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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 14:59:18 +0000Shape-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/705Modeling chemical vapor deposition of thin solid films
https://resolver.caltech.edu/CaltechTHESIS:10042010-153504863
Authors: {'items': [{'id': 'Jabbour-Michel-E', 'name': {'family': 'Jabbour', 'given': 'Michel E.'}, 'show_email': 'NO'}]}
Year: 2000
DOI: 10.7907/pa2d-3n29
Chemical vapor deposition (CVD) is a process by which thin solid films are deposited on solid substrates for various technological applications. Roughly speaking, a multispecies chemically reacting gas flows past a heated substrate on top of which the deposition and subsequent formation of the alloy or compound of interest take place via a series of heterogeneous chemical reactions. The growth rate of the thin film is determined by the competition between the diffusive and convective transports of species in the gas phase, the homogeneous and heterogeneous chemical kinetics, and the morphology of the gas-film interface.
In chapter 2, a thermomechanical macroscopic model is proposed that couples the multicomponent chemically reactive gaseous flow to the bulk of the growing thin solid film via the equations that govern the morphological evolution of the film-gas interface. The surface is modeled as a separate anisotropic elastic phase, and such phenomena as surface species diffusion, heat conduction and chemistry are accounted for. In particular, the driving force at the surface is identified, and a thermodynamically consistent kinetic relation linking it to the growth velocity is proposed. A specialization of this general framework to the case of a multicomponent ideal gas and a linearly elastic solid film separated by an isotropic surface is considered.
In chapter 3, we examine a multicomponent gas flow in a vertical axisymmetric MOCVD reactor whose geometry is characterized by a small aspect ratio (defined as the ratio of the height of the reactor channel to the radius of the substrate) and operating under conditions insuring a small Mach number. A two-parameter asymptotic analysis yields, in the limit of vanishingly small aspect ratio and Mach number, a set of approximate equations governing the gas phase, combined with approximate boundary conditions at the showerhead and the gas-film interface. A specialization to the steady-state approximation is then proposed, and an analytical solution to the approximate problem is derived. It is found that this solution is of the similarity type, thus insuring a uniform temperature and chemical composition profiles along the film surface.
Finally, in chapter 4, the growth of a generic thin film via a ledge-and-terrace mechanism is examined. Of particular interest is the interaction between the microstructure of the surface and the chemical kinetics by which the adsorption/desorption of species along the terraces and the formation of the compound at the steps occur. A simple step-flow model is proposed and its specialization to the case of a binary compound is used to illustrate the complex dependence of the averaged growth rate on the chemical composition of the gas phase as well as on the morphology of the evolving surface.
https://thesis.library.caltech.edu/id/eprint/6093Phase Boundary Propagation in Heterogeneous Media
https://resolver.caltech.edu/CaltechTHESIS:10082010-142653040
Authors: {'items': [{'id': 'Craciun-Bogdan', 'name': {'family': 'Craciun', 'given': 'Bogdan'}, 'show_email': 'NO'}]}
Year: 2002
DOI: 10.7907/JXG6-W865
<p>There has been much recent progress in the study of free boundary problems motivated by phase transformations in materials science. Much of this literature considers fronts propagating in homogeneous media. However, usual materials are heterogeneous due to the presence of defects, grains and precipitates. This thesis addresses the propagation of phase boundaries in heterogeneous media.</p>
<p>A particular motivation is a material undergoing martensitic phase transformation. Given a martensitic material with many non-transforming inclusions, there are well established microscopic laws that give the complex evolution of a particular twin or phase boundary as it encounters the many inclusions. The issue of interest is the overall evolution of this interface and the effect of defects and impurities on this evolution. In particular, if the defects are small, it is desirable to find the effective macroscopic law that governs the overall motion, without having to follow all the microscopic details but implicitly taking them into account. Using a theory of phase transformations based on linear elasticity, we show that the normal velocity of the martensitic phase or twin boundary may be written as a sum of several terms: first a homogeneous (but non-local) term that one would obtain for the propagation of the boundary in a homogeneous medium, second a heterogeneous term describing the effects of the inclusions but completely independent of the phase or twin boundary and third an interfacial energy term proportional to the mean curvature of the boundary.</p>
<p>As a guide to understanding this problem, we begin with two simplified settings which are also of independent interest. First, we consider the homogenization for the case when the normal velocity depends only on position (the heterogeneous term only). This is equivalent to the homogenization of a Hamilton-Jacobi equation. We establish several variational principles which give useful formulas to characterize the effective Hamiltonian. We illustrate the usefulness of these results through examples and we also provide a qualitative study of the effective normal velocity.</p>
<p>Second, we address the case when the interfacial energy is not negligible, so we keep the heterogeneous and curvature terms. This leads to a problem of homogenization of a degenerate parabolic initial value problem. We prove a homogenization theorem and obtain a characterization for the effective normal velocity, which however proves not to be too useful a tool for actual calculations. We therefore study some interesting examples and limiting cases and provide explicit formula in these situations. We also provide some numerical examples.</p>
