Committee Feed
https://feeds.library.caltech.edu/people/Ortiz-M/committee.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenSat, 13 Apr 2024 01:42:10 +0000Dynamic failure behavior of ceramics under multiaxial compression
https://resolver.caltech.edu/CaltechETD:etd-11032003-101839
Authors: {'items': [{'email': 'wchen@purdue.edu', 'id': 'Chen-Weinong', 'name': {'family': 'Chen', 'given': 'Weinong'}, 'show_email': 'NO'}]}
Year: 1995
DOI: 10.7907/0NNE-JD20
An experimental technique has been developed that is capable of (1) dynamically loading the specimen in multiaxial compression; (2) controlling the stress state in the specimen in the range from uniaxial stress to uniaxial strain; and (3) allowing the recovery of the sample after loaded by a single, well defined pulse for the characterization of the failure mode. In this technique, cylindrical ceramic specimens were loaded in the axial direction using a split Hopkinson pressure bar modified to apply a single loading pulse, and were confined laterally either by shrink fit sleeves, or by eletro-magnetic force.
Quasi-static and dynamic multiaxial compression experiments have been performed on a machinable glass ceramic, Macor, and a monolithic engineering ceramic, sintered aluminum nitride (A1N). The cylindrical ceramic specimens were confned laterally by shrink fit sleeves: the amount of confining pressure (0-230 MPa) was varied by using different sleeve materials. The quasi-static axial load was applied by a hydraulic driven Material Test System (MTS), whereas the dynamic axial load was provided by a modified split Hopkinson (Kolsky) pressure bar (SHPB). Under both quasi-static and dynamic loading conditions, the experimental results for both materials showed that the failure mode changed from fragmentation by axial splitting under conditions of uniaxial stress (without lateral confinement) to localized deformation on faults under moderate lateral confinement. The fault initiation process was studied experimentally in detail. Based on the experimental results, a compressive brittle failure process was summarized. A transition from brittle to ductile behavior was observed in Macor under high confinement pressure which was achieved using a second sleeve around the inner sleeve. The compressive failure strengths of both materials increased with increasing confinement pressure under both quasi-static and dynamic loading conditions. The highest dynamic compressive strengths of Macor and A1N measured in the experiments were 1.35 GPa and 5.40 GPa, respectively, whereas their quasi-static compressive strength were measured to be 0.43 GPa and 2.5 GPa, respectively.
Based on the experimental results on A1N together with available data in the literature, a failure/flow criterion was developed for ceramic materials under multiaxial loading. A Mohr-Coulomb criterion and an improved Johnson-Holmquist model were found to fit the experimental data for brittle failure, whereas the materials exhibited pressure insensitive plastic flow at high pressures. Observations made in other types of dynamic experiments (e.g., shock wave loading) were rationalized based on the postulated failure mechanisms and the possibility of plastic flow beyond the Hugoniot elastic limit (HEL). The effect of various material properties on the failure behavior was investigated using the proposed failure criterion. The applicability of the present model to a range of ceramics was also explored and the limitations of the model were outlined.
https://thesis.library.caltech.edu/id/eprint/4379The evolution of damage in ceramic matrix composites
https://resolver.caltech.edu/CaltechETD:etd-01072008-112449
Authors: {'items': [{'id': 'Walter-M-E', 'name': {'family': 'Walter', 'given': 'Mark E.'}, 'show_email': 'NO'}]}
Year: 1996
DOI: 10.7907/w4b4-dx66
In an effort to better understand the evolution of damage in brittle matrix composites, the mechanical behavior of a ceramic matrix composite, unidirectional SiC/CAS (SiC fibers reinforcing a calcium aluminosilicate matrix), was studied. The presented results are based on uniaxial tension experiments for specimens with the fibers aligned in the loading direction. Post-test optical and scanning electron microscopy was also used to identify the various micromechanisms of damage; axial and transverse strain gauges on all four gage section surfaces and in situ acoustic emission and ultrasonic wave speed measurements were used to monitor the evolution of damage. The experimental results demonstrate the existence of "zones of deformation" which are associated with the onset of different damage mechanisms. The energy dissipated in each of these zones was calculated. It is shown that the observed stress-strain behavior can be qualitatively explained in terms of the material properties of the matrix and the fiber, the material processing, and the postulated zones of deformation.
The experimental results for SiC/CAS were compared with an existing shear-lag model, and the shortcomings of the model are discussed. By approximating matrix cracks as penny shaped cracks, a micromechanical model was used to estimate the change in the axial modulus of the composite. These results also present another way to interpret the acoustic emission data.
The evolution of damage in the SiC/CAS experiments was found to be strain rate dependent even within the quasi-static strain rate regime. For higher rate experiments, the transition from elastic to matrix cracked occurred at a stress level that was nearly twice that of the same transition in the lower rate experiments. This phenomenon and the mechanisms which cause it was further investigated with a model material system (a brittle epoxy resin sandwiched between aluminum strips). In situ quantification of the stress during damage initiation and propagation was realized by the optical method of Coherent Gradient Sensing. Based on these results, the reasons for strain rate dependence of the composite are postulated.
Detailed understanding of aspects of the evolution of in brittle matrix composites was achieved with finite element simulations. This modeling was based on an axisymmetric unit cell composed of a fiber and its surrounding matrix. The unit cell was discretized into linearly elastic elements for the fiber and the matrix and cohesive elements which allow cracking in the matrix, fiber-matrix interface, and fiber. The cohesive elements failed according to critical stress and critical energy release rate criteria (in shear and/or in tension). After failing, the cohesive elements could slide with Coulomb friction. The tension and shear aspects of failure were uncoupled. The cohesive elements were used to simulate a Dugdale penny shaped crack in a homogeneous cylinder; results compared well to the analytical solution. In order to solve the composite axisymmetric unit cell problem, inertia and viscous damping were added to the formulation. The resulting dynamic problem was solved implicitly using the Newmark Method. Results were compared to the experiment by assuming that only a given number of unit cells were active at any point during the simulation. The effects of changing material properties (e.g., interface strength and toughness and matrix toughness) and loading rate are discussed. Several aspects of the experimentally observed material response of SiC/CAS composite were reproduced by the numerical simulations.
https://thesis.library.caltech.edu/id/eprint/58Shape-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/705The Multiscale Finite Element Method (MsFEM) and Its Applications
https://resolver.caltech.edu/CaltechETD:etd-11102005-090314
Authors: {'items': [{'email': 'efendiev@math.tamu.edu', 'id': 'Efendiev-Yalchin-R', 'name': {'family': 'Efendiev', 'given': 'Yalchin R.'}, 'orcid': '0000-0001-9626-303X', 'show_email': 'NO'}]}
Year: 1999
DOI: 10.7907/2QJN-2S06
<p>Multiscale problems occur in many scientific and engineering disciplines, in petroleum engineering, material science, etc. These problems are characterized by the great deal of spatial and time scales which make it difficult to analyze theoretically or solve numerically. On the other hand, the large scale features of the solutions are often of main interest. Thus, it is desirable to have a numerical method that can capture the effect of small scales on large scales without resolving the small scale details.</p>
<p>In the first part of this work we analyze the multiscale finite element method (MsFEM) introduced in [28] for elliptic problems with oscillatory coefficients. The idea behind MsFEM is to capture the small scale information through the base functions constructed in elements that are larger than the small scale of the problem. This is achieved by solving for the finite element base functions from the leading order of homogeneous elliptic equation. We analyze MsFEM for different situations both analytically and numerically. We also investigate the origin of the resonance errors associated with the method and discuss the ways to improve them.</p>
<p>In the second part we discuss flow based upscaling of absolute permeability which is an important step in the practical simulations of flow through heterogeneous formations. The central idea is to compute the upscaled, grid-block permeability from fine scale solutions of the flow equation. It is well known that the grid block permeability may be strongly influenced by the boundary conditions imposed on the flow equations and the size of grid blocks. We analyze the effects of the boundary conditions and grid block sizes on the computed grid block absolute permeabilities. Moreover, we employ the ideas developed in the analysis of MsFEM to improve the computed values of absolute permeability.</p>
<p>The last part of the work is the application of MsFEM as well as upscaling of absolute permeability on upscaling of two-phase flow. In this part we consider coarse models using MsFEM. We demonstrate the efficiency of these models for practical problems. Moreover, we show that these models improve the existing approaches.</p>https://thesis.library.caltech.edu/id/eprint/4487Micromechanical 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/6119From Elementary Excitations to Microstructures: the Thermodynamics of Metals and Alloys Across Length Scales
https://resolver.caltech.edu/CaltechTHESIS:12142010-083329053
Authors: {'items': [{'email': 'manleyme@ornl.gov', 'id': 'Manley-Michael-Edward', 'name': {'family': 'Manley', 'given': 'Michael Edward'}, 'show_email': 'NO'}]}
Year: 2001
DOI: 10.7907/WECC-4662
<p>An experimental investigation has been made into the components that determine the phase stability of metals and alloys. Contributions were found to be important across many length scales from electronic excitations to atomic vibrations and finally microstructural strains at the continuum level. The metals and alloy that have been studied are U, Ce, and Pd<sub>3</sub>V.</p>
<p>Time-of-flight (TOF) inelastic neutron scattering spectra were measured on the three crystalline phases of uranium at temperatures from 50 K to 1213 K. Phonon density of states (DOS) curves were obtained from these spectra. For the α-phase, a large decrease in phonon energies with increasing temperature was observed over the entire temperature range. Analysis of the vibrational power spectrum showed that the phonon softening originates with continuous softening of a harmonic solid, as opposed to vibrations in anharmonic potentials. Without anharmonicty, it must be that thermal excitations of the electronic structure are changing the interatomic forces. State-of-the-art electronic band structure calculations are based on the assumption that temperature effects on the electronic structure can be neglected when compared to volume effects (where the volume effects are just a manifestation of anharmonicity). The present results turn that problem upside down by showing that temperature effects are actually more important than volume effects. Vibrational entropies of the phase transitions were (S<sup>β</sup>-S<sup>α</sup>)<sub>vib</sub> = (0.15±0.1) k<sub>B</sub>/atom and (S<sup>γ</sup> -S<sup>β</sup>)<sub>vib</sub> = (0.36±0.1) k<sub>B</sub>/atom.The former accounts for about 35% and the latter 65% of the total entropy of the phase transition. The remaining entropy must be electronic.</p>
<p>TOF inelastic neutron scattering spectra were measured on cerium at temperatures near the fcc (γ) to bcc (δ) transition temperature. Phonon DOS curves were extracted from data acquired over a wide range of momentum transfers. A large softening of the phonon DOS was found in going from γ-cerium to δ-cerium, and this accounts for an increase in vibrational entropy of (0.71 ± 0.05) k<sub>B</sub>/atom. To be consistent with the latent heat of the γ-δ transition, this increase in vibrational entropy must be accompanied by a large decrease in electronic entropy. The results not only confirm the recent discovery of a significant electronic contribution to the γ-δ transition but also suggest that it may be twice as large as previously reported.</p>
<p>TOF inelastic neutron scattering spectra were measured on β-cerium (dhcp) and γ-cerium (fcc) near the phase transition temperature. Phonon densities of states (DOS) were extracted from the TOF spectra. A softening of the phonon DOS occurs in the transition from β-cerium to γ-cerium, accounting for an increase in vibrational entropy of ΔS<sup>γ-β</sup><sub>vib</sub> = (0.09 ±0.05) k<sub>B</sub>/atom. Crystal field levels were extracted from the magnetic scattering for both
phases. The entropy calculated from the crystal field levels and a fit to calorimetry data from the literature was significantly larger in β-cerium than γ-cerium below room temperature. The difference was found to be negligible at the experimental phase transition temperature. There was a contribution to the specific heat from Kondo spin fluctuations that was consistent with the quasielastic magnetic scattering, but the difference between phases was negligible. To be consistent with the latent heat of the β-γ transition, the increase in vibrational entropy at the phase transition may be accompanied by a decrease in electronic entropy not associated with the crystal field splitting or spin fluctuations. At least three sources of entropy need to be considered for the β-γ transition in cerium.</p>
<p>Differences in the heat capacity and thermal expansion of cubic (fcc-disordered) and tetragonal (DO<sub>22</sub>-ordered) Pd<sub>3</sub>V were measured from 40 K to 315 K. Below 100 K the heatcapacity difference was consistent with harmonic vibrations. At higher temperatures, however, the data show significant anharmonic effects. Measurements of elastic constants, densities, and thermal expansion showed that the anharmonic volume expansion contribution (C<sub>p</sub> – C<sub>v</sub>) could account for only about one-third of this anharmonic heat capacity difference. The remainder may originate with elastic and plastic deformation of the polycrystalline microstructure. Strain energy from anisotropic thermal contractions of grains in the tetragonal ordered phase contributes to the heat capacity, but some of this strain energy is eliminated by plastic deformation. The vibrational entropy difference of disordered and ordered Pd<sub>3</sub>V was estimated to be S<sup>dis</sup> – S<sup>ord</sup> = (+0.035± 0.001) k<sub>B</sub>//atom at 300 K, with 70% of this coming from anharmonic effects.</p>
<p>The microstructural contribution to the heat capacity of α-uranium was determined bymeasuring the heat capacity difference between polycrystalline and single crystal samples from 77 K to 320 K. When cooled to 77 K and then heated to about 280 K, the uranium microstructure released (3±2) J/mol of strain energy. On further heating to 300 K the microstructure absorbed energy as the microstructure began to redevelop microstrains. Neutron diffraction measurements on polycrystals predicted the total strain energy stored in the microstructure to be (3.7±0.5) J/mol at 77 K and (1±0.5) J/mol at room temperature in good agreement with the calorimetry.</p>https://thesis.library.caltech.edu/id/eprint/6203Molecular dynamics (MD) studies on phase transformation and deformation behaviors in FCC metals and alloys
https://resolver.caltech.edu/CaltechETD:etd-09172008-112120
Authors: {'items': [{'id': 'Qi-Yue', 'name': {'family': 'Qi', 'given': 'Yue'}, 'show_email': 'NO'}]}
Year: 2001
DOI: 10.7907/9NXP-E603
This thesis focused on the phase transformation and deformation in face center cubic (FCC) metals and alloys. These studies use the new quantum modified Sutton-Chen (QMSC) many-body potentials for Cu, Ni, Ag, and Au and for their alloys through simple combination rules. Various systems and processes are simulated by standard equilibrium molecular dynamics (MD), quasi-static equilibrium MD and non-equilibrium MD (NEMD), cooperated with different periodic boundary conditions. The main topics and their outlines are listed as the following:
1) Melting, glass formation, and crystallization processes in bulk alloys: Using cooling rates in the range of 2*10[superscript 12] to 4*10[superscript 14]K/s, we find that CuNi and pure Cu always form an FCC crystal while Cu[subscript 4]Ag[subscript 6] always forms a glass (with Tg decreasing as the quench rate increases), which confirms the role of size mismatch in glass formability and validates the accuracy of the force field.
