SF-LA repeating sequences, in- cluding their mean moment, mean recurrence times, stress drops, the observed non- trivial scaling between the seismic moment and recurrence times of the repeaters, the ranges of variability in moment and recurrence time, and the ranges of triggering times between the two sequences. Multiple models produce slip behaviors com- parable to observations, indicating that the models cannot be uniquely constrained based on available observations. We also study how small-scale features of hetero- geneity affect model response. We find that smoothing the distribution over scales smaller than governing length scales in the problem, such as the nucleation size in our case, changes the specific evolution of slip, but preserves its key characteristics, such as the range of event variability and triggering times between events. However, smoothing the distribution on larger scales modifies the response qualitatively.</p>
<p>Our study of the earthquake initiation processes on interfaces with normal stress heterogeneity reveals that systematic increase in heterogeneity induces a continuum of behaviors, ranging from purely fault-spanning events to persistent foreshock-like events interspersed between fault-spanning mainshocks. In models with strong heterogeneity, most smaller-scale and larger-scale events initiate from scales much smaller than the nucleation size estimates calculated for uniform interfaces with equivalent average properties. While the variations in normal stress induce inversely proportional variations in the instability length scale often called nucleation size, we find that the nucleation-size variations by themselves are insufficient to cause such behavior, and that the associated strong heterogeneity in frictional strength is also required. In models with uniform friction strength but the same nucleation-size variation, the nucleation processes of larger-scale events are similar to those on uniform interfaces, with an addition of multiple triggered small-scale earthquakes. Our simulations show that several hypothesized scenarios of earthquake nucleation and foreshocks on natural faults may be viable and reflect different types and levels of heterogeneity on different faults the effects of which, in addition, vary as fault conditions evolve. For example, even with strong fault heterogeneity, some large- scale events have foreshocks and some do not, in the same simulation.</p>
<p>The increasing fault heterogeneity generally leads to increasing complexity of the resulting earthquake sequences and moment-rate release (also called source-time function) of large-scale, fault-spanning events, as intuitively expected, although with some saturation at the higher heterogeneity levels. We find that, in the presence of significant normal-stress heterogeneity, source-time functions of many larger-scale events exhibit prolonged seismic initiation phases, similar to some observations, as the events nucleate from the heterogeneity scale and re-rupture the areas pres-lipped quasi-statically and in foreshocks. The source-time functions also reveal that larger-scale events in our models -- that are arrested by velocity-strengthening barriers -- have a more abrupt arrest phase than natural earthquakes, which places constraints on rupture-arresting mechanisms that should be used in modeling. The initial moment rates are similar for events of different eventual sizes on interfaces with strong heterogeneity, implying that, in those cases, large events are just small events that ran away.</p>https://thesis.library.caltech.edu/id/eprint/14507Accelerated Computational Micromechanics
https://resolver.caltech.edu/CaltechTHESIS:03112022-002649428
Authors: {'items': [{'email': 'zhouhao1.38@hotmail.com', 'id': 'Zhou-Hao', 'name': {'family': 'Zhou', 'given': 'Hao'}, 'orcid': '0000-0002-6011-6422', 'show_email': 'NO'}]}
Year: 2022
DOI: 10.7907/r4jb-4e98
<p>The development of new materials is an important component of many cutting edge technologies such as space technology, electronics and medical devices. The properties of advanced materials involve phenomena across multiple scales. The material may be heterogeneous on a scale that is small compared to that of applications, or may spontaneously develop fine-scale structure. Numerical simulation of such phenomena can be an effective tool in understanding the complex physics underlying these materials, thereby assisting the development and refinement of such materials, but can also be challenging.</p>
<p>This thesis develops a new method to exploit the use of graphical processing units and other accelerators for the computational study of complex phenomena in heterogeneous materials. The governing equations are nonlinear partial differential equations, typically second order in space and first order in time. We propose an operator-splitting scheme to solve these equations by observing that these equations come about by a composition of linear differential constraints like kinematic compatibility and balance laws, and nonlinear but local constitutive equations. We formulate the governing equation as an incremental variational principle. We treat both the deformation and the deformation gradient as independent variables, but enforce kinematic compatibility between them as a constraint using an augmented Lagrangian. The resulting local-global problem is solved using the alternating direction method of multipliers. This enables efficient implementation on massively parallel graphical processing units and other accelerators. We use the study of elastic composites in finite elasticity to verify the method, and to demonstrate its numerical performance. We also compare the performance of the proposed method with that of other emerging approaches.</p>