<p>We finally address the problem in full generality in the setting of anti-plane shear. We explicitly evaluate the term induced by the presence of the inclusions and we propose a numerical method that allows us to trace the evolution of the phase boundary. We use this numerical method to evaluate the effect of the inclusions and show that their effect is quite localized. We use it to explain some experimental observations in NiTi.</p>https://thesis.library.caltech.edu/id/eprint/6122Dynamics 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/4442Energy-Minimizing Microstructures in Multiphase Elastic Solids
https://resolver.caltech.edu/CaltechETD:etd-05252004-131315
Authors: {'items': [{'email': 'Isaac.Chenchiah : bristol.ac.uk', 'id': 'Chenchiah-Isaac-Vikram', 'name': {'family': 'Chenchiah', 'given': 'Isaac Vikram'}, 'orcid': '0000-0002-8618-620X', 'show_email': 'YES'}]}
Year: 2004
DOI: 10.7907/RXE5-9A33
<p>This thesis concerns problems of microstructure and its macroscopic consequences in multiphase elastic solids, both single crystals and polycrystals.</p>
<p>The elastic energy of a two-phase solid is a function of its microstructure. Determining the infimum of the energy of such a solid and characterizing the associated extremal microstructures is an important problem that arises in the modeling of the shape memory effect, microstructure evolution (precipitation, coarsening, etc.), homogenization of composites and optimal design. Mathematically, the problem is to determine the relaxation under fixed volume fraction of a two-well energy.</p>
<p>We compute the relaxation under fixed volume fraction for a two-well linearized elastic energy in two dimensions with no restrictions on the elastic moduli and transformation strains; and show that there always exist rank-I or rank-II laminates that are extremal. By minimizing over the volume fraction we obtain the quasiconvex envelope of the energy. We relate these results to experimental observations on the equilibrium morphology and behavior under external loads of precipitates in Nickel superalloys. We also compute the relaxation under fixed volume fraction for a two-well linearized elastic energy in three dimensions when the elastic moduli are isotropic (with no restrictions on the transformation strains) and show that there always exist rank-I, rank-II or rank-III laminates that are extremal.</p>
<p>Shape memory effect is the ability of a solid to recover on heating apparently plastic deformation sustained below a critical temperature. Since utility of shape memory alloys critically depends on their polycrystalline behavior, understanding and predicting the recoverable strains of shape memory polycrystals is a central open problem in the study of shape memory alloys. Our contributions to the solution of this problem are twofold:</p>
<p>We prove a dual variational characterization of the recoverable strains of shape memory polycrystals and show that dual (stress) fields could be signed Radon measures with finite mass supported on sets with Lebesgue measure zero. We also show that for polycrystals made of materials undergoing cubic-tetragonal transformations the strains fields associated with macroscopic recoverable strains are related to the solutions of hyperbolic partial differential equations.</p>https://thesis.library.caltech.edu/id/eprint/2044Atomic 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/4991The 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/8A Micromechanics-Inspired Three-Dimensional Constitutive Model for the Thermomechanical Response of Shape-Memory Alloys
https://resolver.caltech.edu/CaltechETD:etd-05112006-162948
Authors: {'items': [{'id': 'Sadjadpour-Amir', 'name': {'family': 'Sadjadpour', 'given': 'Amir'}, 'show_email': 'NO'}]}
Year: 2006
DOI: 10.7907/MB1W-1V17
<p>The goal of this thesis is to develop a full dimensional micromechanics-inspired constitutive model for polycrystalline shape-memory alloys. The model is presented in two forms: (1) The one-dimensional framework where we picture the ability of the model in capturing main properties of shape memory alloys such as superelasticity and shape-memory effect; (2) The full dimensional model where micromechanics origins of the model, the concepts emerged from those analysis and their relation to macroscopic properties in both single and polycrystals are presented.</p>
<p>We use this framework to study the effects of the texture and anisotropy in the material behavior. Since phase transformation often competes with plasticity in shape-memory alloys, we incorporate that phenomenon into our model. We also demonstrate the ability of the model to predict the response of the material and track the phase transformation process for multi-axial, proportional and non-proportional loading and unloading experiments. We consider both stress-controlled and strain-controlled experiments and develop the model for isothermal, adiabatic and non-adiabatic thermal conditions. Adiabatic heating and loading rate both lead to the apparent hardening at high rates. We also visit this problem and examine the relative role of these two factors.</p>
<p>Finally we extend our model to study the reversible "bcc" to "hcp" martensitic phase transformation in pure iron. We consider a wide range of loading rates ranging from quasistatic to high rate dynamic loading and use our model to describe the evolution of the microstructure along with the effects of the rate hardening and thermal softening.</p>https://thesis.library.caltech.edu/id/eprint/1725Deformation and Fracture of Thin Sheets of Nitinol
https://resolver.caltech.edu/CaltechETD:etd-05252007-000127
Authors: {'items': [{'email': 'samdaly@engineering.ucsb.edu', 'id': 'Daly-Samantha-Hayes', 'name': {'family': 'Daly', 'given': 'Samantha Hayes'}, 'orcid': '0000-0002-7297-1696', 'show_email': 'YES'}]}
Year: 2007
DOI: 10.7907/RATX-WG46