2) The size effects in melting and crystallization in Ni nano clusters, ranging 100 to 8007 atoms: We find a transition from cluster or molecular behavior below ~500 atoms to a mesoscale nanocrystal regime (with well-defined bulk and surface properties and surface melting processes, which leads to T[subscript m,N] = T[subscript m,bulk] - α N[superscript -1/3]) above ~750 atoms. Cooling from the melt leads first to supercooled clusters with icosahedral local structure, then for N>500 the supercooled clusters transform to FCC grains, while clusters with N<500 form icosahedral structures.
3) The deformation behavior of metallic nanowires of pure Ni, NiCu and NiAu alloys, under high rates of uniaxial tensile strain, ranging from 5*10[superscript 8]/s to 5*10[superscript 10]/s: These nanowires are too small to sustain dislocations; instead we find that deformation proceeds through twinning and coherent slipping mechanisms at low strain rate, and amorphization at high strain rate. We find that critical strain rate, beyond which the crystal transformed into glassy state, for NiAu (13% size mismatch) is 100 times slower than that for NiCu (2.5% size mismatch). Thus the critical strain rate also depends on the glass formability.
4) The calculation of the 1/2<110> screw dislocation in nickel (Ni): From a quadrupolar dislocation system with 3-D periodic boundary conditions, we found the screw dislocation dissociated into two partials on {111} planes, and the core energy is 0.5 eV/b. We also studied motion and annihilation process of opposite signed dislocations with different configurations of dissociation planes. On two intersecting or parallel dissociation planes, a cross-slip process is captured and the energy barriers is 0.1eV/b in our simulations.
5) Friction Anisotropy at Ni(100)/(100) interface: We carried out a series of NEMD simulations for sliding of Ni(100) interfaces under a constant force. We found that the clean, flat, and incommensurate interface has a very small static friction coefficient, as analytical theory predicted. However surface roughness can increase the static friction on the incommensurate interfaces dramatically, and increase the friction on the commensurate interfaces to a lesser extent. The dynamic frictional coefficients are comparable to the experimental values and show the same anisotropic behavior, thus explaining the difference between theory and experiment.
https://thesis.library.caltech.edu/id/eprint/3597Dynamic Initiation and Propagation of Cracks in Unidirectional Composite Plates
https://resolver.caltech.edu/CaltechTHESIS:10112010-152127073
Authors: {'items': [{'id': 'Coker-Demirkan', 'name': {'family': 'Coker', 'given': 'Demirkan'}, 'orcid': '0000-0001-7385-7089', 'show_email': 'NO'}]}
Year: 2001
DOI: 10.7907/yrm2-4b88
<p>Dynamic crack growth along weak planes is a significant mode of failure in composites and other layered/sandwiched structures and is also the principal mechanism of shallow crustal earthquakes. In order to shed light on this phenomenon dynamic crack initiation and propagation characteristics of a model fiber-reinforced unidirectional graphite/epoxy composite plate was investigated experimentally. Dynamic fracture experiments were conducted by subjecting the composite plates to in-plane, symmetric and asymmetric, impact loading. The lateral shearing interferometric technique of coherent gradient sensing (CGS) in conjunction with high-speed photography was used to visualize the failure process in real time. It was found that mode-I cracks propagated subsonically with crack speeds increasing to the neighborhood of the Rayleigh wave speed of the composite. Also in mode-I, the dependence of the dynamic initiation fracture toughness on the loading rate was determined and was found to be constant for low loading rates and to increase rapidly above K̇<sup>d</sup><sub>I</sub> > 10⁵. The dynamic crack propagation toughness, <i>K<sub>ID</sub></i>, was observed to decrease with crack tip speed up to the Rayleigh wave speed of the composite.</p>
<p>For asymmetric, mode-II, types of loading the results revealed highly unstable and intersonic shear-dominated crack growth along the fibers. These cracks propagated with unprecedented speeds reaching 7400 m/s which is the dilatational wave speed of the composite along the fibers. For intersonic crack growth, the interferograms featured a shock wave structure typical of disturbances traveling with speeds higher than one of the characteristic wave speeds in the solid. In addition high speed thermographic measurements are conducted that show concentrated hot spots behind the crack tip indicating non-uniform crack face frictional contact. In addition, shear dominated dynamic crack growth is investigated along composite/Homalite interfaces subjected to impact loading. The crack growth phenomenon was observed usivvvvng dynamic photoelasticity in conjunction with high-speed photography. Three quantized intersonic and supersonic crack tip speed regimes were identified. First conclusive evidence of crack growth at supersonic speeds with respect to lower speed material and sonic speeds with respect to the unidirectional composite was obtained. Furthermore, this investigation documents the first experimental observation of a mother/daughter crack mechanism allowing a subsonic crack to evolve into an intersonic crack.</p>
https://thesis.library.caltech.edu/id/eprint/6127Three-Dimensional Cohesive Modeling of Impact Damage of Composites
https://resolver.caltech.edu/CaltechTHESIS:10112010-130530819
Authors: {'items': [{'email': 'rena@uclm.es', 'id': 'Yu-Chengxiang-Rena', 'name': {'family': 'Yu', 'given': 'Chengxiang Rena'}, 'orcid': '0000-0003-4176-0324', 'show_email': 'YES'}]}
Year: 2001
DOI: 10.7907/nd8e-tc84
<p>The objective of this work is to establish the applicability of cohesive theories of fracture in situations involving material interface, material heterogeneity (e.g., layered composites), material anisotropy(e.g., fiber-reinforced composites), shear cracks, intersonic dynamic crack growth and dynamic crack branching. The widely used cohesive model is extended to orthotropic range. The so-developed computational tool, completed by a self-adaptive fracture procedure and a frictional contact algorithm, is capable of following the evolution of three-dimensional damage processes, modeling the progressive decohesion of interfaces and anisotropic materials. The material parameters required by cohesive laws are directly obtained from static experiments. The ability of the methodology to simulate diverse problems such as delamination between fibers of graphite/epoxy composites, as well as sandwich structures and branching within brittle bulk materials has been demonstrated.</p>https://thesis.library.caltech.edu/id/eprint/6126Investigation 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/6354Dynamic Failure Characteristics in Layered Materials and Structures
https://resolver.caltech.edu/CaltechTHESIS:04252011-111825843
Authors: {'items': [{'id': 'Xu-Luoyu-Roy', 'name': {'family': 'Xu', 'given': 'Luoyu Roy'}, 'show_email': 'NO'}]}
Year: 2002
DOI: 10.7907/wver-8342
Systematic investigations were carried out to understand the general nature of dynamic failure mechanisms in layered materials and structures such as composite and
sandwich structures, thin films, layered armors and layered rock. A series of impact experiments on model-layered specimens were conducted using high-speed photography
and dynamic photoelasticity.
For the first time, the sequence and interaction of two major dynamic failure modes in layered materials-inter-layer cracking and intra-layer cracking were revealed
in real time. For heterogeneous three-layer systems, shear-dominated inter-layer cracking was always the first failure event for specimens subjected to low-speed impact. Interlayer cracking generally nucleated from interfacial locations where the inter-layer shear stress acquired a local maximum. Depending on impact speed and bond strength
characteristics, inter-layer cracks were very transient and often became intersonic even under moderate impact speeds. Intra-layer cracking always initiated after the development of inter-layer cracks as a result of inter-layer crack kinking into the adjacent layer. The resulting intra-layer mode I cracks often accelerated and branched as they
attained high speeds, causing core layer fragmentation. For homogenous-layered systems composed of bonded layers of Homalite, intra-layer cracks appeared in the form of cracks
radiating from the impact site. As soon as these cracks approached an interface, interlayer cracks were often induced depending on the angle between the crack path and the interface. Direct experimental evidence of the dynamic equivalent of "Cook-Gordon mechanism" was recorded, i.e., two intersonic interfacial cracks nucleated and propagated along the interface before a fan of mode I incident cracks was ever able to reach the interface. Also, significant dependence of the failure characteristics on impact speeds and interfacial strengths was found. For the heterogeneous three-layer system subjected to a high impact speed, two clear shear shock waves associated with the intersonic inter-layer cracks were observed at the specimen center. Shock waves were also observed along the interface in heterogeneous three-layer systems featuring weak and ductile bonds. The impact momentum and loading duration were identified as two important parameters in damage spreading for a given impact energy.
Motivated by the experimental observations of crack deflection/penetration at an interface, a novel wedge-loaded impact specimen was designed to explore the basic
mechanics nature of this phenomenon. The deflection/penetration behavior of an incoming dynamic crack at an interface was found to depend on the interfacial angle and the interfacial fracture toughness. A dynamic fracture model, together with an energy criterion, were proposed and were found to agree reasonably well with the experimental observations.https://thesis.library.caltech.edu/id/eprint/6350Direct Energy Bandgap Group IV Alloys and Nanostructures
https://resolver.caltech.edu/CaltechETD:etd-02142002-211940
Authors: {'items': [{'email': 'regina@its.caltech.edu', 'id': 'Ragan-Regina', 'name': {'family': 'Ragan', 'given': 'Regina'}, 'orcid': '0000-0002-8694-5683', 'show_email': 'YES'}]}
Year: 2002
DOI: 10.7907/1WKJ-RZ66
<p>Novel group IV nanostructures were fabricated and the optical properties
of such nanostructures were investigated for monolithic integration of optically
active materials with silicon. The Sn<sub>x</sub>Ge<sub>1-x</sub> alloy system was studied due to the
previous demonstration of an indirect to direct energy bandgap transition for
strain-relieved Sn<sub>x</sub>Ge<sub>1-x</sub> films on Si(001). In addition, quantum confined
structures of Sn were fabricated and the optical properties were investigated.
Due to the small electron effective mass of α-Sn, quantum confinement effects are
expected at relatively large radii.</p>
<p>Coherently strained, epitaxial Sn<sub>x</sub>Ge<sub>1-x</sub> films on Ge(001) substrates were
synthesized with film thickness exceeding 100 nm for the first time. The
demonstration of dislocation-free Sn<sub>x</sub>Ge<sub>1-x</sub> films is a step toward the fabrication
of silicon-based integrated infrared optoelectronic devices. The optical
properties of coherently strained Sn<sub>x</sub>Ge<sub>1-x</sub>/Ge(001) alloys were investigated both
theoretically and experimentally. Deformation potential theory calculations
were performed to predict the effect of coherency strain on the extrema points of
the conduction band and the valence band. The energy bandgap of
Sn<sub>x</sub>Ge<sub>1-x</sub>/Ge(001) alloys was measured via Fourier transform infrared
spectroscopy. Coherency strain did not change the Sn<sub>x</sub>Ge<sub>1-x</sub> energy bandgap
when the strain axis was along [001] but deformation potential theory predicted
the absence of an indirect to direct energy bandgap transition when the strain
axis was along [111].</p>
<p>In addition to being the only group IV alloy exhibiting a direct energy
bandgap, when grown beyond a critical thickness, Sn<sub>x</sub>Ge<sub>1-x</sub>/Ge(001) exhibits an
interesting phenomenon during MBE growth. Sn segregates via surface
diffusion to the crest of a surface undulation during growth and forms ordered
Sn-enriched Sn<sub>x</sub>Ge<sub>1-x</sub> rods oriented along [001]. The Sn<sub>x</sub>Ge<sub>1-x</sub> alloy system was
used as a model system to gain insight to the physical mechanisms governing
self-assembly and ordering during molecular beam epitaxy.</p>
<p>Sn nanowires were fabricated in anodic alumina templates with lengths
exceeding 1 μm and diameters on the order of 40 nm. Anodic alumina templates
can be fabricated non-lithographically with ordered domains of hexagonally
packed pores greater than 1 μm and pore densities on the order of 10<sup>11</sup> cm<sup>-2</sup>. The
achievement of single crystal Sn nanowires fabricated using pressure injection in
porous alumina templates was demonstrated.</p>
<p>The fabrication of α-Sn quantum dots embedded in Ge was achieved by
annealing 1 μm thick Sn<sub>x</sub>Ge<sub>1-x</sub> films at 750°C. The measured diameter of the
quantum dots was 32 nm and a 10% size variation was observed. Quantum size
effects were observed in α-Sn quantum dots. Optical transmittance
measurements yield a value of 0.45 eV for the direct energy bandgap as a result
of quantum confinement. A high degree of tunability of the bandgap energy
with the quantum dot radius is expected for α-Sn. Thus quantum-confined
structures of α-Sn are promising for optoelectronic device applications.</p>https://thesis.library.caltech.edu/id/eprint/632Dynamics 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/4442Cohesive Models of Fatigue Crack Growth and Stress-Corrosion Cracking
https://resolver.caltech.edu/CaltechETD:etd-12032004-161201
Authors: {'items': [{'email': 'olivier_thanh_nguyen@yahoo.com', 'id': 'Nguyen-Olivier-Thanh', 'name': {'family': 'Nguyen', 'given': 'Olivier Thanh'}, 'show_email': 'YES'}]}
Year: 2002
DOI: 10.7907/C3KP-4M44
The aim of this dissertation was to develop models of fatigue crack growth and stress-corrosion cracking by investigating cohesive theories of fracture. These models were integrated in a finite-element framework embedding a contact algorithm and techniques of remeshing and adaptive meshing.