<p>We apply the method to understand the mechanisms responsible for a remarkable in-plane liquid-like property of liquid crystal elastomers (LCEs). LCEs are rubber-like solids where rod-like nematic molecules are incorporated into the main or a side polymer chain. They undergo isotropic to nematic phase transition accompanied by spontaneous deformation which can be exploited for actuation. Further, they display a soft behavior at low temperatures due to the reorientation of the nematic directors. Recent experiments show that LCEs exhibit an in-plane liquid-like behavior under multiaxial loading, where there is shear strain with no shear stress. Our numerical studies of LCEs provides insights into the director distribution and reorientation in polydomain specimens, and how these lead to the observed liquid-like behavior. The results show good agreement with experimental observations. In addition to providing insight, this demonstrates the ability of our computational approach to study multiple coupled fields.</p>
<p>The core ideas behind the method developed in this thesis are then applied elsewhere. First, we use it to study multi-stable deployable engineering structures motivated by origami. The approach uses two descriptions of origami kinematics, angle/face based approach and vertex/truss based approach independently, and enforces the relationship between them as a constraint. This is analogous to the treatment of kinematic compatibility above where both the deformation and deformation gradient are used as independent variables. The constraint is treated using a penalty. Stable and rigid-foldable configurations are identified by minimizing the penalty using alternate directions, and pathways between stable states are found using the nudged elastic band method. The approach is demonstrated using various examples.</p>
<p>Second, we use a balance law or equilibrium to the problem of determining the stress field from high resolution x-ray diffraction. This experimental approach determines the stress field locally, and errors lead to non-equilibriated fields. It is hypothesized that imposing equilibrium leads to a more accurate stress reconstruction. We use Hodge decomposition to project a non-equilibriated stress field onto the divergence-free (equilibriated) subspace. This projection is numerically implemented using fast Fourier transforms. This method is first verified using synthetic data, and then applied to experimental data obtained from a beta-Ti alloy. It results in large corrections near grain boundaries.</p>https://thesis.library.caltech.edu/id/eprint/14513Methods for Control of Granular Material Attributes
https://resolver.caltech.edu/CaltechTHESIS:08172022-000450303
Authors: {'items': [{'email': 'rabm1993@gmail.com', 'id': 'Buarque-de-Macedo-Robert-Andrew', 'name': {'family': 'Buarque de Macedo', 'given': 'Robert Andrew'}, 'orcid': '0000-0002-2218-4117', 'show_email': 'NO'}]}
Year: 2023
DOI: 10.7907/1h8f-se14
A granular material is a collection of discrete, solid particles. This substance is ubiquitous in nature and industry, with examples ranging from soils, jointed rocks, foodstuffs, ball bearings, powders, and even asteroids. As such, understanding granular materials is necessary for making sense of the physical world. Tremendous progress has been made in directly simulating granular materials in the previous decades, in particular via the discrete element method (DEM). Nevertheless, there remains ample opportunity for manipulating granular materials to achieve specific outcomes by leveraging the DEM. The research presented in this thesis utilizes DEM simulations to develop tools and strategies for manipulating granular material to achieve desired attributes. These attributes include the shape of individual grains, the structure of granular tunnels, and mesoscopic packing characteristics such as packing fraction and coordination number. Optimization of granular materials is considered at 3 different scales: at the single grain scale (100 grains), at the scale of granular structures such as arches (101 grains), and at the mesoscopic scale (103 grains). The first component of this thesis considers automated design of individual grain shapes that embody user-specified morphological properties via genetic algorithms. Next, excavation in granular materials is considered. It is studied how ants can so successfully manipulate granular materials to achieve stable systems by mapping the forces around real ant tunnels. Ant tunnels are simulated using a DEM which can handle arbitrary shaped grains: the Level-Set Discrete Element Method (LS-DEM). Finally, tools are developed for controlling mesoscopic attributes of granular materials as a function of grain shape. To do so, genetic algorithms and a deep generative model are combined with LS-DEM. The methodologies introduced in this thesis serve as a foundation for controlling granular material attributes. Such techniques can be leveraged to engineer granular materials, with applications ranging from swarm robotics, robotic grippers, mechanically tunable fabrics for armor, and robotic excavation.https://thesis.library.caltech.edu/id/eprint/15001Singularity Formation in the High-Dimensional Euler Equations and Sampling of High-Dimensional Distributions by Deep Generative Networks