Nickel-Titanium (Nitinol) is a Shape Memory Alloy (SMA) that exhibits superelasticity (pseudoelasticity) and shape memory by a solid-solid state diffusion-less phase transformation. Phase transformation and the resulting strain localization in Nitinol has long been a topic of study, both for its inherent scientific interest and also because of the large number of practical applications of this bimetallic alloy. Although Nitinol devices are extensively used in the medical industry, there is a fundamental gap in the amount of high-quality quantitative experimental data detailing strain localization. The numerous applications of shape memory alloys provide the motivation to understand the deformation and failure mechanisms of these materials, particularly their fatigue and fracture behavior. By using an in-situ optical technique called Digital Image Correlation (DIC), quantitative measures of strain localization in Nitinol are presented for the first time in both deformation and failure modes. In addition, a finite element small-scale transformation analysis near a crack tip in Nitinol subjected to mode-I loading under plane stress conditions is performed for the first time. The experimental results and finite element analysis provide new and detailed insights concerning the structure of phase transformation and crack tip fields in Nitinol.https://thesis.library.caltech.edu/id/eprint/2067Electronic 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/1822Nonlocal Microstructural Mechanics of Active Materials
https://resolver.caltech.edu/CaltechETD:etd-06122006-161234
Authors: {'items': [{'email': 'kaushikdayal@gmail.com', 'id': 'Dayal-Kaushik', 'name': {'family': 'Dayal', 'given': 'Kaushik'}, 'orcid': '0000-0002-0516-3066', 'show_email': 'YES'}]}
Year: 2007
DOI: 10.7907/YGR6-H428
<p>This thesis deals with two aspects of the mechanics of symmetry-breaking defects such as phase boundaries, inclusions and free surfaces, and their role in the macroscopic response of active materials. We first examine the problem of kinetics using a nonlocal theory, and then study the role of geometry in active materials with fields that are not confined to the material.</p>
<p>Classical PDE continuum models of active materials are not closed, and require nucleation and kinetic information or regularization as additional constitutive input. We examine this problem in the peridynamic formulation, a nonlocal continuum model that uses integral equations to account for long-range forces that are important at small scales, and allows resolution of the structure of interfaces. Our analysis shows that kinetics is inherent to the theory. Viewing nucleation as a dynamic instability at small times, we obtain interesting scaling results and insight into nucleation in regularized theories. We also exploit the computational ease of this theory to study an unusual mechanism that allows a phase boundary to bypass an inclusion.</p>
<p>Shifting focus to problems of an applied nature, we consider issues in the design of ferroelectric optical/electronic circuit elements. Free surfaces and electrodes on these devices generate electrical fields that must be resolved over all space, and not just within the body. These fields greatly enhance the importance of geometry in understanding the electromechanical response of these materials, and give rise to strong size and shape dependence. We describe a computational method that transforms this problem into a local setting in an accurate and efficient manner. We apply it to three examples: closure domains, a ferroelectric slab with segmented electrodes and a notch subjected to electro-mechanical loading.</p>https://thesis.library.caltech.edu/id/eprint/2558Structure and Evolution of Martensitic Phase Boundaries
https://resolver.caltech.edu/CaltechETD:etd-05292007-211950
Authors: {'items': [{'email': 'patrick.dondl@mathematik.uni-freiburg.de', 'id': 'Dondl-Patrick-Werner', 'name': {'family': 'Dondl', 'given': 'Patrick Werner'}, 'orcid': '0000-0003-3035-7230', 'show_email': 'YES'}]}
Year: 2007
DOI: 10.7907/89AW-3S87
<p>This work examines two major aspects of martensitic phase boundaries. The first part studies numerically the deformation of thin films of shape memory alloys by using subdivision surfaces for discretization. These films have gained interest for their possible use as actuators in microscale electro-mechanical systems, specifically in a pyramid-shaped configuration. The study of such configurations requires adequate resolution of the regions of high strain gradient that emerge from the interplay of the multi-well strain energy and the penalization of the strain gradient through a surface energy term. This surface energy term also requires the spatial numerical discretization to be of higher regularity, i.e., it needs to be continuously differentiable. This excludes the use of a piecewise linear approximation. It is shown in this thesis that subdivision surfaces provide an attractive tool for the numerical examination of thin phase transforming structures. We also provide insight in the properties of such tent-like structures.</p>
<p>The second part of this thesis examines the question of how the rate-independent hysteresis that is observed in martensitic phase transformations can be reconciled with the linear kinetic relation linking the evolution of domains with the thermodynamic driving force on a microscopic scale. A sharp interface model for the evolution of martensitic phase boundaries, including full elasticity, is proposed. The existence of a solution for this coupled problem of a free discontinuity evolution to an elliptic equation is proved. Numerical studies using this model show the pinning of a phase boundary by precipitates of non-transforming material. This pinning is the first step in a stick-slip behavior and therefore a rate-independent hysteresis.</p>