For the fatigue model, we developed a phenomenological cohesive law which exhibits unloading-reloading hysteresis. This model qualitatively predicts fatigue crack growth rates in metals under constant amplitude regime for short and long cracks, as well as growth retardation due to overload. Quantitative predictions were obtained in the case of long cracks.
We developed a chemistry-dependent cohesive law which serves as a basis for the stress-corrosion cracking model. In order to determine this cohesive law, two approaches, based on energy relaxation and the renormalization group, were used for coarse-graining interplanar potentials. We analyzed the cohesive behavior of a large--but finite--number of interatomic planes and found that the macroscopic cohesive law adopts a universal asymptotic form. The resulting stress-corrosion crack growth rates agreed well with those observed experimentally in 'static' fatigue tests given in the literature.
https://thesis.library.caltech.edu/id/eprint/4745Variational 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/2227Variational 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/2077A 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/2287Discrete Exterior Calculus
https://resolver.caltech.edu/CaltechETD:etd-05202003-095403
Authors: {'items': [{'email': 'hirani@illinois.edu', 'id': 'Hirani-Anil-Nirmal', 'name': {'family': 'Hirani', 'given': 'Anil Nirmal'}, 'orcid': '0000-0003-3506-1703', 'show_email': 'YES'}]}
Year: 2003
DOI: 10.7907/ZHY8-V329
<p>This thesis presents the beginnings of a theory of discrete exterior calculus (DEC). Our approach is to develop DEC using only discrete combinatorial and geometric operations on a simplicial complex and its geometric dual. The derivation of these may require that the objects on the discrete mesh, but not the mesh itself, are interpolated.</p>
<p>Our theory includes not only discrete equivalents of differential forms, but also discrete vector fields and the operators acting on these objects. Definitions are given for discrete versions of all the usual operators of exterior calculus. The presence of forms and vector fields allows us to address their various interactions, which are important in applications. In many examples we find that the formulas derived from DEC are identitical to the existing formulas in the literature. We also show that the circumcentric dual of a simplicial complex plays a useful role in the metric dependent part of this theory. The appearance of dual complexes leads to a proliferation of the operators in the discrete theory.</p>
<p>One potential application of DEC is to variational problems which come equipped with a rich exterior calculus structure. On the discrete level, such structures will be enhanced by the availability of DEC. One of the objectives of this thesis is to fill this gap. There are many constraints in numerical algorithms that naturally involve differential forms. Preserving such features directly on the discrete level is another goal, overlapping with our goals for variational problems.</p>
<p>In this thesis we have tried to push a purely discrete point of view as far as possible. We argue that this can only be pushed so far, and that interpolation is a useful device. For example, we found that interpolation of functions and vector fields is a very convenient. In future work we intend to continue this interpolation point of view, extending it to higher degree forms, especially in the context of the sharp, Lie derivative and interior product operators. Some preliminary ideas on this point of view are presented in the thesis. We also present some preliminary calculations of formulas on regular nonsimplicial complexes</p>https://thesis.library.caltech.edu/id/eprint/1885Constrained 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 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/2187Foundations of Computational Geometric Mechanics
https://resolver.caltech.edu/CaltechETD:etd-03022004-000251
Authors: {'items': [{'email': 'mleok@math.ucsd.edu', 'id': 'Leok-Melvin', 'name': {'family': 'Leok', 'given': 'Melvin'}, 'orcid': '0000-0002-8326-0830', 'show_email': 'YES'}]}
Year: 2004
DOI: 10.7907/KDV0-WR34
<p>Geometric mechanics involves the study of Lagrangian and Hamiltonian mechanics using geometric and symmetry techniques. Computational algorithms obtained from a discrete Hamilton's principle yield a discrete analogue of Lagrangian mechanics, and they exhibit excellent structure-preserving properties that can be ascribed to their variational derivation.</p>
<p>We construct discrete analogues of the geometric and symmetry methods underlying geometric mechanics to enable the systematic development of computational geometric mechanics. In particular, we develop discrete theories of reduction by symmetry, exterior calculus, connections on principal bundles, as well as generalizations of variational integrators.</p>
<p>Discrete Routh reduction is developed for abelian symmetries, and extended to systems with constraints and forcing. Variational Runge-Kutta discretizations are considered in detail, including the extent to which symmetry reduction and discretization commute. In addition, we obtain the Reduced Symplectic Runge-Kutta algorithm, which is a discrete analogue of cotangent bundle reduction.</p>
<p>Discrete exterior calculus is modeled on a primal simplicial complex, and a dual circumcentric cell complex. Discrete notions of differential forms, exterior derivatives, Hodge stars, codifferentials, sharps, flats, wedge products, contraction, Lie derivative, and the Poincar?emma are introduced, and their discrete properties are analyzed. In examples such as harmonic maps and electromagnetism, discretizations arising from discrete exterior calculus commute with taking variations in Hamilton's principle, which implies that directly discretizing these equations yield numerical schemes that have the structure-preserving properties associated with variational schemes.</p>
<p>Discrete connections on principal bundles are obtained by introducing the discrete Atiyah sequence, and considering splittings of the sequence. Equivalent representations of a discrete connection are considered, and an extension of the pair groupoid composition that takes into account the principal bundle structure is introduced. Discrete connections provide an intrinsic coordinatization of the reduced discrete space, and the necessary discrete geometry to develop more general discrete symmetry reduction techniques.</p>
<p>Generalized Galerkin variational integrators are obtained by discretizing the action integral through appropriate choices of finite-dimensional function space and numerical quadrature. Explicit expressions for Lie group, higher-order Poincaré, higher-order symplectic-energy-momentum, and pseudospectral variational integrators are presented, and extensions such as spatio-temporally adaptive and multiscale variational integrators are briefly described.</p>https://thesis.library.caltech.edu/id/eprint/831Thermomechanical Variational Principles for Dissipative Materials with Application to Strain Localization in Bulk Metallic Glasses
https://resolver.caltech.edu/CaltechETD:etd-05282004-152537
Authors: {'items': [{'id': 'Yang-Qiang', 'name': {'family': 'Yang', 'given': 'Qiang'}, 'show_email': 'NO'}]}
Year: 2004
DOI: 10.7907/6FV2-KV63
<p>This thesis is concerned with variational principles for general coupled thermomechanical problems in dissipative materials including finite elastic and plastic deformation, non-Newtonian viscosity, rate sensitivity, arbitrary flow and hardening rule, as well as heat conduction. It is shown that there exists a potential function such that both the conservation of energy and balance of linear momentum are the Euler-Lagrange equations of its first variation. Inspired from the time-discretized version of the variational formulation, we present a procedure for variational thermomechanical update, which generalizes the isothermal approach under a variational thermodynamic framework. This variational formulation then serves as a basis for temperature change as well as constitutive updates.</p>
<p>An important application of the variational formulation is to optimize the shear band thickness in strain localization processes. We show that this optimization takes the form of a configurational-force equilibrium and results in a well-defined band thickness. We further implement displacement discontinuities into a class of strain-localization finite elements. These elements consist of two surfaces, attached to the abutting volume elements, which can separate and slip relative to each other, and thus enable the accurate and efficient simulation of the dynamical formation of stain localization.</p>
<p>The variational formulation also leads to a finite-deformation continuum modeling of bulk metallic glasses. It is shown that the strain softening of bulk metallic glasses is due to the increase of free volume (and thus the decrease of viscosity), while temperature rise accelerates the localization of the deformation. The model reproduces the constitutive behavior of Vitreloy 1 bulk metallic glass at various strain rates and temperatures.</p>https://thesis.library.caltech.edu/id/eprint/2194A 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/4059The 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/8Theory 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/5084Atomic 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/4303Coarse Analysis of Multiscale Systems: Diffuser Flows, Charged Particle Motion, and Connections to Averaging Theory
https://resolver.caltech.edu/CaltechETD:etd-05272005-165938
Authors: {'items': [{'id': 'Fung-Jimmy', 'name': {'family': 'Fung', 'given': 'Jimmy'}, 'orcid': '0000-0002-6612-2209', 'show_email': 'NO'}]}
Year: 2005
DOI: 10.7907/wn0z-gn57
<p>We describe a technique for the efficient computation of the dominant-scale dynamics of a fluid system when only a high-fidelity simulation is available. Such a technique is desirable when governing equations for the dominant scales are unavailable, when model reduction is impractical, or when the original high-fidelity computation is expensive. We adopt the coarse analysis framework proposed by I. G. Kevrekidis (Comm. Math. Sci. 2003), where a computational superstructure is designed to use short-time, high-fidelity simulations to extract the dominant features for a multiscale system. We apply this technique to compute the dominant features of the compressible flow through a planar diffuser. We apply the proper orthogonal decomposition to classify the dominant and subdominant scales of diffuser flows. We derive a suitable coarse projective Adams-Bashforth time integration routine and apply it to compute averaged diffuser flows. The results include accurate tracking of the dominant-scale dynamics for a range of parameter values for the computational superstructure. These results demonstrate that coarse analysis methods are useful for solving fluid flow problems of a multiscale nature.</p>
<p>In order to elucidate the behavior of coarse analysis techniques, we make comparisons to averaging theory. To this end, we derive governing equations for the average motion of charged particles in a magnetic field in a number of different settings. First, we apply a novel procedure, inspired by WKB theory and Whitham averaging, to average the variational principle. The resulting equations are equivalent to the guiding center equations for charged particle motion; this marks an instance where averaging and variational principles commute. Secondly, we apply Lagrangian averaging techniques, previously applied in fluid mechanics, to derive averaged equations. Making comparisons to the WKB/Whitham-style derivation allows for the necessary closure of the Lagrangian averaging formulation. We also discuss the Hamiltonian setting and show that averaged Hamiltonian systems may be derivable using concepts from coarse analysis. Finally, we apply a prototypical coarse analysis procedure to the system of charged particles and generate trajectories that resemble guiding center trajectories. We make connections to perturbation theory to derive guidelines for the design of coarse analysis techniques and comment on the prototypical coarse analysis application.</p>https://thesis.library.caltech.edu/id/eprint/2163Vibrational 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/3306Configurational 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/1724Coarse-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/4498Electronic 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/1822Constitutive 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/4238A Computational Model for Intergranular Stress Corrosion Cracking
https://resolver.caltech.edu/CaltechETD:etd-05142009-135909
Authors: {'items': [{'email': 'julian.rimoli@gmail.com', 'id': 'Rimoli-Julian-Jose', 'name': {'family': 'Rimoli', 'given': 'Julian Jose'}, 'orcid': '0000-0002-8707-2968', 'show_email': 'NO'}]}
Year: 2009
DOI: 10.7907/K1HJ-DZ56
Stress corrosion cracking (SCC) is a very common failure mechanism characterized by a slow, environmentally induced crack propagation in structural components. Time-to-failure tests and crack-growth-rate tests are widespread practices for studying the response of various materials undergoing SCC. However, due to the large amount of factors affecting the phenomenon and the scattered data, they do not provide enough information for quantifying the effects of main SCC mechanisms. This thesis is concerned with the development of a novel 3-dimensional, multiphysics model for understanding the intergranular SCC of polycrystalline materials under the effect of impurity-enhanced decohesion. This new model is based upon: (i) a robust algorithm capable of generating the geometry of polycrystals for objects of arbitrary shape; (ii) a continuum finite element model of the crystals including crystal plasticity; (iii) a grain boundary diffusion model informed with first-principles computations of diffusion coefficients; and (iv) an intergranular cohesive model described by concentration-dependent constitutive relations also derived from first-principles. Results are validated and compared against crack-growth-rate and initiation time tests.