https://resolver.caltech.edu/CaltechTHESIS:09202022-034157716
Authors: {'items': [{'email': 'zhangsm1995@gmail.com', 'id': 'Zhang-Shumao', 'name': {'family': 'Zhang', 'given': 'Shumao'}, 'orcid': '0000-0003-3071-3362', 'show_email': 'NO'}]}
Year: 2023
DOI: 10.7907/8had-3a90
<p>High dimensionality brings both opportunities and challenges to the study of applied mathematics. This thesis consists of two parts. The first part explores the singularity formation of the axisymmetric incompressible Euler equations with no swirl in ℝⁿ, which is closely related to the Millennium Prize Problem on the global singularity of the Navier-Stokes equations. In this part, the high dimensionality contributes to the singularity formation in finite time by enhancing the strength of the vortex stretching term. The second part focuses on sampling from a high-dimensional distribution using deep generative networks, which has wide applications in the Bayesian inverse problem and the image synthesis task. The high dimensionality in this part becomes a significant challenge to the numerical algorithms, known as the curse of dimensionality.</p>
<p>In the first part of this thesis, we consider the singularity formation in two scenarios. In the first scenario, for the axisymmetric Euler equations with no swirl, we consider the case when the initial condition for the angular vorticity is C<sup>α</sup> Hölder continuous. We provide convincing numerical examples where the solutions develop potential self-similar blow-up in finite time when the Hölder exponent α < α*, and this upper bound α* can asymptotically approach 1 - 2/n. This result supports a conjecture from Drivas and Elgindi [37], and generalizes it to the high-dimensional case. This potential blow-up is insensitive to the perturbation of initial data. Based on assumptions summarized from numerical experiments, we study a limiting case of the Euler equations, and obtain α* = 1 - 2/n which agrees with the numerical result. For the general case, we propose a relatively simple one-dimensional model and numerically verify its approximation to the Euler equations. This one-dimensional model might suggest a possible way to show this finite-time blow-up scenario analytically. Compared to the first proved blow-up result of the 3D axisymmetric Euler equations with no swirl and Hölder continuous initial data by Elgindi in [40], our potential blow-up scenario has completely different scaling behavior and regularity of the initial condition. In the second scenario, we consider using smooth initial data, but modify the Euler equations by adding a factor ε as the coefficient of the convection terms to weaken the convection effect. The new model is called the weak convection model. We provide convincing numerical examples of the weak convection model where the solutions develop potential self-similar blow-up in finite time when the convection strength ε < ε*, and this upper bound ε* should be close to 1 - 2/n. This result is closely related to the infinite-dimensional case of an open question [37] stated by Drivas and Elgindi. Our numerical observations also inspire us to approximate the weak convection model with a one-dimensional model. We give a rigorous proof that the one-dimensional model will develop finite-time blow-up if ε < 1 - 2/n, and study the approximation quality of the one-dimensional model to the weak convection model numerically, which could be beneficial to a rigorous proof of the potential finite-time blow-up.</p>
<p>In the second part of the thesis, we propose the Multiscale Invertible Generative Network (MsIGN) to sample from high-dimensional distributions by exploring the low-dimensional structure in the target distribution. The MsIGN models a transport map from a known reference distribution to the target distribution, and thus is very efficient in generating uncorrelated samples compared to MCMC-type methods. The MsIGN captures multiple modes in the target distribution by generating new samples hierarchically from a coarse scale to a fine scale with the help of a novel prior conditioning layer. The hierarchical structure of the MsIGN also allows training in a coarse-to-fine scale manner. The Jeffreys divergence is used as the objective function in training to avoid mode collapse. Importance sampling based on the prior conditioning layer is leveraged to estimate the Jeffreys divergence, which is intractable in previous deep generative networks. Numerically, when applied to two Bayesian inverse problems, the MsIGN clearly captures multiple modes in the high-dimensional posterior and approximates the posterior accurately, demonstrating its superior performance compared with previous methods. We also provide an ablation study to show the necessity of our proposed network architecture and training algorithm for the good numerical performance. Moreover, we also apply the MsIGN to the image synthesis task, where it achieves superior performance in terms of bits-per-dimension value over other flow-based generative models and yields very good interpretability of its neurons in intermediate layers.</p>https://thesis.library.caltech.edu/id/eprint/15033Shock Compression of Body-Centered Cubic Metals from the Atomistic to Continuum Scale: Iron and Molybdenum
https://resolver.caltech.edu/CaltechTHESIS:05052023-185856720
Authors: {'items': [{'email': 'vatsagandhi@gmail.com', 'id': 'Gandhi-Vatsa-Bhupeshkumar', 'name': {'family': 'Gandhi', 'given': 'Vatsa Bhupeshkumar'}, 'orcid': '0000-0002-6752-113X', 'show_email': 'YES'}]}