<p>In an approximate model, the existence of a critical pinning force as well as the existence of solutions traveling with an average velocity are proved rigorously. For this shallow phase boundary approximation, the depinning behavior is studied numerically. We find a universal power-law linking the driving force to the average velocity of the interface. For a smooth local force due to an inhomogeneous but periodic environment we find a critical exponent of 1/2.</p>
https://thesis.library.caltech.edu/id/eprint/2251Study of Constitutive Behavior of Ferroelectrics via Self-Consistent Modeling and Neutron Diffraction
https://resolver.caltech.edu/CaltechETD:etd-05252007-154233
Authors: {'items': [{'id': 'Motahari-Seyed-Maziar', 'name': {'family': 'Motahari', 'given': 'Seyed-Maziar'}, 'show_email': 'NO'}]}
Year: 2007
DOI: 10.7907/55PX-GT55
<p>The central goal of this study is to develop a reliable self-consistent model to describe the constitutive behavior of polycrystalline ferroelectrics and to predict their lattice strain and texture evolution. Starting with the model developed by Huber et al. formulations and refinements were added to increase both the functionality and the accuracy of the model’s results. These refinements include methods for calculating lattice strain, tracking the number of domains contributing to diffraction patterns, locking the domain switching at a specified level, inputting initial grain orientation distribution, and a correction for a major flaw in the previous model: the phenomenon of reverse domain switching.</p>
<p>To validate the model’s predictions, in-situ neutron diffraction experiments were conducted on polycrystalline BaTiO₃ under uniaxial compression. It was found that the data analysis required a close inspection due to lattice strain anisotropy and leading to a systematic study of different analysis methods: the single peak method, the regular whole-pattern Rietveld method (with no strain anisotropy), and the improved Rietveld method which offers limited strain anisotropy analysis. The latter was judged to be the most appropriate for ferroelectrics and it was further improved by new formulations to permit lattice strain anisotropy analysis for tetragonal and hexagonal crystal structures.</p>
<p>The comparison of model predictions and diffraction data from BaTiO₃ yielded the following observations: (i) domain switching starts at very low stresses (< 10 MPa) and proceeds gradually; (ii) domains with c-axes closer to the loading axis start switching earlier and experience more switching; (iii) lattice-plane-specific (hkl) strains, with the exception of (111), exhibit apparent hardening after switching starts. The level of agreement between the model and the experimental data was satisfactory, particularly considering the relative simplicity of the model. Keeping in mind the basic assumptions present in the model, it can be a useful analytical tool in the study of ferroelectric constitutive behavior when combined with diffraction experiments.</p>https://thesis.library.caltech.edu/id/eprint/2074Effective Behavior of Dielectric Elastomer Composites
https://resolver.caltech.edu/CaltechETD:etd-08272007-145455
Authors: {'items': [{'email': 'lixiutian@gmail.com', 'id': 'Tian-Lixiu', 'name': {'family': 'Tian', 'given': 'Lixiu'}, 'show_email': 'YES'}]}
Year: 2008
DOI: 10.7907/CZNF-JB47
<p>The class of electroactive polymers has been developed to a point where real life applications as ``artificial muscles" are conceivable. These actuator materials provide attractive advantages: they are soft, lightweight, can undergo large deformation, possess fast response time and are resilient. However, widespread application has been hindered by their limitations: the need for a large electric field, relatively small forces and energy density. However, recent experimental work shows great promise that this limitation can be overcome by making composites of two materials with high contrast in their dielectric modulus. In this thesis, a theoretical framework is derived to describe the electrostatic effect of the dielectric elastomers. Numerical experiments are conducted to explain the reason for the promising experimental results and to explore better microstructures of the composites to enhance the favorable properties.</p>
<p>The starting point of this thesis is a general variational principle, which characterizes the behavior of solids under combined mechanical and electrical loads. Based on this variational principle, we assume the electric field is small as of order ε½, assume further the deformation is caused by the electrostatic effects; the deformation field is then of order ε. Using the tool of Γ-convergence, we derive a small-strain model in which the electric field and the deformation field are decoupled which results in a huge simplification of the problem.</p>
<p>Based on this small-strain model, employing the powerful tool of two-scale convergence, we derive the effective properties for dielectric composites conducting small strains. A formula of the effective electromechanical coupling coefficients is given in terms of the unit cell solutions.</p>
<p>Armed with these theoretical results, we carry out numerical experiments about the effective properties of different kind of composites. A very careful analysis of the numerical results provides a deep understanding of the mechanism of the enhancement in strain by making composites of different microstructures.</p>https://thesis.library.caltech.edu/id/eprint/3248Phase-Shifting Full-Field Interferometric Methods for In-Plane Tensorial Stress Determination for Fracture Studies
https://resolver.caltech.edu/CaltechETD:etd-05272009-094456
Authors: {'items': [{'email': 'slbkramer@gmail.com', 'id': 'Kramer-Sharlotte-Lorraine-Bolyard', 'name': {'family': 'Kramer', 'given': 'Sharlotte Lorraine Bolyard'}, 'orcid': '0000-0001-6015-8385', 'show_email': 'NO'}]}
Year: 2009
DOI: 10.7907/M9NV-T722