https://thesis.library.caltech.edu/id/eprint/1808Modeling Metallic Single Crystal Plastic Hardening Through the Evolution of Dislocation Subgrain Structures
https://resolver.caltech.edu/CaltechETD:etd-03132009-154225
Authors: {'items': [{'email': 'ben.l.hansen@gmail.com', 'id': 'Hansen-Benjamin-Lee', 'name': {'family': 'Hansen', 'given': 'Benjamin Lee'}, 'show_email': 'NO'}]}
Year: 2009
DOI: 10.7907/C052-3119
<p>A single crystal plasticity theory for insertion into finite element simulation is formulated using sequential laminates to model subgrain dislocation structures. It is known that local models do not adequately account for latent hardening, as latent hardening is not only a material property, but a nonlocal property (e.g., grain size and shape). The addition of the nonlocal energy from the formation of subgrain structure dislocation walls and the boundary layer misfits provide both latent and self hardening of crystal slip. Latent hardening occurs as the formation of new dislocation walls limit motion of new mobile dislocations, thus hardening future slip systems. Self hardening is accomplished by evolution of the subgrain structure length scale. No multiple slip hardening terms are included.</p>
<p>The substructure length scale is computed by minimizing the nonlocal energy. The minimization of the nonlocal energy is a competition between the dislocation wall and boundary layer energy. The nonlocal terms are also directly minimized within the subgrain model as they impact deformation response. The geometrical relationship between the dislocation walls and slip planes affecting dislocation mean free path is accounted for giving a first-order approximation to shape effects. A coplanar slip model is developed due to requirements when modeling the subgrain structure. This subgrain structure plasticity model is noteworthy as all material parameters are experimentally determined rather than fit. The model also has an inherit path dependency due to the formation of the subgrain structures. Validation is accomplished by comparison to single crystal tension test results.</p>
https://thesis.library.caltech.edu/id/eprint/950Uncertainty Quantification Using Concentration-of-Measure Inequalities
https://resolver.caltech.edu/CaltechETD:etd-05292009-165215
Authors: {'items': [{'email': 'lenny.lucas@gmail.com', 'id': 'Lucas-Leonard-Joseph', 'name': {'family': 'Lucas', 'given': 'Leonard Joseph'}, 'show_email': 'YES'}]}
Year: 2009
DOI: 10.7907/DRAM-H941
This work introduces a rigorous uncertainty quantification framework that exploits concentration–of–measure inequalities to bound failure probabilities using a well-defined certification campaign regarding the performance of engineering systems. The framework is constructed to be used as a tool for deciding whether a system is likely to perform safely and reliably within design specifications. Concentration-of-measure inequalities rigorously bound probabilities-of-failure and thus supply conservative certification criteria, in addition to supplying unambiguous quantitative definitions of terms such as margins, epistemic and aleatoric uncertainties, verification and validation measures, and confidence factors. This methodology unveils clear procedures for computing the latter quantities by means of concerted simulation and experimental campaigns. Extensions to the theory include hierarchical uncertainty quantification, and validation with experimentally uncontrollable random variables.https://thesis.library.caltech.edu/id/eprint/2282The Optimal Transportation Meshfree Method for General Fluid Flows and Strongly Coupled Fluid-Structure Interaction Problems
https://resolver.caltech.edu/CaltechETD:etd-06012009-104937
Authors: {'items': [{'email': 'fhabbal@ices.utexas.edu', 'id': 'Habbal-Feras', 'name': {'family': 'Habbal', 'given': 'Feras'}, 'show_email': 'NO'}]}
Year: 2009
DOI: 10.7907/MHQX-3Z52
This thesis develops a novel meshfree numerical method for simulating general fluid flows. Drawing from concepts in optimal mass transport theory and in combination with the notion of material point sampling and meshfree interpolation, the optimal transport meshfree (OTM) method provides a rigorous mathematical framework for numerically simulating three-dimensional general fluid flows with general, and possibly moving boundaries (as in fluid-structure interaction simulations). Specifically, the proposed OTM method generalizes the Benamou-Brenier differential formulation of optimal mass transportation problems which leads to a multi-field variational characterization of general fluid flows including viscosity, equations of state and general geometries and boundary conditions. With the use of material point sampling in conjunction with local max-entropy shape functions, the OTM method leads to a meshfree formulation bearing a number of salient features. Compared with other meshfree methods that face significant challenges to enforce essential boundary conditions as well as couple to other methods, such as the finite element method, the OTM method provides a new paradigm in meshfree methods. The OTM method is numerically validated by simulating the classical Riemann benchmark example for Euler flow. Furthermore, in order to highlight the ability of the OTM to simulate Navier-Stokes flows within general, moving three-dimensional domains, and naturally couple with finite elements, an illustrative strongly coupled FSI example is simulated. This illustrative FSI example, consisting of a gas-inflated sphere impacting the ground, is simulated as a toy model of the final phase of NASA's landing scheme devised for Mars missions, where a network of airbags are deployed to dissipate the energy of impact.
https://thesis.library.caltech.edu/id/eprint/5220The Optimal Transportation Method in Solid Mechanics
https://resolver.caltech.edu/CaltechETD:etd-05212009-173044
Authors: {'items': [{'email': 'bxl295@case.edu', 'id': 'Li-Bo', 'name': {'family': 'Li', 'given': 'Bo'}, 'orcid': '0000-0002-0127-8210', 'show_email': 'YES'}]}
Year: 2009
DOI: 10.7907/FAT3-0247
This dissertation is concerned with the development of a robust and efficient meshless method, the Optimal Transportation Method (OTM), for general solid flows involving extremely large deformation, fast, transient loading and hydrodynamic phenomena. This method is a Lagrangian particle method through an integration of optimal transportation theory with meshless interpolation and material point integrations. The theoretical framework developed in this thesis generalized the Benamou-Brenier differential formulation of optimal transportation problems and leads to a multi-field variational characterization of solid flows, including elasticity, inelasticity, equation of state, and general geometries and boundary conditions. To this end, the accuracy, robustness and versatility of OTM is assessed and demonstrated with convergence and stability test, Taylor anvil test and a series of full three-dimensional simulations of high/hyper-velocity impact examples with the aid of a novel meshless dynamic contact algorithm presented in this thesis.
https://thesis.library.caltech.edu/id/eprint/5193Dynamic Optical Investigations of Hypervelocity Impact Damage
https://resolver.caltech.edu/CaltechTHESIS:05282010-183132978
Authors: {'items': [{'email': 'les@caltech.edu', 'id': 'Lamberson-Leslie-Elise', 'name': {'family': 'Lamberson', 'given': 'Leslie Elise'}, 'orcid': '0000-0002-1340-4667', 'show_email': 'NO'}]}
Year: 2010
DOI: 10.7907/AQJH-3D60
One of the prominent threats in the endeavor to develop next-generation space assets is the risk of space debris impact in earth’s orbit and micrometeoroid impact damage in near-earth orbit and deep space. To date, there is no study available which concentrates on the analysis of dynamic crack growth from hypervelocity impacts on such structures, resulting in their eventual catastrophic degradation. Experiments conducted using a unique two-stage light-gas gun facility have examined the in situ dynamic fracture of brittle polymers subjected to this high-energy-density event. Optical techniques of caustics and photoelasticity, combined with high-speed photography up to 100 million frames per second, analyze crack growth behavior of Mylar and Homalite 100 thin plates after impact by a 1.8 mm diameter nylon 6-6 right cylindrical slug at velocities ranging from 3 to 7 km/s (7000–15500 mph). Crack speeds in both polymers averaged between 0.2 and 0.47 cR, the Rayleigh wave speed (450–1000 mph). Shadow spots and surrounding caustics reveal time histories of the dynamic stress intensity factor, as well as the energy release rate ahead of the mode-I, or opening, crack tips. Results indicate that even under extreme impact conditions of out of-plane loading, highly localized heating, and energetic impact phenomena involving plasma formation and ejecta, the dynamic fracture process occurs during a deformation regime dominated by in-plane loading. These findings imply that the reliability of impacted, thin-walled, plate and shell space structures, idealized by the experimental configuration investigated, can be predicted by the well defined principles of classical dynamic fracture mechanics.https://thesis.library.caltech.edu/id/eprint/5888Energy and Force Stepping Integrators in Lagrangian Mechanics
https://resolver.caltech.edu/CaltechTHESIS:10052010-230939247
Authors: {'items': [{'email': 'magonzal@caltech.edu', 'id': 'Gonzalez-Marcial', 'name': {'family': 'Gonzalez', 'given': 'Marcial'}, 'show_email': 'NO'}]}
Year: 2011
DOI: 10.7907/SP10-A207
The overarching goal of this thesis is to develop new numerical time integration schemes for Lagrangian mechanics that better cope with the challenges of understanding the dynamic behavior of materials. We specifically address the formulation of convergent time integration schemes that exhibit good long-term behavior---such as conferred by symplecticity and exact conservation properties---and that have the ability to automatically and asynchronously modulate the time step in different regions of the domain. We achieve these properties in a progression of three developments: (i) energy-stepping, (ii) force-stepping, and (iii) asynchronous energy-stepping integrators. These developments are based on a new method of approximation for Lagrangian mechanics, proposed in this thesis, that consists of replacing the Lagrangian of the system by a sequence of approximate Lagrangians that can be solved exactly. Then, energy-stepping integrators result from replacing the potential energy by a piecewise constant approximation, force-stepping integrators result from replacing the potential energy by a piecewise affine approximation, and asynchronous energy-stepping integrators result from replacing localized potential energies by piecewise constant approximations. Throughout the dissertation, the properties of these time integrators are theoretically predicted and born out by a number of selected examples of application. Furthermore, we address the challenges of understanding the propagation of solitary waves in granular crystals at low impact velocity conditions by investigating the role of energy-trapping effects with the numerical time integration schemes developed in this work.