Year: 2023
DOI: 10.7907/kwf1-7y79
<p>Fundamental understanding of material behavior under extreme conditions is crucial for designing high strength, light weight, and high temperature resistance materials, and for modeling planetary physics problems such as behavior of the core and impact phenomena. Under extreme conditions, materials not only exhibit a different mechanical, thermal, and failure response but can also undergo structural changes, such as phase transformations, which significantly alters their material properties. This motivates studying their dynamic response and developing constitutive models for applications such as hypersonics, high speed manufacturing, impact and blast of structures, aircraft and spacecraft shielding, meteorite impact, and collision of planets. Despite the importance, experimental investigations of shock induced phase transitions, inelastic material behavior, and elastic-plastic anisotropy under multi-axial stress states and at microscopic length scales of metals still remains largely unexplored. Thus, the focus of this thesis is on the shock compression behavior of body-centered cubic (BCC) metals, specifically iron and molybdenum, under compression-shear loading and at the atomistic-continuum spatial scales. In particular, the role of solid-solid phase transformation of body-centered cubic (BCC) iron on material strength and the orientation dependence of single crystal molybdenum on its elastic-plastic transition is investigated.</p>
<p>Iron in its high pressure hexagonal close-packed (HCP) ϵ-phase is critical in geological and planetary applications such as inner cores of rocky planets and hypervelocity impacts of asteroids, and meteorites. Thus, understanding plasticity behavior of iron under these condensed matter states is important to develop more accurate models for such applications and to understand deformation mechanisms of inner planetary cores. Because the ϵ-phase is unstable, iron reverts to its ambient α-phase (BCC) upon release making it difficult to probe the strength behavior using conventional methods. Additionally, solid-solid phase transformations provide a unique opportunity to study material strength as they are crucial for expanding the design space for various load-bearing applications. In the first part of the thesis, the pressure dependent dynamic strength behavior of both the ambient BCC α-phase and high-pressure HCP ϵ-phase of iron at strain rates on the order of 1 X 10⁵ s⁻¹ and pressures up to 42 GPa is investigated. Pressure shear plate impact experiments are conducted using a sandwich configuration to decouple the effect of pressure and shear thereby allowing to probe shear strength once the sample reaches an equilibrated state of pressure but prior to release. The strength of the ϵ-phase is observed to be more than double the strength of α-phase possibly due to microstructural evolution during phase transformation. Additionally, the evolution of yield properties with pressure, temperature, and strain is presented for the first time, enabling more accurate modeling of extreme deformation phenomena associated with iron-rich celestial bodies such as planetary collisions.</p>
<p>Molybdenum, its alloys, and other body-centered cubic (BCC) refractory metals are critical in geological and planetary applications such as structural properties of terrestrial planetary composition, formation of the earth-moon system, and hypervelocity impacts of rocky planets. Additionally, the high temperature specific strength, creep resistance, and ductility of BCC refractory metals make them ideal for aerospace and armor/anti-armor applications. Under high strain-rate inelastic loadings, the macroscopic response of these metals is often influenced by the atomistic mechanisms including dislocation motion and deformation twinning. Current material models rely on investigations that involve continuum measurements followed by postmortem microstructural analysis of recovered samples. However, these may not reflect the material behavior during the passage of the shock wave and, thus, requires real-time in-situ atomistic characterization to link the microstructure to macroscopic response. In the second part of the thesis, plate impact experiments coupled with both laser interferometry continuum measurements and <i>in-situ</i> dynamic Laue x-ray diffraction (XRD), at the Advanced Photon Source (APS), are conducted on single crystal molybdenum. Here, the role of crystal orientation, either [100] or [111], on deformation mechanisms during the elastic-plastic transition and the steady state response is explored at pressures ranging from 9-19 GPa. Complementary simulation methodology is developed to analyze the evolution of the Laue diffraction spots captured during impact. By extracting the lattice strain and stresses from XRD images, dislocation slip along [110]〈111〉 and [112]〈111〉 is found to be the probable deformation mechanism during compression with negligible anisotropy observed at the Hugoniot state. For the first time, real-time evidence of molybdenum undergoing deformation twinning along [112̅]〈111〉 during shock release beyond a critical pressure of 16 GPa irrespective of the loading orientation is presented.</p>https://thesis.library.caltech.edu/id/eprint/15152Modeling Deformations of Active Rods, Ribbons, and Plates
https://resolver.caltech.edu/CaltechTHESIS:07202022-212008345