<p>Anisotropic fracture criteria can be established with understanding of full-field stresses near a crack. The anisotropy of the stresses implies that the full in-plane tensorial stress is required, but current experimental optical techniques only give the sum or difference of principal stresses, motivating development of experimental methods that combines two experimental techniques to determine all of the stress components, such as the proposed hybrid experimental method of phase-shifting photoelasticity and transmission Coherent Gradient Sensing (CGS). This thesis establishes this method for stress determination around cracks in photoelastic materials.</p>
<p>This experimental method first requires a new theory for the use of CGS, a wavefront shearing interferometry technique, for photoelastic materials. The first analysis of transmission wavefront shearing interferometry for photoelastic materials is experimentally demonstrated using CGS in full field for a compressed polycarbonate plate with a side V-shaped notch with good agreement with theoretical data. For the hybrid experimental method, a six-step phase-shifting photoelasticity method determines principal stress directions and the difference of principal stresses, and the transmission CGS method utilizes a standard four-step phase-shifting method to measure the x and y first derivatives of the sum of principal stresses, which are numerically integrated for the sum of principal stresses. The full-field principal stresses may then be separated, followed by the Cartesian and polar coordinate stresses using the principal stress directions and the polar angle. The method is first demonstrated for in-plane tensorial stress determination for a compressed polycarbonate plate with a side V-shaped notch with good comparison to theoretical stress fields. The CGS-photoelasticity experimental method is then applied to determine stresses around Mode I-dominant cracks in Homalite-100. The experimental stress fields have excellent agreement with the full-field 2D asymptotic crack solution using the Mode I and Mode II stress intensity factor values calculated from the experimental data. With this foundation of stress determination around cracks in photoelastic materials and with some future analysis, this experimental method can be extended to determine stresses in anisotropic crystals for fracture studies.</p>
https://thesis.library.caltech.edu/id/eprint/2176Wrinkling of Dielectric Elastomer Membranes
https://resolver.caltech.edu/CaltechETD:etd-09222008-161217
Authors: {'items': [{'email': 'lzheng@caltech.edu', 'id': 'Zheng-Ling', 'name': {'family': 'Zheng', 'given': 'Ling'}, 'show_email': 'NO'}]}
Year: 2009
DOI: 10.7907/RTAB-GX13
<p>Wrinkling of thin membranes due to different in-plane loading and boundary conditions has drawn attention of researchers in structural engineering since the development of thin webs for early aircraft structures. More recently, prestressed lightweight membrane structures have been proposed for future space missions, for example solar sails, the next generation space telescope sunshield and space-based radar systems. These structures are often partially wrinkled during operation. The formation of wrinkles alters the load paths and the structural stiffness of the membranes. More importantly its occurrence degrades the surface accuracy of these structures, which is a key design parameter.</p>
<p>This dissertation focuses on wrinkling of thin rectangular membranes subjected to uniaxial tension and investigates the onset and profiles of wrinkles using both experimental and numerical approaches.</p>
<p>An optical method, which integrates fringe projection method with four-frame phase-shifting technique, pre-conditioned conjugate gradient phase unwrapping algorithm and series-expansion carrier removal technique was developed in order to measure the full-field out-of-plane displacement of membranes, and an optical system was constructed including a uniaxial tension testbed, a LCD projector and a CCD camera. A series of uniaxial tensile tests were carried out on silicone rubber membranes of varying dimensions and aspect ratios in order to investigate the effect of geometric factors such as membrane dimension and aspect ratio on wrinkling onset; and a series of measurements were performed on each membrane at several desired strain levels to understand the evolution of the wrinkles, in particular wrinkle amplitude and wavelength.</p>
<p>A numerical study was carried out using the commercial finite element software ABAQUS to further understand the important characteristics of wrinkling of thin membranes observed in the physical model. Geometrically nonlinear finite element models of membrane structures were constructed with thin-shell elements. A series of simulations were carried out for different membrane dimensions. The critical buckling load and buckling modes was predicted for each dimension using a pre-buckling eigenvalue analysis. The desirable buckling mode was selected and introduced into the structure as a geometric imperfection. The formation and growth of wrinkles were simulated in the post-buckling analysis.</p>
<p>Finally, an idea of suppressing wrinkle instabilities of dielectric elastomer membranes using through-thickness electric field was proposed and verified in both experiment and numerical simulations.</p>https://thesis.library.caltech.edu/id/eprint/3701A Constitutive Relation for Shape-Memory Alloys
https://resolver.caltech.edu/CaltechETD:etd-09292008-204618
Authors: {'items': [{'email': 'akelly@caltech.edu', 'id': 'Kelly-Alex', 'name': {'family': 'Kelly', 'given': 'Alex'}, 'show_email': 'NO'}]}
Year: 2009
DOI: 10.7907/YMT5-AX47
<p>The novel nonlinear thermoelastic behavior of shape-memory alloys (SMAs) makes them increasingly desirable as components in many advanced technological applications. In order to incorporate these materials into engineering designs, it is important to develop an understanding of their constitutive response. The purpose of this thesis is to develop a constitutive model of shape-memory polycrystals that is faithful to the underlying micromechanics while remaining simple enough for utility in engineering analysis and design.</p>