https://thesis.library.caltech.edu/id/eprint/6103Discrete Mechanics and Optimal Control for Space Trajectory Design
https://resolver.caltech.edu/CaltechTHESIS:05252011-164957222
Authors: {'items': [{'email': 'moore.ashley@gmail.com', 'id': 'Moore-Ashley', 'name': {'family': 'Moore', 'given': 'Ashley'}, 'show_email': 'YES'}]}
Year: 2011
DOI: 10.7907/ZXTG-V056
<p>Space trajectory design is often achieved through a combination of dynamical systems theory and optimal control. The union of trajectory design techniques utilizing invariant manifolds of the planar circular restricted three-body problem and the optimal control scheme Discrete Mechanics and Optimal Control (DMOC) facilitates the design of low-energy trajectories in the N-body problem. In particular, DMOC is used to optimize a trajectory from the Earth to the Moon in the 4-body problem, removing the mid-course change in velocity usually necessary for such a trajectory while still exploiting the structure from the invariant manifolds.</p>
<p>This thesis also focuses on how to adapt DMOC, a method devised with a constant step size, for the highly nonlinear dynamics involved in trajectory design. Mesh refinement techniques that aim to reduce discretization errors in the solution and energy evolution and their effect on DMOC optimization are explored and compared with trajectories created using time adaptive variational integrators.</p>
<p>Furthermore, a time adaptive form of DMOC is developed that allows for a variable step size that is updated throughout the optimization process. Time adapted DMOC is based on a discretization of Hamilton's principle applied to the time adapted Lagrangian of the optimal control problem. Variations of the discrete action of the optimal control Lagrangian lead to discrete Euler-Lagrange equations that can be enforced as constraints for a boundary value problem. This new form of DMOC leads to the accurate and efficient solution of optimal control problems with highly nonlinear dynamics. Time adapted DMOC is tested on several space trajectory problems including the elliptical orbit transfer in the 2-body problem and the reconfiguration of a cubesat.</p>
https://thesis.library.caltech.edu/id/eprint/6441Topics in Multiscale Modeling of Metals and Metallic Alloys
https://resolver.caltech.edu/CaltechTHESIS:11222010-114324484
Authors: {'items': [{'email': 'venturin@caltech.edu', 'id': 'Venturini-Gabriela-Natalia', 'name': {'family': 'Venturini', 'given': 'Gabriela Natalia'}, 'show_email': 'NO'}]}
Year: 2011
DOI: 10.7907/D6YS-B365
<p>In a number of areas of application, the behavior of systems depends sensitively on properties that pertain to the atomistic scale, i. e., the angstrom and femtosecond scales. However, generally the behaviors of interest are macroscopic and are characterized by slow evolution on the scale of meters and years. This broad disparity of length and time scales places extraordinary challenges in computational material science.</p>
<p>The overarching objective of this dissertation is to address the problem of multiple space and time scales in atomistic systems undergoing slow macroscopic evolution while retaining full atomistic detail. Our approach may be summarized as follows:</p>
<p>(1) The issue of accounting for finite temperature in coarse grained systems has not been solved entirely. For finite temperature systems at equilibrium, constructing an effective free energy in terms of a reduced set of atomic degrees of freedom is still an open area of research. In particular, the thermal vibrations of the missing degrees of freedom need to be accounted for. This is specially important if the aim of the simulation is to determine the dynamic properties of a system, or to allow the transmission of dynamic information between regions of different spatial discretization. To this end, we introduce a framework to simulate (spatially) coarse dynamic systems using the Quasicontinuum method (QC). The equations of motion are strictly derived from dissipative Lagrangian mechanics, which provides a classical Langevin implementation where the characteristic time is governed by the vibrations of the finest length scale in the computational cell. In order to assess the framework's ability to transmit information across scales, we study the phonon impoverish spectra in coarse regions and the resulting underestimation of thermal equilibrium properties.</p>
<p>(2) Atomistic simulations have been employed for the past thirty years to determine structural and thermodynamic (equilibrium) properties of solids and their defects over a wide range of temperatures and pressures. The traditional Monte Carlo (MC) and Molecular Dynamics (MD) methods, while ideally suited to these calculations, require appreciable computational resources in order to calculate the long-time averages from which properties are obtained. In order to permit a reasonably quick, but accurate determination of the equilibrium properties of interest, we present an extension of the “maximum entropy” method to build effective alloy potentials while avoiding the treatment of all the system's atomic degrees of freedom. We assess the validity of the model by testing its ability to reproduce experimental measurements.</p>
<p>(3) Based upon these effective potentials, we present a numerical framework capable of following the time evolution of atomistic systems over time windows currently beyond the scope of traditional atomistic methods such as Molecular Dynamics (MD) or Monte Carlo (MC). This is accomplished while retaining the underlying atomistic description of the material. We formulate a discrete variational setting in which the simulation of time-dependent phenomena is reduced to a sequence of incremental problems, each characterized by a variational principle. In this fashion we are able to study the interplay between deformation and diffusion using time steps or strain rates that are orders of magnitude larger or smaller than their MD|MC counterparts.</p>
<p>(4) We formulate a new class of “Replica Time Integrators” (RTIs) that allows for the two-way transmission of thermal phonons across mesh interfaces. This two-way transmission is accomplished by representing the state of the coarse region by a collection of identical copies or “replicas” of itself. Each replica runs at its own slow time step and is out-of-phase with respect to the others by one fast time step. Then, each replica is capable of absorbing from the fine region the elementary signal that is in phase with the replica. Conversely, each replica is capable of supporting --and transmitting to the fine region-- an elementary signal of a certain phase. Since fine and coarse regions evolve asynchronously in time, RTIs permit both spatial and temporal coarse graining of the system of interest. Using a combination of phase-error analysis and numerical testing we find that RTIs are convergent, and allow step waves and thermal phonons to cross mesh interfaces in both directions losslessly. </p>
https://thesis.library.caltech.edu/id/eprint/6188Modeling the Behavior of Fiber Reinforced Sandwich Structures Subjected to Underwater Explosions
https://resolver.caltech.edu/CaltechTHESIS:11052010-113423550
Authors: {'items': [{'email': 'luigiemp@gmail.com', 'id': 'Perotti-Luigi-Emanuele', 'name': {'family': 'Perotti', 'given': 'Luigi Emanuele'}, 'show_email': 'YES'}]}
Year: 2011
DOI: 10.7907/83JD-HN76
<p>Fiber composite material panels and sandwich panels possess both a high resistance to weight ratio and a high stiffness to weight ratio. Due to these features, fiber composite panels are used widely in aeronautic and marine structures, where the improvement of the structural performance while keeping a low weight is crucial. Sandwich structures, consisting of a foam core enclosed by two external layers of fiber reinforced material, seem to be promising in minimizing the total weight, maintaining structural rigidity and improving the resistance under exceptional loads, such as those due to explosions. Full scale experiments to test the performance of real fiber composite sandwich structures subjected to underwater explosions would be very complex and expensive. Therefore, the capability to numerically simulate the response of sandwich structures undergoing explosive loading will provide a powerful and unique tool to analyze and optimize their design by investigating the influence of different parameters. Obviously, small scale laboratory tests will still be essential to validate and calibrate the computational model before its use.</p>
<p>The present research focuses on the development of a computational scheme to model the behavior of large sandwich panels subjected to underwater explosions. The description of the sandwich requires the definition of the material behavior of the components, i.e., the foam core and the external sheets, of the structural behavior of the thin shell structure, and of the interaction with the surrounding fluid. Several finite kinematics material models taken from the recent literature have been used, and a new simple model for fiber reinforced composites has been developed and validated. The thin shell structure is modeled with an existing in-house built non-local shell finite element code (SFC), equipped with fracturing capabilities. The coupling between the behavior of the shells and the action of the fluid as a consequence of an underwater explosion is modeled here with the aid of an existing fluid-solid interaction (FSI) code. In this study, the FSI code has been expanded in order to include the possibility of simulating fiber composite materials. New algorithms and new control indicators, such as global measures of energy dissipation, have also been developed. The new capabilities of the fluid-solid coupled solver have been verified and validated before applying the solver to realistic problems. In the applications part of the present research, two different methods for applying the pressure load due to an underwater explosion are compared. The first method is simpler, and consists in applying a prescribed pressure profile without considering FSI. In the second method, the explosive charge is modeled as a spherical energy deposition and the full FSI is considered. The simpler method is used to assess the role of different design parameters of the face sheets on the overall response of sandwich panels when subjected to impulsive loads. Subsequently, the best sandwich design obtained from these initial simulations is used for the evaluation of the mechanical performance of the hull section of an existing Argentinean navy vessel. The final application of the proposed computational scheme is a parametric analysis of the hull section, considering different weights of the explosive charge and different distances of the explosion location from the hull wall.</p>
<p>Finally, with awareness of the limits of the adopted approach, several alternative schemes to improve the dynamical analysis of sandwich panels impulsively loaded are presented and discussed. In particular, two different kinds of shell finite elements are introduced. The proposed shell elements are based on alternative approximation schemes, which may model in a more realistic way the behavior of sandwich structures under extreme loads.</p>
https://thesis.library.caltech.edu/id/eprint/6172Multiscale 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/6165Mechanics 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/6271Coarse-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/6473Repeatability of Joint-Dominated Deployable Masts
https://resolver.caltech.edu/CaltechTHESIS:05242011-022845109
Authors: {'items': [{'email': 'olive@caltech.edu', 'id': 'Stohlman-Olive-Remington', 'name': {'family': 'Stohlman', 'given': 'Olive Remington'}, 'show_email': 'NO'}]}
Year: 2011
DOI: 10.7907/D3AR-G573
<p>Deployable masts are a class of structure that can be stowed in a small volume and expanded into long, slender, and stable booms. Their greatest benefit as space structures is their packing ratio: masts can typically be packed to a fraction of their deployed length at a diameter only modestly wider than their deployed width. This thesis is concerned with precision deployable masts, which can be stowed and deployed with repeatability of the tip position of better than 1 mm over 60 m. The methods of investigation are experimental measurements of a sample mast and numerical modeling of the mast with specially attention to hysteretic joints.</p>
<p>A test article of an ADAM mast was used for the experimental work. Two categories of experi- ment were pursued: measurements of mast components as inputs to the model, and measurements of full bays as validation cases for the model. Measurements of the longeron ball end joint friction, cable preload, and latch behavior are of particular note, and were evaluated for their variability. Further measurements were made of a bay in torsion and a short two-bay mast in shear, showing that there is residual displacement in this mast after shear loading is applied and released.</p>
<p>The modeling approach is described in detail, with attention to the treatment of the mast latches, which lock the structure in its deployed configuration. A user element subroutine was used within the framework of the Abaqus finite element analysis solver to model the behavior of the latches with high fidelity.</p>
<p>Validation cases for the model are presented in comparison with experimental observations of a two-bay mast. These cases show that the model captures a number of important and complex nonlinear effects of the hysteretic mast components. Parametric studies of the impacts of component behaviors and modeling practices are explored, emphasizing the impacts of part variability and the idealization of the mast latching mechanisms.</p>https://thesis.library.caltech.edu/id/eprint/6422Multiscale 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/6187Multiscale Geometric Integration of Deterministic and Stochastic Systems
https://resolver.caltech.edu/CaltechTHESIS:05262011-171044915
Authors: {'items': [{'email': 't.t.snail@gmail.com', 'id': 'Tao-Molei', 'name': {'family': 'Tao', 'given': 'Molei'}, 'show_email': 'NO'}]}
Year: 2011
DOI: 10.7907/6J83-7C18
<p>In order to accelerate computations and improve long time accuracy of numerical simulations, this thesis develops multiscale geometric integrators.</p>
<p>For general multiscale stiff ODEs, SDEs, and PDEs, FLow AVeraging integratORs (FLAVORs) have been proposed for the coarse time-stepping without any identification of the slow or the fast variables. In the special case of deterministic and stochastic mechanical systems, symplectic, multisymplectic, and quasi-symplectic multiscale integrators are easily obtained using this strategy.</p>
<p>For highly oscillatory mechanical systems (with quasi-quadratic stiff potentials and possibly high-dimensional), a specialized symplectic method has been devised to provide improved efficiency and accuracy. This method is based on the introduction of two highly nontrivial matrix exponentiation algorithms, which are generic, efficient, and symplectic (if the exact exponential is symplectic).</p>
<p>For multiscale systems with Dirac-distributed fast processes, a family of symplectic, linearly-implicit and stable integrators has been designed for coarse step simulations. An application is the fast and accurate integration of constrained dynamics.</p>
<p>In addition, if one cares about statistical properties of an ensemble of trajectories, but not the numerical accuracy of a single trajectory, we suggest tuning friction and annealing temperature in a Langevin process to accelerate its convergence.</p>
<p>Other works include variational integration of circuits, efficient simulation of a nonlinear wave, and finding optimal transition pathways in stochastic dynamical systems (with a demonstration of mass effects in molecular dynamics).</p>https://thesis.library.caltech.edu/id/eprint/6457Clefted 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/7141Simulation of Richtmyer-Meshkov Flows for Elastic-Plastic Solids in Planar and Converging Geometries Using an Eulerian Framework
https://resolver.caltech.edu/CaltechTHESIS:02202013-185004693
Authors: {'items': [{'email': 'alejandro_lopez_ortega@hotmail.com', 'id': 'Lopez-Ortega-Alejandro', 'name': {'family': 'Lopez Ortega', 'given': 'Alejandro'}, 'show_email': 'YES'}]}
Year: 2013
DOI: 10.7907/4WJ6-D795
This thesis presents a numerical and analytical study of two problems of interest involving shock waves propagating through elastic-plastic media: the motion of converging (imploding) shocks and the Richtmyer-Meshkov (RM) instability. Since the stress conditions encountered in these cases normally produce large deformations in the materials, an Eulerian description, in which the spatial coordinates are fixed, is employed. This formulation enables a direct comparison of similarities and differences between the present study of phenomena driven by shock-loading in elastic-plastic solids, and in fluids, where they have been studied extensively. In the first application, Whitham's shock dynamics (WSD) theory is employed for obtaining an approximate description of the motion of an elastic-plastic material processed by a cylindrically/spherically converging shock. Comparison with numerical simulations of the full set of equations of motion reveal that WSD is an accurate tool for characterizing the evolution of converging shocks at all stages. The study of the Richtmyer-Meshkov flow (i.e., interaction between the interface separating two materials of different density and a shock wave incoming at an angle) in solids is performed by means of analytical models for purely elastic solids and numerical simulations when plasticity is included in the material model. To this effect, an updated version of a previously developed multi-material, level-set-based, Eulerian framework for solid mechanics is employed. The revised code includes the use of a multi-material HLLD Riemann problem for imposing material boundary conditions, and a new formulation of the equations of motion that makes use of the stretch tensor while avoiding the degeneracy of the stress tensor under rotation. Results reveal that the interface separating two elastic solids always behaves in a stable oscillatory or decaying oscillatory manner due to the existence of shear waves, which are able to transport the initial vorticity away from the interface. In the case of elastic-plastic materials, the interface behaves at first in an unstable manner similar to a fluid. Ejecta formation is appreciated under certain initial conditions while in other conditions, after an initial period of growth, the interface displays a quasi-stationary long-term behavior due to stress relaxation. The effect of secondary shock-interface interactions (re-shocks) in converging geometries is also studied. A turbulent mixing zone, similar to what is observed in gas--gas interfaces, is created, especially when materials with low strength driven by moderate to strong shocks are considered.https://thesis.library.caltech.edu/id/eprint/7488Interplay 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/7785Modeling, Simulation, and Design of Self-Assembling Space Systems: Accurate Collision Detection, Robust Time Integration, and Optimal Control
https://resolver.caltech.edu/CaltechTHESIS:09132012-125328533
Authors: {'items': [{'email': 'gwendolynbrook@gmail.com', 'id': 'Johnson-G-B', 'name': {'family': 'Johnson', 'given': 'Gwendolyn Brook'}, 'show_email': 'YES'}]}
Year: 2013
DOI: 10.7907/73S0-Y593
Motivated by issues inherent in modeling and designing self-assembling systems (e.g. multiple collisions, collisions between non-smooth bodies, clumping and jamming behaviors, etc.), the goal of this thesis is to develop robust numerical tools that enable ecient and accurate direct simulation of self assembling systems and the application of optimal control methods to this type of system. The systems will be alternately modeled using linear nite elements, rigid bodies, or chains of rigid bodies. To this end, this work begins with development of a linear programming based collision detection algorithm for general convex polyhedral bodies. The resulting linear program has several features which render it extremely useful in determining the force system at the time of contact in numerical collision integrators. With robust collision detection in hand, three related numerical integration methods for dynamics with collisions are treated; a direct potential-based approach, and exact collision integrator in a discrete variational setting, and a decomposition-based algorithm, again in the discrete variational setting. Finally, several control problems are treated in the Discrete Mechanics and Optimal Control{Constrained (DMOCC) framework in which collisions between non-smooth bodies either need to be avoided or explicitly included in the optimal control problem. A globally stable feedback controller and a family of trajectories for spacecraft docking are also developed and tested with an accurate representation of an optimized CubeSat docking system.https://thesis.library.caltech.edu/id/eprint/7203Investigation of Hypervelocity Impact Phenomena Using Real-time Concurrent Diagnostics