Authors: {'items': [{'email': 'kevinakorner@gmail.com', 'id': 'Korner-Kevin-Andreas', 'name': {'family': 'Korner', 'given': 'Kevin Andreas'}, 'orcid': '0000-0002-2967-9657', 'show_email': 'NO'}]}
Year: 2023
DOI: 10.7907/2zb0-m166
<p>Slender structures are mechanical components which have at least one spatial dimension much smaller than another. Some canonical examples are beams, rods, ribbons, plates, and shells. Although these systems have been studied for many centuries, the focus of development has generally been limited to small strains and the onset of buckling modes. Outside of this regime, both geometric and material non-linearities contribute significant complexity to the analytical and computational techniques which can be applied to these problems. Despite this, large deformations demonstrate tremendous potential in engineering applications, particularly with soft materials. This thesis examines various methods of modeling slender structures. We focus on large strain behaviors, often accentuated by spontaneous strains generated with active materials. These systems demonstrate a wide range of interesting and useful behaviors, such as bifurcations, snap-through, and cyclic deformations.</p>https://thesis.library.caltech.edu/id/eprint/14984Physics-Based and Data-Driven Computational Models of Inelastic Deformations
https://resolver.caltech.edu/CaltechTHESIS:05312023-212652388
Authors: {'items': [{'email': 'ericocegueda@berkeley.edu', 'id': 'Ocegueda-Eric', 'name': {'family': 'Ocegueda', 'given': 'Eric'}, 'orcid': '0000-0001-7845-6890', 'show_email': 'NO'}]}
Year: 2023
DOI: 10.7907/3gqd-zp93
<p>Crystalline materials inevitably exhibit inelastic deformation when applied to large enough loads. The behavior in this inelastic regime is a coupling of physics across several length scales: from initiating as defects at the atomic scale, interacting with crystal defects, and finally spanning multiple grains and influencing macroscopic stress behavior. These length-scale interactions make predicting material response an open challenge and an avenue for leveraging microscale physics for material design. This thesis examines developing physics-based and data-driven computational models to capture complex inelastic behavior at appropriate length scales.</p>
<p>First, we present a mesoscale model for capturing deformation twinning physics at the polycrystal scale. Mechanical twinning is a form of inelastic deformation observed in low-symmetry crystals, such as magnesium and other hexagonal close-packed (hcp) metals. Twinning, unlike slip, forms as bands collectively across grains with complex local morphology propagating into bulk behavior, drastically affecting strength and ductility. We, thus, propose a model where twinning is treated using a phase-field approach, while dislocation slip is considered using crystal plasticity. Lattice reorientation, length-scale effects, interactions between dislocations and twin boundaries, and twin and slip interactions with grain boundaries are all carefully considered. We first outline the model and its implementation using a novel approach of accelerated computational micromechanics in a two-dimensional, single twin-slip system, polycrystal case to demonstrate its capabilities. Finally, we consider multiple twin-slip systems and conduct three-dimensional simulations of polycrystalline magnesium. We summarize the insights gained from these studies and the implications on the macroscale behavior of hcp materials.</p>
<p>The second part of the thesis focuses on data-driven models for capturing microscopic history-dependent phenomena for multiscale modeling applications. The multiscale modeling framework has seen increased usage over the last few decades for its ability to capture complex material behavior over a range of time/length scales by solving a macroscale problem directly with a constitutive relation defined implicitly by the solution of a microscale problem. However, this implementation is computationally expensive -- needing to solve a microscale problem at each point and time of the macroscopic calculation. In this study, we examine the use of machine learning by utilizing data generated through repeated solutions of a microscale problem to: (i) gain insights into the history dependent macroscopic internal variables that govern the response and (ii) create a computationally efficient surrogate. We do so by introducing a recurrent neural operator, which can provide accurate approximations of the stress response and insights into the physics of the macroscopic problem. We illustrate these capabilities on a laminate composite and polycrystal made of elasto-viscoplastic materials, summarize insights on the learned internal variables, and accuracy of stress predictions.</p>https://thesis.library.caltech.edu/id/eprint/15246Mechanical Response of Lattice Structures under High Strain-Rate and Shock Loading
https://resolver.caltech.edu/CaltechTHESIS:09152022-195715025
Authors: {'items': [{'email': 'jackweeks8@gmail.com', 'id': 'Weeks-John-Stephen', 'name': {'family': 'Weeks', 'given': 'John Stephen IV'}, 'orcid': '0000-0002-7971-5919', 'show_email': 'YES'}]}
Year: 2023
DOI: 10.7907/9v5k-1157