<p>We present a model in which the material microstructure is represented macroscopically as a recoverable transformation strain that is constrained by the texture of the polycrystal. The point of departure in this model is the recognition that the mechanics of the onset of martensitic transformation are fundamentally different from those of its saturation. Consequently, the constraint on the set of recoverable strains varies throughout the transformation process. The effects of constraint geometry on the constitutive response of SMAs are studied. Several well known properties of SMAs are demonstrated. Finally the model is simply implemented in a commercial finite-element package as a proof of the concept.</p>
https://thesis.library.caltech.edu/id/eprint/3823Shape Changing Transformations: Interactions with Plasticity and Electrochemical Processes
https://resolver.caltech.edu/CaltechTHESIS:05282010-141343271
Authors: {'items': [{'email': 'farshid_roumi@yahoo.com', 'id': 'Roumi-Farshid', 'name': {'family': 'Roumi', 'given': 'Farshid'}, 'show_email': 'NO'}]}
Year: 2010
DOI: 10.7907/P94H-4B23
<p>Solids undergo phase transformations where the crystal structure changes with temperature, chemical potential, stress, applied electric fields, or other external parameters. These occur by either long-range diffusion of atoms (diffusional phase transformation) or by some form of cooperative, homogeneous movement of many atoms that results in changes in crystal structure (displacive phase transformation). In the latter case, these movements are usually less than the interatomic distances, and the atoms maintain their coordination. The most common example of displacive phase transformations is martensitic transformation. The martensitic transformation in steel is economically very important and can result in very different behavior in the product. Other examples of martensitic transformations are shape memory alloys which are lightweight, solid-state alternatives to conventional actuators such as hydraulic, pneumatic, and motor-based systems.</p>
<p>The martensitic transformation usually only depends on temperature and stress and, in contrast to diffusion-based transformations, is not time dependent. In shape memory alloys the transformation is reversible. On the other hand in steel, the martensite formation from austenite by rapidly cooling carbon-steel is not reversible; so steel does not have shape memory properties.</p>
<p>In Chapters 2 and 3, we study the interesting yet very complicated behavior of martensitic transformation interactions with plastic deformations. A good example here is steel, which has been known for thousands of years but still is believed to be a very complicated material. Steel can show different behavior depending on its complex microstructure. Thus understanding the formation mechanisms is crucial for the interpretation and optimization of its properties. As an example, low alloyed steels with transformation induced plasticity (TRIP), metastable austenite steels, are known for strong hardening and excellent elongation and strength. It is suggested that the strain-induced transformation of small amounts of untransformed (retained) austenite into martensite during plastic deformation is a key to this excellent behavior.</p>
<p>In Chapters 4 and 5, we study the interactions of solid-solid phase transformations with electrochemical processes. It is suggested that electronic and ionic structures depends on lattice parameters, thus it is expected that structural transformations can lead to dramatic changes in material properties. These transformations can also change the energy barrier and hysteresis. It is known that compatible interfaces can reduce elastic energy and hysteresis, thus may extend the life of the system. Solid-solid transformations change the crystalline structure. These geometry changes can have long range effects and cause stresses in the whole material. The generated stress field itself changes the total free energy, due to the change in elastic energy, and thus, the electrochemical potential and processes are affected. An example is olivine phosphates which are candidates for cathode material in Li-ion batteries. These materials undergo an orthorhombic to orthorhombic phase transition. Experiments in the literature have suggested that elastic compatibility can affect rates of charge/discharge in the battery. Our theory provides some insight into this observation.</p>https://thesis.library.caltech.edu/id/eprint/5883Coarse-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/6473Coupled Effects of Mechanics, Geometry, and Chemistry on Bio-Membrane Behavior
https://resolver.caltech.edu/CaltechTHESIS:06062013-102758695
Authors: {'items': [{'email': 'gianghak4@gmail.com', 'id': 'Giang-Ha-Thanh', 'name': {'family': 'Giang', 'given': 'Ha Thanh'}, 'show_email': 'NO'}]}
Year: 2013
DOI: 10.7907/BVSK-K782
<p>Lipid bilayer membranes are models for cell membranes--the structure that helps regulate cell function. Cell membranes are heterogeneous, and the coupling between composition and shape gives rise to complex behaviors that are important to regulation. This thesis seeks to systematically build and analyze complete models to understand the behavior of multi-component membranes.</p>
<p>We propose a model and use it to derive the equilibrium and stability conditions for a general class of closed multi-component biological membranes. Our analysis shows that the critical modes of these membranes have high frequencies, unlike single-component vesicles, and their stability depends on system size, unlike in systems undergoing spinodal decomposition in flat space. An important implication is that small perturbations may nucleate localized but very large deformations. We compare these results with experimental observations.</p>