https://resolver.caltech.edu/CaltechTHESIS:06072013-143355354
Authors: {'items': [{'email': 'jmmihaly@gmail.com', 'id': 'Mihaly-Jonathan-Michael', 'name': {'family': 'Mihaly', 'given': 'Jonathan Michael'}, 'show_email': 'YES'}]}
Year: 2013
DOI: 10.7907/V3A7-7686
Hypervelocity impact of meteoroids and orbital debris poses a serious and growing threat to spacecraft. To study hypervelocity impact phenomena, a comprehensive ensemble of real-time concurrently operated diagnostics has been developed and implemented in the Small Particle Hypervelocity Impact Range (SPHIR) facility. This suite of simultaneously operated instrumentation provides multiple complementary measurements that facilitate the characterization of many impact phenomena in a single experiment. The investigation of hypervelocity impact phenomena described in this work focuses on normal impacts of 1.8 mm nylon 6/6 cylinder projectiles and variable thickness aluminum targets. The SPHIR facility two-stage light-gas gun is capable of routinely launching 5.5 mg nylon impactors to speeds of 5 to 7 km/s. Refinement of legacy SPHIR operation procedures and the investigation of first-stage pressure have improved the velocity performance of the facility, resulting in an increase in average impact velocity of at least 0.57 km/s. Results for the perforation area indicate the considered range of target thicknesses represent multiple regimes describing the non-monotonic scaling of target perforation with decreasing target thickness. The laser side-lighting (LSL) system has been developed to provide ultra-high-speed shadowgraph images of the impact event. This novel optical technique is demonstrated to characterize the propagation velocity and two-dimensional optical density of impact-generated debris clouds. Additionally, a debris capture system is located behind the target during every experiment to provide complementary information regarding the trajectory distribution and penetration depth of individual debris particles. The utilization of a coherent, collimated illumination source in the LSL system facilitates the simultaneous measurement of impact phenomena with near-IR and UV-vis spectrograph systems. Comparison of LSL images to concurrent IR results indicates two distinctly different phenomena. A high-speed, pressure-dependent IR-emitting cloud is observed in experiments to expand at velocities much higher than the debris and ejecta phenomena observed using the LSL system. In double-plate target configurations, this phenomena is observed to interact with the rear-wall several micro-seconds before the subsequent arrival of the debris cloud. Additionally, dimensional analysis presented by Whitham for blast waves is shown to describe the pressure-dependent radial expansion of the observed IR-emitting phenomena. Although this work focuses on a single hypervelocity impact configuration, the diagnostic capabilities and techniques described can be used with a wide variety of impactors, materials, and geometries to investigate any number of engineering and scientific problems.https://thesis.library.caltech.edu/id/eprint/7869Extracting Material Response from Simple Mechanical Tests on Hardening-Softening-Hardening Viscoplastic Solids
https://resolver.caltech.edu/CaltechTHESIS:05142014-151151819
Authors: {'items': [{'email': 'nishanthini089@gmail.com', 'id': 'Mohan-Nisha', 'name': {'family': 'Mohan', 'given': 'Nisha'}, 'show_email': 'YES'}]}
Year: 2014
DOI: 10.7907/MMTW-FF91
<p>Compliant foams are usually characterized by a wide range of desirable mechanical properties. These properties include viscoelasticity at different temperatures, energy absorption, recoverability under cyclic loading, impact resistance, and thermal, electrical, acoustic and radiation-resistance. Some foams contain nano-sized features and are used in small-scale devices. This implies that the characteristic dimensions of foams span multiple length scales, rendering modeling their mechanical properties difficult. Continuum mechanics-based models capture some salient experimental features like the linear elastic regime, followed by non-linear plateau stress regime. However, they lack mesostructural physical details. This makes them incapable of accurately predicting local peaks in stress and strain distributions, which significantly affect the deformation paths. Atomistic methods are capable of capturing the physical origins of deformation at smaller scales, but suffer from impractical computational intensity. Capturing deformation at the so-called meso-scale, which is capable of describing the phenomenon at a continuum level, but with some physical insights, requires developing new theoretical approaches.</p>
<p>A fundamental question that motivates the modeling of foams is ‘how to extract the intrinsic material response from simple mechanical test data, such as stress vs. strain response?’ A 3D model was developed to simulate the mechanical response of foam-type materials. The novelty of this model includes unique features such as the hardening-softening-hardening material response, strain rate-dependence, and plastically compressible solids with plastic non-normality. Suggestive links from atomistic simulations of foams were borrowed to formulate a physically informed hardening material input function. Motivated by a model that qualitatively captured the response of foam-type vertically aligned carbon nanotube (VACNT) pillars under uniaxial compression [2011,“Analysis of Uniaxial Compression of Vertically Aligned Carbon Nanotubes,” J. Mech.Phys. Solids, 59, pp. 2227–2237, Erratum 60, 1753–1756 (2012)], the property space exploration was advanced to three types of simple mechanical tests: 1) uniaxial compression, 2) uniaxial tension, and 3) nanoindentation with a conical and a flat-punch tip. The simulations attempt to explain some of the salient features in experimental data, like <br />
1) The initial linear elastic response. <br />
2) One or more nonlinear instabilities, yielding, and hardening.</p>
<p>The model-inherent relationships between the material properties and the overall stress-strain behavior were validated against the available experimental data. The material properties include the gradient in stiffness along the height, plastic and elastic compressibility, and hardening. Each of these tests was evaluated in terms of their efficiency in extracting material properties. The uniaxial simulation results proved to be a combination of structural and material influences. Out of all deformation paths, flat-punch indentation proved to be superior since it is the most sensitive in capturing the material properties.</p>https://thesis.library.caltech.edu/id/eprint/8235High Strain Composites and Dual-Matrix Composite Structures
https://resolver.caltech.edu/CaltechTHESIS:05292014-191924394
Authors: {'items': [{'email': 'maqueda@gmail.com', 'id': 'Maqueda-Jiménez-Ignacio', 'name': {'family': 'Maqueda Jiménez', 'given': 'Ignacio'}, 'show_email': 'YES'}]}
Year: 2014
DOI: 10.7907/Z34C-NY82
<p>Most space applications require deployable structures due to the limiting size of current launch vehicles. Specifically, payloads in nanosatellites such as CubeSats require very high compaction ratios due to the very limited space available in this typo of platform. Strain-energy-storing deployable structures can be suitable for these applications, but the curvature to which these structures can be folded is limited to the elastic range. Thanks to fiber microbuckling, high-strain composite materials can be folded into much higher curvatures without showing significant damage, which makes them suitable for very high compaction deployable structure applications. However, in applications that require carrying loads in compression, fiber microbuckling also dominates the strength of the material. A good understanding of the strength in compression of high-strain composites is then needed to determine how suitable they are for this type of application.</p>
<p>The goal of this thesis is to investigate, experimentally and numerically, the microbuckling in compression of high-strain composites. Particularly, the behavior in compression of unidirectional carbon fiber reinforced silicone rods (CFRS) is studied. Experimental testing of the compression failure of CFRS rods showed a higher strength in compression than the strength estimated by analytical models, which is unusual in standard polymer composites. This effect, first discovered in the present research, was attributed to the variation in random carbon fiber angles respect to the nominal direction. This is an important effect, as it implies that microbuckling strength might be increased by controlling the fiber angles. With a higher microbuckling strength, high-strain materials could carry loads in compression without reaching microbuckling and therefore be suitable for several space applications.</p>
<p>A finite element model was developed to predict the homogenized stiffness of the CFRS, and the homogenization results were used in another finite element model that simulated a homogenized rod under axial compression. A statistical representation of the fiber angles was implemented in the model. The presence of fiber angles increased the longitudinal shear stiffness of the material, resulting in a higher strength in compression. The simulations showed a large increase of the strength in compression for lower values of the standard deviation of the fiber angle, and a slight decrease of strength in compression for lower values of the mean fiber angle. The strength observed in the experiments was achieved with the minimum local angle standard deviation observed in the CFRS rods, whereas the shear stiffness measured in torsion tests was achieved with the overall fiber angle distribution observed in the CFRS rods.</p>
<p>High strain composites exhibit good bending capabilities, but they tend to be soft out-of-plane. To achieve a higher out-of-plane stiffness, the concept of dual-matrix composites is introduced. Dual-matrix composites are foldable composites which are soft in the crease regions and stiff elsewhere. Previous attempts to fabricate continuous dual-matrix fiber composite shells had limited performance due to excessive resin flow and matrix mixing. An alternative method, presented in this thesis uses UV-cure silicone and fiberglass to avoid these problems. Preliminary experiments on the effect of folding on the out-of-plane stiffness are presented. An application to a conical log-periodic antenna for CubeSats is proposed, using origami-inspired stowing schemes, that allow a conical dual-matrix composite shell to reach very high compaction ratios.</p>https://thesis.library.caltech.edu/id/eprint/8431Strength 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/8630Optimal 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/7993A 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/8819Discrete Modeling of Granular Media: A NURBS-based Approach
https://resolver.caltech.edu/CaltechTHESIS:12042014-104112714
Authors: {'items': [{'email': 'kengwit@gmail.com', 'id': 'Lim-Keng-Wit', 'name': {'family': 'Lim', 'given': 'Keng-Wit'}, 'show_email': 'YES'}]}
Year: 2015
DOI: 10.7907/Z9W093V4
This dissertation is concerned with the development of a new discrete element method (DEM) based on Non-Uniform Rational Basis Splines (NURBS). With NURBS, the new DEM is able to capture sphericity and angularity, the two particle morphological measures used in characterizing real grain geometries. By taking advantage of the parametric nature of NURBS, the Lipschitzian dividing rectangle (DIRECT) global optimization procedure is employed as a solution procedure to the closest-point projection problem, which enables the contact treatment of non-convex particles. A contact dynamics (CD) approach to the NURBS-based discrete method is also formulated. By combining particle shape flexibility, properties of implicit time-integration, and non-penetrating constraints, we target applications in which the classical DEM either performs poorly or simply fails, i.e., in granular systems composed of rigid or highly stiff angular particles and subjected to quasistatic or dynamic flow conditions. The CD implementation is made simple by adopting a variational framework, which enables the resulting discrete problem to be readily solved using off-the-shelf mathematical programming solvers. The capabilities of the NURBS-based DEM are demonstrated through 2D numerical examples that highlight the effects of particle morphology on the macroscopic response of granular assemblies under quasistatic and dynamic flow conditions, and a 3D characterization of material response in the shear band of a real triaxial specimen.https://thesis.library.caltech.edu/id/eprint/8734Micromechanical 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 Continuum Model for Slip-Twinning Interactions in Magnesium and Magnesium Alloys
https://resolver.caltech.edu/CaltechTHESIS:01252016-164549986
Authors: {'items': [{'email': 'yingryic@gmail.com', 'id': 'Chang-Yingrui-Ray', 'name': {'family': 'Chang', 'given': 'Yingrui (Ray)'}, 'show_email': 'YES'}]}
Year: 2016
DOI: 10.7907/Z96M34RX
<p>Due to their high specific strength and low density, magnesium and magnesium-based alloys have gained great technological importance in recent years. However, their underlying hexagonal crystal structure furnishes Mg and its alloys with a complex mechanical behavior because of their comparably smaller number of energetically favorable slip systems. Besides the commonly studied slip mechanism, another way to accomplish general deformation is through the additional mechanism of deformation-induced twinning. The main aim of this thesis research is to develop an efficient continuum model to understand and ultimately predict the material response resulting from the interaction between these two mechanisms.</p>
<p>The constitutive model we present is based on variational constitutive updates of plastic slips and twin volume fractions and accounts for the related lattice reorientation mechanisms. The model is applied to single- and polycrystalline pure magnesium. We outline the finite-deformation plasticity model combining basal, pyramidal, and prismatic dislocation activity as well as a convexification based approach for deformation twinning. A comparison with experimental data from single-crystal tension-compression experiments validates the model and serves for parameter identification. The extension to polycrystals via both Taylor-type modeling and finite element simulations shows a
characteristic stress-strain response that agrees well with experimental observations for polycrystalline magnesium. The presented continuum model does not aim to represent the full details of individual twin-dislocation interactions, yet it is sufficiently efficient to allow for finite element simulations while qualitatively capturing the underlying microstructural deformation mechanisms.</p>https://thesis.library.caltech.edu/id/eprint/9548Microscopic Origin of Macroscopic Strength in Granular Media: A Numerical and Analytical Approach
https://resolver.caltech.edu/CaltechTHESIS:05042016-174005898
Authors: {'items': [{'email': 'alexjerves982@hotmail.com', 'id': 'Jerves-Cobo-Alex-Xavier', 'name': {'family': 'Jerves Cobo', 'given': 'Alex Xavier'}, 'orcid': '0000-0002-6556-8727', 'show_email': 'YES'}]}
Year: 2016
DOI: 10.7907/Z9GB2211
<p>Constitutive modeling in granular materials has historically been based on macroscopic experimental observations that, while being usually effective at predicting the bulk behavior of these type of materials, suffer important limitations when it comes to understanding the physics behind grain-to-grain interactions that induce the material to macroscopically behave in a given way when subjected to certain boundary conditions.</p>
<p>The advent of the discrete element method (DEM) in the late 1970s helped scientists and engineers to gain a deeper insight into some of the most fundamental mechanisms furnishing the grain scale. However, one of the most critical limitations of classical DEM schemes has been their inability to account for complex grain morphologies. Instead, simplified geometries such as discs, spheres, and polyhedra have typically been used. Fortunately, in the last fifteen years, there has been an increasing development of new computational as well as experimental techniques, such as non-uniform rational basis splines (NURBS) and 3D X-ray Computed Tomography (3DXRCT), which are contributing to create new tools that enable the inclusion of complex grain morphologies into DEM schemes.</p>
<p>Yet, as the scientific community is still developing these new tools, there is still a gap in thoroughly understanding the physical relations connecting grain and continuum scales as well as in the development of discrete techniques that can predict the emergent behavior of granular materials without resorting to phenomenology, but rather can directly unravel the micro-mechanical origin of macroscopic behavior.</p>
<p>In order to contribute towards closing the aforementioned gap, we have developed a micro-mechanical analysis of macroscopic peak strength, critical state, and residual strength in two-dimensional non-cohesive granular media, where typical continuum constitutive quantities such as frictional strength and dilation angle are explicitly related to their corresponding grain-scale counterparts (e.g., inter-particle contact forces, fabric, particle displacements, and velocities), providing an across-the-scale basis for better understanding and modeling granular media.</p>
<p>In the same way, we utilize a new DEM scheme (LS-DEM) that takes advantage of a mathematical technique called level set (LS) to enable the inclusion of real grain shapes into a classical discrete element method. After calibrating LS-DEM with respect to real experimental results, we exploit part of its potential to study the dependency of critical state (CS) parameters such as the critical state line (CSL) slope, CSL intercept, and CS friction angle on the grain's morphology, i.e., sphericity, roundness, and regularity.</p>
<p>Finally, we introduce a first computational algorithm to ``clone'' the grain morphologies of a sample of real digital grains. This cloning algorithm allows us to generate an arbitrary number of cloned grains that satisfy the same morphological features (e.g., roundness and aspect ratio) displayed by their real parents and can be included into a DEM simulation of a given mechanical phenomenon. In turn, this will help with the development of discrete techniques that can directly predict the engineering scale behavior of granular media without resorting to phenomenology.</p>
https://thesis.library.caltech.edu/id/eprint/9701Fabrication, Characterization, And Deformation of 3D Structural Meta-Materials
https://resolver.caltech.edu/CaltechTHESIS:07132015-150843708
Authors: {'items': [{'email': 'Lauren.c.montemayor@gmail.com', 'id': 'Montemayor-Lauren-Christine', 'name': {'family': 'Montemayor', 'given': 'Lauren Christine'}, 'show_email': 'NO'}]}
Year: 2016
DOI: 10.7907/Z9D21VH2
Current technological advances in fabrication methods have provided pathways to creating architected structural meta-materials similar to those found in natural organisms that are structurally robust and lightweight, such as diatoms. Structural meta-materials are materials with mechanical properties that are determined by material properties at various length scales, which range from the material microstructure (nm) to the macro-scale architecture (μm – mm). It is now possible to exploit material size effect, which emerge at the nanometer length scale, as well as structural effects to tune the material properties and failure mechanisms of small-scale cellular solids, such as nanolattices.