<p>Lattice structures are a class of architected cellular materials composed of similar unit cells with structural components of rods, plates, or sheets. Current additive manufacturing (AM) techniques allow control and tunability of unit cell geometries, which enable lattice structures to demonstrate exceptional mechanical properties such as high stiffness- and strength-to-mass ratios and energy absorption. Lattice structures exist on two length scales corresponding to the unit cell and continuum material, and therefore demonstrate mechanical behavior dependent on structural geometry and base material. These effects extend to the dynamic regime where lattice structures demonstrate distinct deformation modes under varying strain-rate loading. Experimental investigation of the dynamic and shock compression behavior of lattice structures remains largely unstudied and is the central focus of this thesis where the high strain-rate, transient dynamic, and shock compression behaviors of different topologies of lattice materials are explored.</p>
<p>The first part of this thesis investigates the high strain-rate behavior of lattice structures via polymeric Kelvin lattices with rod- and plate-based geometries and relative densities of 15-30%. High strain-rate behavior is characterized by deformation modes similar to that of low strain-rate behavior. High strain-rate experiments (1000/s) are performed and validated using a viscoelastic polycarbonate split-Hopkinson (Kolsky) pressure bar system coupled with high-speed imaging. Both low and high strain-rate experiments show the formation of a localized deformation band which initiates in the middle of the specimen. Strain-rate effects of lattice specimens are observed to correlate with effects of the base polymer material and mechanical properties depend strongly on the relative density of the lattice specimen and exhibit distinct scaling with geometry type (rod, plate) and loading rate despite a similar unit cell shape. Explicit finite element simulations with a tensile failure material model are then used to validate deformation modes and scaling/property trends, and match those observed in experiments. </p>
<p>The second part of this thesis explores the transient dynamic and transition to shock compression behavior of lattice structures using polymeric lattices with cubic, Kelvin, and octet-truss topologies with relative densities of about 8%. Transient dynamic behavior is characterized by a compaction wave initiating at an impact surface and additional deformation bands with modes similar to low strain-rate modes of deformation. Dynamic testing is conducted through gas gun direct impact experiments (25 - 70 m/s) with high-speed imaging coupled with digital image correlation (DIC) and a polycarbonate Hopkinson pressure bar. Full-field DIC measurements are used to characterize distinct mechanical behaviors induced by topology such as elastic wave speeds, deformation modes, and particle velocities. At lower impact velocities, a transient dynamic response is observed. At higher impact velocities, shock compression behavior occurs and is characterized by a sole compaction wave initiating and propagating from the impact surface of the lattice. One-dimensional continuum shock theory with Eulerian forms of the Rankine-Hugoniot jump conditions is used with full-field measurements to quantify a non-steady shock response and the varied effect of topology on material behaviors. </p>
<p>The final part of this thesis examines the steady-state shock compression behavior of lattice structures through stainless steel 316L (SS316L) octet-truss lattices with relative densities of 10-30%. Powder gun plate impact experiments (270 - 390 m/s) with high-speed imaging and DIC are conducted and reveal a two-wave structure consisting of an elastic precursor wave and a planar compaction (shock) wave. Local shock parameters of lattice structures are defined using full-field DIC measurements and a linear shock velocity (u<sub>s</sub>) versus particle velocity (u<sub>p</sub>) relation is found to approximate measurements with a unit slope and linear fit constant equal to the crushing speed. One-dimensional continuum shock analysis is again performed using Eulerian forms of the Rankine-Hugoniot jump conditions to extract relevant mechanical quantities. Explicit finite element simulations of the lattice specimens using the Johnson-Cook constitutive model exhibit similar shock behavior to experiments. The simulations reveal a linear u<sub>s</sub>-u<sub>p</sub> relation and corresponding Hugoniot calculations agree with experimental trends. Notably, 1D shock theory is applied to simulations without resorting to a u<sub>s</sub>-u<sub>p</sub> relation for the base material, which characterizes this deformation regime and compaction wave as a `structural shock.'</p>
<p>Major contributions of this thesis include experimental demonstration of ranged strain-rate behaviors for lattice structures of various base materials and topologies including low strain-rate, high strain-rate, transient dynamic, and shock compression regimes; use of full-field quantitative visualization techniques for local mechanical behavior and shock analysis; and finally, characterization of a 'structural' shock compression regime in lattice structures.</p>https://thesis.library.caltech.edu/id/eprint/15030Time-Dependent Failure of Thin-Ply Composite Laminates
https://resolver.caltech.edu/CaltechTHESIS:05312023-210300139
Authors: {'items': [{'email': 'ubamanyu.k@gmail.com', 'id': 'Ubamanyu-Kanthasamy-Uba', 'name': {'family': 'Ubamanyu', 'given': 'Kanthasamy (Uba)'}, 'orcid': '0000-0002-3679-6173', 'show_email': 'YES'}]}
Year: 2023
DOI: 10.7907/x286-g488