<p>We also study open membranes to gain insight into long tubular membranes that arise for example in nerve cells. We derive a complete system of equations for open membranes by using the principle of virtual work. Our linear stability analysis predicts that the tubular membranes tend to have coiling shapes if the tension is small, cylindrical shapes if the tension is moderate, and beading shapes if the tension is large. This is consistent with experimental observations reported in the literature in nerve fibers. Further, we provide numerical solutions to the fully nonlinear equilibrium equations in some problems, and show that the observed mode shapes are consistent with those suggested by linear stability. Our work also proves that beadings of nerve fibers can appear purely as a mechanical response of the membrane. </p> https://thesis.library.caltech.edu/id/eprint/7851Interplay 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/7785A Variational Framework for Spectral Discretization of the Density Matrix in Kohn-Sham Density Functional Theory
https://resolver.caltech.edu/CaltechTHESIS:04132015-160812309
Authors: {'items': [{'email': 'xin.wang.cindy@gmail.com', 'id': 'Wang-Xin-C', 'name': {'family': 'Wang', 'given': 'Xin C.'}, 'orcid': '0000-0003-3854-4831', 'show_email': 'NO'}]}
Year: 2015
DOI: 10.7907/Z99021QK
Kohn-Sham density functional theory (KSDFT) is currently the main work-horse of quantum
mechanical calculations in physics, chemistry, and materials science. From a mechanical
engineering perspective, we are interested in studying the role of defects in the
mechanical properties in materials. In real materials, defects are typically found at
very small concentrations e.g., vacancies occur at parts per million,
dislocation density in metals ranges from $10^{10} m^{-2}$ to $10^{15} m^{-2}$,
and grain sizes vary from nanometers to micrometers in polycrystalline materials, etc. In order to model materials at
realistic defect concentrations using DFT, we would need
to work with system sizes beyond millions of atoms. Due to the cubic-scaling
computational cost with respect to the number of atoms in conventional DFT implementations, such system sizes are
unreachable. Since the early 1990s, there has been a huge interest in developing DFT
implementations that have linear-scaling computational cost. A promising
approach to achieving linear-scaling cost is to approximate the density matrix in
KSDFT. The focus of this
thesis is to provide a firm mathematical framework to study the convergence of
these approximations. We reformulate the Kohn-Sham density
functional theory as a nested variational problem in the density matrix,
the electrostatic potential, and a field dual to the electron density. The
corresponding functional is linear in the density matrix and thus amenable to
spectral representation. Based on this reformulation, we introduce a new
approximation scheme, called spectral binning, which does not require smoothing
of the occupancy function and thus applies at arbitrarily low temperatures. We
proof convergence of the approximate solutions with respect to spectral binning
and with respect to an additional spatial discretization of the domain. For a
standard one-dimensional benchmark problem, we present numerical experiments for
which spectral binning exhibits excellent convergence characteristics and
outperforms other linear-scaling methods. https://thesis.library.caltech.edu/id/eprint/8819Collective Behavior of Asperities as a Model for Friction and Adhesion
https://resolver.caltech.edu/CaltechTHESIS:05172015-152006825
Authors: {'items': [{'email': 'sriphy@gmail.com', 'id': 'Hulikal-Sampath-Kumaran-Srivatsan', 'name': {'family': 'Hulikal Sampath Kumaran', 'given': 'Srivatsan'}, 'show_email': 'NO'}]}
Year: 2015
DOI: 10.7907/Z94M92HM
<p>Understanding friction and adhesion in static and sliding contact of surfaces is important in numerous physical phenomena and technological applications. Most surfaces are rough at the microscale, and thus the real area of contact is only a fraction of the nominal area. The macroscopic frictional and adhesive response is determined by the collective behavior of the population of evolving and interacting microscopic contacts. This collective behavior can be very different from the behavior of individual contacts. It is thus important to understand how the macroscopic response emerges from the microscopic one.</p>
<p>In this thesis, we develop a theoretical and computational framework to study the collective behavior. Our philosophy is to assume a simple behavior of a single asperity and study the collective response of an ensemble. Our work bridges the existing well-developed studies of single asperities with phenomenological laws that describe macroscopic rate-and-state behavior of frictional interfaces. We find that many aspects of the macroscopic behavior are robust with respect to the microscopic response. This explains why qualitatively similar frictional features are seen for a diverse range of materials.</p>
<p>We first show that the collective response of an ensemble of one-dimensional independent viscoelastic elements interacting through a mean field reproduces many qualitative features of static and sliding friction evolution. The resulting macroscopic behavior is different from the microscopic one: for example, even if each contact is velocity-strengthening, the macroscopic behavior can be velocity-weakening. The framework is then extended to incorporate three-dimensional rough surfaces, long- range elastic interactions between contacts, and time-dependent material behaviors such as viscoelasticity and viscoplasticity. Interestingly, the mean field behavior dominates and the elastic interactions, though important from a quantitative perspective, do not change the qualitative macroscopic response. Finally, we examine the effect of adhesion on the frictional response as well as develop a force threshold model for adhesion and mode I interfacial cracks.</p>https://thesis.library.caltech.edu/id/eprint/8861Shock Wave Propagation in Composites and Electro-Thermomechanical Coupling of Ferroelectric Materials
https://resolver.caltech.edu/CaltechTHESIS:05272016-104209268
Authors: {'items': [{'email': 'vinamraagrawal786@gmail.com', 'id': 'Agrawal-Vinamra', 'name': {'family': 'Agrawal', 'given': 'Vinamra'}, 'orcid': '0000-0002-1698-1371', 'show_email': 'YES'}]}
Year: 2016
DOI: 10.7907/Z98G8HN8