This work demonstrates the fabrication and mechanical properties of 3-dimensional hollow nanolattices in both tension and compression. Hollow gold nanolattices loaded in uniaxial compression demonstrate that strength and stiffness vary as a function of geometry and tube wall thickness. Structural effects were explored by increasing the unit cell angle from 30° to 60° while keeping all other parameters constant; material size effects were probed by varying the tube wall thickness, t, from 200nm to 635nm, at a constant relative density and grain size. In-situ uniaxial compression experiments reveal an order-of-magnitude increase in yield stress and modulus in nanolattices with greater lattice angles, and a 150% increase in the yield strength without a concomitant change in modulus in thicker-walled nanolattices for fixed lattice angles. These results imply that independent control of structural and material size effects enables tunability of mechanical properties of 3-dimensional architected meta-materials and highlight the importance of material, geometric, and microstructural effects in small-scale mechanics.
This work also explores the flaw tolerance of 3D hollow-tube alumina kagome nanolattices with and without pre-fabricated notches, both in experiment and simulation. Experiments demonstrate that the hollow kagome nanolattices in uniaxial tension always fail at the same load when the ratio of notch length (a) to sample width (w) is no greater than 1/3, with no correlation between failure occurring at or away from the notch. For notches with (a/w) > 1/3, the samples fail at lower peak loads and this is attributed to the increased compliance as fewer unit cells span the un-notched region. Finite element simulations of the kagome tension samples show that the failure is governed by tensile loading for (a/w) < 1/3 but as (a/w) increases, bending begins to play a significant role in the failure. This work explores the flaw sensitivity of hollow alumina kagome nanolattices in tension, using experiments and simulations, and demonstrates that the discrete-continuum duality of architected structural meta-materials gives rise to their flaw insensitivity even when made entirely of intrinsically brittle materials.
https://thesis.library.caltech.edu/id/eprint/9058Topology Optimization of Silicon Anode Structures for Lithium-Ion Battery Applications
https://resolver.caltech.edu/CaltechTHESIS:02292016-100659735
Authors: {'items': [{'email': 'sarah.mitchell.072@gmail.com', 'id': 'Mitchell-Sarah-Louise', 'name': {'family': 'Mitchell', 'given': 'Sarah Louise'}, 'show_email': 'NO'}]}
Year: 2016
DOI: 10.7907/Z9JW8BT2
This thesis presents a topology optimization methodology for the systematic design of optimal multifunctional silicon anode structures in lithium-ion batteries. In order to develop next generation high performance lithium-ion batteries, key design challenges relating to the silicon anode structure must be addressed, namely the lithiation-induced mechanical degradation and the low intrinsic electrical conductivity of silicon. As such, this work considers two design objectives of minimum compliance under design dependent volume expansion, and maximum electrical conduction through the structure, both of which are subject to a constraint on material volume. Density-based topology optimization methods are employed in conjunction with regularization techniques, a continuation scheme, and mathematical programming methods. The objectives are first considered individually, during which the iteration history, mesh independence, and influence of prescribed volume fraction and minimum length scale are investigated. The methodology is subsequently extended to a bi-objective formulation to simultaneously address both the compliance and conduction design criteria. A weighting method is used to derive the Pareto fronts, which demonstrate a clear trade-off between the competing design objectives. Furthermore, a systematic parameter study is undertaken to determine the influence of the prescribed volume fraction and minimum length scale on the optimal combined topologies. The developments presented in this work provide a foundation for the informed design and development of silicon anode structures for high performance lithium-ion batteries. https://thesis.library.caltech.edu/id/eprint/9594A 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/9053Metaconcrete: Engineered Aggregates for Enhanced Dynamic Performance
https://resolver.caltech.edu/CaltechTHESIS:07072015-124133131
Authors: {'items': [{'email': 'steffie.j.mitchell@gmail.com', 'id': 'Mitchell-Stephanie-Jane', 'name': {'family': 'Mitchell', 'given': 'Stephanie Jane'}, 'orcid': '0000-0002-7303-8216', 'show_email': 'NO'}]}
Year: 2016
DOI: 10.7907/Z9H12ZXN
This work presents the development and investigation of a new type of concrete for the attenuation of waves induced by dynamic excitation. Recent progress in the field of metamaterials science has led to a range of novel composites which display unusual properties when interacting with electromagnetic, acoustic, and elastic waves. A new structural metamaterial with enhanced properties for dynamic loading applications is presented, which is named <em>metaconcrete</em>. In this new composite material the standard stone and gravel aggregates of regular concrete are replaced with spherical engineered inclusions. Each metaconcrete aggregate has a layered structure, consisting of a heavy core and a thin compliant outer coating. This structure allows for resonance at or near the eigenfrequencies of the inclusions, and the aggregates can be tuned so that resonant oscillations will be activated by particular frequencies of an applied dynamic loading. The activation of resonance within the aggregates causes the overall system to exhibit negative effective mass, which leads to attenuation of the applied wave motion. To investigate the behavior of metaconcrete slabs under a variety of different loading conditions a finite element slab model containing a periodic array of aggregates is utilized. The frequency dependent nature of metaconcrete is investigated by considering the transmission of wave energy through a slab, which indicates the presence of large attenuation bands near the resonant frequencies of the aggregates. Applying a blast wave loading to both an elastic slab and a slab model that incorporates the fracture characteristics of the mortar matrix reveals that a significant portion of the supplied energy can be absorbed by aggregates which are activated by the chosen blast wave profile. The transfer of energy from the mortar matrix to the metaconcrete aggregates leads to a significant reduction in the maximum longitudinal stress, greatly improving the ability of the material to resist damage induced by a propagating shock wave. The various analyses presented in this work provide the theoretical and numerical background necessary for the informed design and development of metaconcrete aggregates for dynamic loading applications, such as blast shielding, impact protection, and seismic mitigation.https://thesis.library.caltech.edu/id/eprint/9052Stability of Electrode-Electrolyte Interfaces During Charging in Lithium Batteries
https://resolver.caltech.edu/CaltechTHESIS:11222015-173649284
Authors: {'items': [{'email': 'pnatsias@gmail.com', 'id': 'Natsiavas-Panagiotis-Philippos', 'name': {'family': 'Natsiavas', 'given': 'Panagiotis Philippos'}, 'show_email': 'NO'}]}
Year: 2016
DOI: 10.7907/Z93R0QR8
In this thesis we study the growth of a Li electrode-electrolyte interface in the presence of an elastic prestress. In particular, we focus our interest on Li-air batteries with a solid electrolyte, LIPON, which is a new type of secondary or rechargeable battery. Theoretical studies and experimental evidence show that during the process of charging the battery the replated lithium adds unevenly to the electrode surface. This phenomenon eventually leads to dendrite formation as the battery is charged and discharged numerous times. In order to suppress or alleviate this deleterious effect of dendrite growth, we put forth a study based on a linear stability analysis. Taking into account all the mechanisms of mass transport and interfacial kinetics, we model the evolution of the interface. We find that, in the absence of stress, the stability of a planar interface depends on interfacial diffusion properties and interfacial energy. Specifically, if Herring-Mullins capillarity-driven interfacial diffusion is accounted for, interfaces are unstable against all perturbations of wavenumber larger than a critical value. We find that the effect of an elastic prestress is always to stabilize planar interfacial growth by increasing the critical wavenumber for instability. A parametric study results in quantifying the extent of the prestress stabilization in a manner that can potentially be used in the design of Li-air batteries. Moreover, employing the theory of finite differences we numerically solve the equation that describes the evolution of the surface profile and present visualization results of the surface evolution by time. Lastly, numerical simulations performed in a commercial finite element software validate the theoretical formulation of the interfacial elastic energy change with respect to the planar interface.https://thesis.library.caltech.edu/id/eprint/9282A Fully-Nonlocal Energy-based Formulation and High-performance Realization of the Quasicontinuum Method
https://resolver.caltech.edu/CaltechTHESIS:09152015-212147583
Authors: {'items': [{'email': 'jeff.amelang@gmail.com', 'id': 'Amelang-Jeffrey-Scott', 'name': {'family': 'Amelang', 'given': 'Jeffrey Scott'}, 'show_email': 'YES'}]}
Year: 2016
DOI: 10.7907/Z9SB43PH
The quasicontinuum (QC) method was introduced to coarse-grain crystalline atomic ensembles in order to bridge the scales from individual atoms to the micro- and mesoscales. Though many QC formulations have been proposed with varying characteristics and capabilities, a crucial cornerstone of all QC techniques is the concept of summation rules, which attempt to efficiently approximate the total Hamiltonian of a crystalline atomic ensemble by a weighted sum over a small subset of atoms. In this work we propose a novel, fully-nonlocal, energy-based formulation of the QC method with support for legacy and new summation rules through a general energy-sampling scheme. Our formulation does not conceptually differentiate between atomistic and coarse-grained regions and thus allows for seamless bridging without domain-coupling interfaces. Within this structure, we introduce a new class of summation rules which leverage the affine kinematics of this QC formulation to most accurately integrate thermodynamic quantities of interest. By comparing this new class of summation rules to commonly-employed rules through analysis of energy and spurious force errors, we find that the new rules produce no residual or spurious force artifacts in the large-element limit under arbitrary affine deformation, while allowing us to seamlessly bridge to full atomistics. We verify that the new summation rules exhibit significantly smaller force artifacts and energy approximation errors than all comparable previous summation rules through a comprehensive suite of examples with spatially non-uniform QC discretizations in two and three dimensions. Due to the unique structure of these summation rules, we also use the new formulation to study scenarios with large regions of free surface, a class of problems previously out of reach of the QC method. Lastly, we present the key components of a high-performance, distributed-memory realization of the new method, including a novel algorithm for supporting unparalleled levels of deformation. Overall, this new formulation and implementation allows us to efficiently perform simulations containing an unprecedented number of degrees of freedom with low approximation error.https://thesis.library.caltech.edu/id/eprint/9155Data Driven Computing
https://resolver.caltech.edu/CaltechTHESIS:09122017-092017294
Authors: {'items': [{'email': 'imtrenton@yahoo.com', 'id': 'Kirchdoerfer-Trenton-Thomas', 'name': {'family': 'Kirchdoerfer', 'given': 'Trenton Thomas'}, 'orcid': '0000-0003-2290-1857', 'show_email': 'YES'}]}
Year: 2018
DOI: 10.7907/Z9Z899MV
Data Driven Computing is a new field of computational analysis which uses provided data to directly produce predictive outcomes. This thesis first establishes definitions of Data-Driven solvers and working examples of static mechanics problems to demonstrate efficacy. Significant extensions are then explored to both accommodate noisy data sets and apply the deveoloped methods to dynamic problems within mechanics. Possible method improvements discuss incorporation of data quality metrics and adaptive data sampling, while new applications focus on multi-scale analysis and the need for public databases to support constitutive data collaboration.