<p>The demand for larger and lighter structures for next-generation space designs necessitates the use of deployable structures. Among the materials that hold promise for such applications, thin-laminate fiber composites with thicknesses less than 200 μm stand out due to their strength-to-weight ratio, packaging efficiency, and ability to deploy using stored strain energy. However, designing deployable structures with thin-laminate composites is challenging as they need to be stiff enough to withstand loads during deployment while also having a small volume in the packaged configuration. Complicating matters further, stress relaxation of the polymer matrix within the composite during long-term stowage in response to an imposed curvature can drastically impact both the deployment process and the performance of the structure in its deployed state, even leading to catastrophic failure in the stowed configuration.</p>
<p>This thesis presents a comprehensive study of the time-dependent failure behavior of thin-laminate fiber composites under bending, with a focus on a fundamental material-level understanding. The work is divided into three main parts. First, a novel test method called Flattening to Rupture (FTR) test was developed to effectively load composite coupons under long-term bending, enabling the measurement of time-dependent rupture and identification of the underlying failure mechanisms. Second, numerical simulations using the Abaqus/Standard finite element software were developed to understand the sequence of rupture events and the influence of several parameters that affect time-dependent rupture. Finally, a statistical approach was proposed to model the stochastic nature of the failure of thin composite laminates.</p>
<p>The contributions of this thesis extend the understanding of the microscale failure mechanisms involved in the time-dependent failure of fiber composites. These new insights pave the way for the efficient design of tightly and safely packaged deployable structures under long-term loading. The findings of this research can be utilized to optimize the design and performance of deployable space structures made of fiber composites, leading to new technologies that can advance space exploration.</p>https://thesis.library.caltech.edu/id/eprint/15245Optimal Design of Soft Responsive Actuators and Impact Resistant Structures
https://resolver.caltech.edu/CaltechTHESIS:06022023-013553184
Authors: {'items': [{'email': 'akers049@gmail.com', 'id': 'Akerson-Andrew-James', 'name': {'family': 'Akerson', 'given': 'Andrew James'}, 'orcid': '0000-0002-4382-1226', 'show_email': 'YES'}]}
Year: 2023
DOI: 10.7907/dx05-p030
<p>The rapid pace of development of new responsive and structural materials along with significant advances in synthesis techniques, which may incorporate multiple materials in complex architectures, provides an opportunity to design functional devices and structures of unprecedented performance. These include implantable medical devices, soft-robotic actuators, wearable haptic devices, mechanical protection, and energy storage or conversion devices. However, the full realization of the potential of these emerging techniques requires a robust, reliable, and systematic design approach. This thesis explores this through optimal design methods. By investigating pressing engineering problems which exploit these advances in materials and manufacturing, we develop optimal design methods to realize next-generation structures.</p>
<p>We begin by reviewing classical optimal design methods, the mathematical difficulties they raise, and the practical approaches of overcoming these difficulties. We introduce the canonical problem of compliance minimization of a linear elastic structure. After illustrating the intricacies of this seemingly simple problem, we detail contemporary methods used to address the underlying mathematical issues.</p>
<p>We then turn to extending these classical methods for emerging materials and technologies. We must incorporate optimal design with rich physical models, develop computational approaches for efficient numerics, and study mathematical regularization to obtain well-posed optimization problems. Additionally, care must be taken when selecting an application-tailored objective function which captures the desired behavior. Finally, we must also take into account manufacturing constraints in scenarios where the fabrication pathway affects the structural layout. We address these issues by exploring model optimal design problems. While these serve to ground the fundamental study, they are also relevant, pressing engineering problems.</p>
<p>The first application we consider is the design of responsive structures. Recent developments in material synthesis and 3D printing of anisotropic materials, such as liquid crystal elastomers (LCE), have facilitated the realization of structures with arbitrary morphology and tailored material orientation. These methods may also produce integrated structures of passive and active material. This creates a trade-off between stiffness and actuation flexibility when designing such structures. Thus, we turn to optimal design. This is complicated by anisotropic behavior and finite deformations, manufacturing constraints, and choice of objective function. Like many optimal design problems, the naive formulations are ill-posed giving rise to mesh dependence, lack of convergence, and other numerical deficiencies. So, starting with a simple setting using linear kinematics and working all the way to finite deformation, we develop a systematic mathematical theory that motivates, and then rigorously proves, an alternate well-posed formulation. We examine suitable objective functions, before studying a series of examples in both small and finite deformation. However, the manufacturing process constrains the design as extrusion-based 3D printing aligns nematic directors along the print path. We extended the formulation with these considerations to produce print-aware designs while also recovering the fabrication pathway. We demonstrate the formulation by designing and producing physical realizations of these actuators.</p>