https://thesis.library.caltech.edu/id/eprint/10431Proliferation 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/10365An 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/11142Stochastic 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/11542Predicting 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/11432A Fully-Nonlocal Quasicontinuum Method to Model the Nonlinear Response of Periodic Truss Lattices
https://resolver.caltech.edu/CaltechTHESIS:05242019-115317802
Authors: {'items': [{'email': 'gpphlipot@yahoo.com', 'id': 'Phlipot-Gregory-Paul', 'name': {'family': 'Phlipot', 'given': 'Gregory Paul'}, 'orcid': '0000-0003-2721-8678', 'show_email': 'YES'}]}
Year: 2019
DOI: 10.7907/3MPP-Q119
We present a framework for the efficient, yet accurate description of general periodic truss networks based on concepts of the quasicontinuum (QC) method. Previous research in coarse-grained truss models has focused either on simple bar trusses or on two-dimensional beam lattices undergoing small deformations. Here, we extend the truss QC methodology to nonlinear deformations, general periodic beam lattices, and three dimensions. We introduce geometric nonlinearity into the model by using a corotational beam description at the level of individual truss members. Coarse-graining is achieved by the introduction of representative unit cells and a polynomial interpolation analogous to traditional QC. General periodic lattices defined by the periodic assembly of a single unit cell are modeled by retaining all unique degrees of freedom of the unit cell (identified by a lattice decomposition into simple Bravais lattices) at each macroscopic point in the simulation, and interpolating each degree of freedom individually. We show that this interpolation scheme accurately captures the homogenized properties of periodic truss lattices for uniform deformations. In order to showcase the efficiency and accuracy of the method, we compare coarse-grained simulations to fully-resolved simulations for various test problems, including: brittle fracture toughness prediction, static and dynamic indentation with geometric and material nonlinearities, and uniaxial tension of a truss lattice plate with a cylindrical hole. We also discover the notion of stretch locking --- a phenomenon where certain lattice topologies are over-constrained, resulting in artificially stiff behavior similar to volumetric locking in finite elements --- and show that using higher-order interpolation instead of affine interpolation significantly reduces the error in the presence of stretch locking in 2D and 3D. Overall, the new technique shows convincing agreement with exact, discrete results for a wide variety of lattice architectures, and offers opportunities to reduce computational expenses in structural lattice simulations and thus to efficiently extract the effective mechanical performance of discrete networks.https://thesis.library.caltech.edu/id/eprint/11541Modifying Ultrasound Waveform Parameters to Control, Influence, or Disrupt Cells
https://resolver.caltech.edu/CaltechTHESIS:05242020-045332969
Authors: {'items': [{'email': 'drmittelstein@gmail.com', 'id': 'Mittelstein-David-Reza', 'name': {'family': 'Mittelstein', 'given': 'David Reza'}, 'orcid': '0000-0001-8747-0483', 'show_email': 'NO'}]}
Year: 2020
DOI: 10.7907/71ak-w328
<p>Ultrasound can be focused into deep tissues with millimeter precision to perform non-invasive ablative therapy for diseases such as cancer. In most cases, this ablation uses high intensity ultrasound to deposit non-selective thermal or mechanical energy at the ultrasound focus, damaging both healthy bystander tissue and cancer cells. Here we describe an alternative low intensity pulsed ultrasound approach known as “oncotripsy” that leverages the distinct mechanical properties of neoplastic cells to achieve inherent cancer selectivity. We show that when applied at a specific frequency and pulse duration, focused ultrasound selectively disrupts a panel of breast, colon, and leukemia cancer cell models in suspension without significantly damaging healthy immune or red blood cells. Mechanistic experiments reveal that the formation of acoustic standing waves and the emergence of cell-seeded cavitation lead to cytoskeletal disruption, expression of apoptotic markers, and cell death. The inherent selectivity of this low intensity pulsed ultrasound approach offers a potentially safer and thus more broadly applicable alternative to non-selective high intensity ultrasound ablation.</p>
<p>In this dissertation, I describe the oncotripsy theory in its initial formulation, the experimental validation and investigation of testable predictions from that theory, and the refinement of said theory with new experimental evidence. Throughout, I describe how careful modifications to the ultrasound waveform directly can significantly impact how the ultrasound bio-effects control, influence, or disrupt cells in a selective and controlled manner.</p>
https://thesis.library.caltech.edu/id/eprint/13721Variational 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/11744High-Cycle Dynamic Cell Fatigue with Applications on Oncotripsy
https://resolver.caltech.edu/CaltechTHESIS:01202020-210729635
Authors: {'items': [{'email': 'erika.fis@gmail.com', 'id': 'Figueroa-Schibber-Erika', 'name': {'family': 'Figueroa-Schibber', 'given': 'Erika'}, 'orcid': '0000-00002-6629-297X', 'show_email': 'NO'}]}
Year: 2020
DOI: 10.7907/0425-SN62
<p>The method of <i>oncotripsy</i> (from Greek, <i>onco-</i> meaning "tumor" and <i>–tripsy</i> "to break") exploits aberrations in the material properties and morphology of cancerous cells to target them selectively using tuned low-intensity pulsed ultrasound. Compared to other noninvasive ultrasound treatments that ablate malignant tissue, oncotripsy has the capability of targeting unhealthy tissue with minimal damage to healthy cells in the ablation process.</p>
<p>We propose a model of oncotripsy that follows as an application of cell dynamics, statistical mechanical theory of network elasticity and 'birth-death' kinetics to describe processes of damage and repair of the cytoskeleton. We also develop a reduced dynamical model that approximates the three-dimensional dynamics of the cell and facilitates parameter studies, including sensitivity analysis and process optimization.</p>
<p>The dynamical system encompasses the relative motion of the nucleus to the cell membrane and a state variable measuring the extent of damage to the cytoskeleton. The dynamical system evolves in time as a result of structural dynamics and kinetics of cytoskeletal damage and repair. The resulting dynamics are complex and exhibits behavior on multiple time scales, including the period of vibration and attenuation, the characteristic time of cytoskeletal healing, the pulsing period and the time of exposure to the ultrasound. Damage on the cells develops in the order of millions of ultrasound cycles, and the failure mechanism is explained as a fatigue process. We also account for cell variability and estimate the attendant variance of the time-to-death of a cell population. We show that the dynamical model predicts — and provides a conceptual basis for understanding — the oncotripsy effect and other trends observed in experiments.</p>https://thesis.library.caltech.edu/id/eprint/13628Application of Path-Independent Integrals to Soil-Structure Interaction
https://resolver.caltech.edu/CaltechTHESIS:11212019-100323260
Authors: {'items': [{'email': 'ajgarciasuarez@gmail.com', 'id': 'García-Suárez-Antonio-Joaquín', 'name': {'family': 'García Suárez', 'given': 'Antonio Joaquín'}, 'orcid': '0000-0001-8830-4348', 'show_email': 'NO'}]}
Year: 2020
DOI: 10.7907/MMWW-B046
<p>Assessing seismic pressure increment on buried structures is a critical step in the design of infrastructure in earthquake-prone areas. Due to intrinsic complexities derived from the need to match the solution in the far-field to the localized solution around the structure, the near-field, researchers have aimed at finding simplified models focused on engineering variables as the seismic earth thrust. One such model is the so-called Younan-Veletsos model, which pivots on a stringent assumption on the stress tensor.</p>
<p>At the same time, the might of the path-independent integrals of solid mechanics to deal with problems in Geotechnical Engineering at large, and Soil-Structure Interaction in particular, has remained unexplored, despite of a rich landscape of potential applications. The unbridled success of these path-independent integrals in Fracture Mechanics, a discipline which cannot be understood without them currently, may be mirrored in problems in Geotechnical Engineering, since the two fields, despite appearing very detached from each other at first glance, share deep traits: in both cases, the system under consideration can be conceptualized as a domain with simple, easy-to-assess regions (the areas where remote loading is applied and the far-field, respectively) and also with other complex, hard-to-understand regions (the crack tip, the near-field).</p>
<p>We present the first derivation of the exact solution of the Younan-Veletsos problem, which is later analyzed to reveal phenomena not captured by previous approximate solutions. Then, we introduce a novel model which relies on the path-independent Rice’s J-integral, a customary tool in Fracture Mechanics, which is applied here in the Soil-structure Interaction context for the first time. This novel model captures those features of the exact solution that were missed by prior approximations. The capabilities of the J-integral to, first, find an upper bound of the force induced by earthquakes over the walls of underground structures, under some conditions, and, second, to understand the soil-structure kinematic interaction phenomenon are also assessed.</p>
<p>Additionally, the intermediate step of analyzing of the far-field yielded some results concerning Site Response Analysis which are also included in the text.</p>https://thesis.library.caltech.edu/id/eprint/13587Multiscale, Data-Driven and Nonlocal Modeling of Granular Materials
https://resolver.caltech.edu/CaltechTHESIS:12182020-181342301
Authors: {'items': [{'email': 'konkarapiperis@gmail.com', 'id': 'Karapiperis-Konstantinos', 'name': {'family': 'Karapiperis', 'given': 'Konstantinos'}, 'orcid': '0000-0002-6796-8900', 'show_email': 'NO'}]}
Year: 2021
DOI: 10.7907/7rtg-x780
<p>Granular materials are ubiquitous in both nature and technology. They play a key role in many applications ranging from storing food and energy to building reusable habitats and soft robots. Yet, predicting the continuum mechanical response of granular materials continues to present extraordinary challenges, despite the apparently simple laws that govern particle-scale interactions. This is largely due to the complex history dependence arising from the continuous rearrangement of their internal structure, and the nonlocality emerging from their self-organization. There is clearly an urge to develop methods that adequately address these two aspects, while bridging the long-standing divide between the grain- and the continuum scale.</p>
<p>This dissertation introduces novel theoretical and computational approaches for behavior prediction in granular solids. To begin with, we develop a framework for investigating their incremental behavior from the perspective of plasticity theory. It relies on systematically probing, through level-set discrete element calculations, the response of granular assemblies from the same initial state to multiple directions is stress space. We then extract the state- and history-dependent elasticity and plastic flow, and investigate the evolution of pertinent internal variables. We specifically study assemblies of sand particles characterized by X-ray computed tomography, as well as morphologically simpler counterparts of the same systems. Naturally arising from this investigation is the concept of a granular genome. Next, inspired by the abundance of generated high-fidelity micromechanical data, we develop an alternative data-driven approach for behavior prediction. This new multiscale modeling paradigm completely bypasses the need to define a constitutive law. Instead, the problem is directly formulated on a material data set, generated by grain-scale calculations, while pertinent constraints and conservation laws are enforced. We particularly focus on the sampling of the mechanical phase space, and develop two methods for parametrizing material history, one thermodynamically motivated and one statistically inspired. In the remainder of the thesis, we direct our attention to the understanding and modeling of nonlocality. We base our investigation on data derived from a discrete element simulation of a sample of sand subjected to triaxial compression and undergoing shear banding. By representing the granular system as a complex network, we study the self-organized and cooperative evolution of topology, kinematics and kinetics within the shear band. We specifically characterize the evolution of fundamental topological structures called force cycles, and propose a novel order parameter for the system, the minimal cycle coefficient. We find that this coefficient governs the stability of force chains, which succumb to buckling as they grow beyond a characteristic maximum length. We also analyze the statistics of nonaffine kinematics, which involve rotational and vortical particle motion. Finally, inspired by these findings, we extend the previously introduced data-driven paradigm to include nonaffine kinematics within a weakly nonlocal micropolar continuum description. By formulating the problem on a phase space augmented by higher-order kinematics and their conjugate kinetics, we bypass for the first time the need to define an internal length scale, which is instead discovered from the data. By carrying out a data-driven prediction of shear banding, we find that this nonlocal extension of the framework resolves the ill-posedness inherent to the classical continuum description. Finally, by comparing with available experimental data on the same problem, we are able to validate our theoretical developments.</p>https://thesis.library.caltech.edu/id/eprint/14036Understanding 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/14125Accelerated 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/14513Optimal 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/15274Modeling 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/14984