<p>Next, we explore optimal design of impact resistant structures. The complex physics and numerous failure modes of structural impact creates challenges when designing for impact resistance. Here, we apply gradient-based topology optimization to the design of such structures. We start by constructing a variational model of an elastic-plastic material enriched with gradient phase-field damage, and present a novel method to accurately and efficiently compute its transient dynamic time evolution. Sensitivities over this trajectory are computed through the adjoint method, and we develop a numerical method to solve the resulting adjoint dynamical system. We demonstrate this formulation by studying the optimal design of 2D solid-void structures undergoing blast loading. Then, we explore the trade-offs between strength and toughness in the design of a spall-resistant structure composed of two materials of differing properties undergoing dynamic impact.</p>
<p>We conclude by summarizing the presented work and discuss the contribution towards the overarching goal of optimal design for emerging materials technologies. From our study, key issues have arose which must be addressed to further progress the field. We examine these and lay a pathway for future studies which will allow optimal design to tackle complicated, pressing engineering problems.</p>https://thesis.library.caltech.edu/id/eprint/15274Design, Fabrication, and Mechanical Analysis of Intertwined and Frictional Micro-Architected Materials
https://resolver.caltech.edu/CaltechTHESIS:06242022-190238579
Authors: {'items': [{'email': 'wmoestopo@gmail.com', 'id': 'Moestopo-Widianto-Putra', 'name': {'family': 'Moestopo', 'given': 'Widianto Putra'}, 'orcid': '0000-0002-7617-4280', 'show_email': 'NO'}]}
Year: 2023
DOI: 10.7907/ycqd-1f27
<p>Natural biomaterials, e.g., shells, bone, and wood, are typically comprised of hard and soft constituent materials that are hierarchically ordered to achieve mechanical resilience, light weight, and multifunctionality. Advanced fabrication techniques have enabled the creation of precisely architected materials with exceptional mechanical properties unattainable by their constituent materials, yet they are often designed with fully interconnected structural members whose junctions are detrimental to their performance because they serve as stress concentrations for damage accumulation and lower mechanical resilience. Most studies have also focused on understanding the stretching, bending, and buckling of the structural members, while explorations toward contact interactions within structural members remain limited. We address these challenges by (i) introducing a new three-dimensional (3D) hierarchical architecture in which fibers are interwoven to construct effective beams, (ii) introducing the concept of knots into the hierarchical architecture framework, and (iii) developing a model to study the effects of structural element length scale on the energy dissipation capability of a frictional architected material.</p>
<p>We first explore the effective lattice response of hierarchical woven microlattices, and we demonstrate the superior ability of woven architectures to achieve high tensile and compressive strains via smooth reconfiguration of woven microfibers in the effective beams and junctions without failure events. We study how fiber topology and constituent materials influence the mechanical behaviors of hierarchical intertwined structures, and we compare our results with theory. Our study reveals that knot topology allows a new regime of deformation capable of shape-retention, leading to increased absorbed energy and failure strain compared to structures with woven topology. Agreements between experimental results and a model for long overhand knots suggest that the model can aid the optimization of the mechanical performance of microwoven materials. We then adapt classical contact mechanics and adhesion models to explore the influence of the size of structural elements in a frictional architected material on its energy dissipation capability. Our model shows that the energy dissipation capability of our frictional architected material can be significantly increased when it is scaled down from the mm-scale to the sub-micron length scale.</p>
<p>Our woven hierarchical design offers a pathway to make traditionally stiff and brittle materials more deformable and introduces a new building block for 3D architected materials with complex nonlinear mechanics. The unique tightening mechanism introduced by knotted topology unlocks new ways to create shape-reconfigurable, highly extensible, and extremely energy-absorbing bulk, 3D architected materials with mechanical properties that can be tuned not only by their geometries and bulk properties, but also by the surface interactions experienced by the structural elements. Lastly, our modeling work shows the potential of creating highly dissipative architected materials with shape-retention capability via carefully architected structural elements.</p>https://thesis.library.caltech.edu/id/eprint/14963