<p>How is material behavior at the macro scale influenced by its properties and structure at the micro and meso-scales? How do heterogeneities influence the properties and the response of a material? How does nonlinear coupling of electro-thermo-mechanical properties influence the behavior of a ferroelectric material? How can design at the micro-scale be exploited to obtain selective response? These questions have been topics of significant interest in the materials and mechanics community. Recently, new materials like multifunctional composites and metamaterials have been developed, targeted at selective applications. These materials find applications in areas like energy harvesting, damage mitigation, biomedical devices, and various aerospace applications. The current thesis explores these questions with two major thrusts: (i) internal reflects of shocks in composite media and (ii) shocks in ferroelectric media.</p>
<p>Under the application of high-pressure, high strain rate loading, such as during high velocity impact, shock waves are generated in the material. They can cause the material to achieve very high stress states, and if transmitted without mitigation, can lead to failure of key components. An important question here is 'Can we design materials which can successfully mitigate damage due to shocks?' In a heterogeneous material, like a layered composite, the traveling waves undergo scattering due to internal reflections. In order to understand internal reflections, an idealized problem that focuses on nonlinear shocks and ignores less important elastic waves was formulated and studied in detail. The problem is studied by classifying all possible interactions in the material and then solving corresponding Riemann problems. Using dynamic programming tools, a new algorithm is designed that uses these solutions to generate a complete picture of the impact process. Different laminate designs are explored to study optimal design, by varying individual layer properties and their arrangement. Phenomena like spallation and delamination are also investigated.</p>
<p>Upon high strain rate loading, ferroelectric materials like lead zirconate titanate (PZT) undergo ferroelectric to anti-ferroelectric phase transition leading to large pulsed current output. These materials have thus found applications as pulsed power generators. The problem of shock induced depolarization and the associated electro-thermo-mechanical coupling of ferroelectric materials is studied in this thesis using theoretical and numerical methods. A large deformation dynamic analysis of such materials is conducted to study phase boundary propagation in the medium. The presence of high electrical fields can lead to formation of charges in the material, such as surface charge on the phase boundary. Using conservation laws and the second law of thermodynamics, a set of governing equations are formulated that dictate the phase boundary propagation in isothermal and adiabatic environments. Due to the possibility of surface charges on the phase boundary, the curvature of the phase boundary starts to play a role in the driving force acting on the phase boundary. The equations of motion and driving force see the contribution of nonlinear electro-thermomechanical coupling in the material. Using the equations derived, a canonical problem of impact on a ferroelectric material is studied. A new finite-volume, front-tracking method is developed to solve these equations. Finally, results from numerical simulations are compared to the experimental results.</p>https://thesis.library.caltech.edu/id/eprint/9783The Deformations of Thin Nematic Elastomer Sheets
https://resolver.caltech.edu/CaltechTHESIS:06022017-081925673
Authors: {'items': [{'email': 'plucinsp@gmail.com', 'id': 'Plucinsky-Paul-P', 'name': {'family': 'Plucinsky', 'given': 'Paul P.'}, 'orcid': '0000-0003-2060-8657', 'show_email': 'YES'}]}
Year: 2017
DOI: 10.7907/Z9765CCT
<p>Thin structures exhibit a broad range of mechanical responses as the competition between stretching and bending in these structures can result in buckling and localized deformations like folding and tension wrinkling. Active materials also exhibit a broad range of mechanical responses as features that manifest themselves at the microscale in these materials result in mechanical couplings at the engineering scale (thermal/electrical/dissipative) and novel function (e.g., the shape memory effect and piezoelectricity in select metal alloys and the immense fracture toughness of hydrogels). Given this richness in behaviors, my research broadly aims to address the following questions: What happens when active materials are incorporated into thin structures? Do phenomena inherent to these materials compete with or enhance those inherent to thin structures? Does this interplay result in entirely new and unexpected phenomena? And can all this be exploited to design new functions in engineering systems?</p>
<p>In this thesis, we explore these questions in the context of a theoretical study of thin sheets of nematic liquid crystal elastomer. These materials are active rubbery solids made of cross-linked polymer chains that have liquid crystals either incorporated into the main chain or pendent from them. Their structure enables a coupling between the mechanical elasticity of the polymer network and the ordering of the liquid crystals, and this in turn results in fairly complex mechanical behavior including large spontaneous distortion due to temperature change, soft-elasticity and fine-scale microstructure.</p>
<p>We study thin sheets of nematic elastomer. First, we show that thin of sheets of a particular class of nematic elastomer can resist wrinkling when stretched. Second, we show that thin sheets of another class of nematic elastomer can be actuated into a multitude of complex shapes. In order to obtain these results, we systematically develop two dimensional theories for thin sheets starting from a well-accepted first principles theory for nematic elastomers. These characterize (i) the mechanical response due to instabilities such as structural wrinkling and fine-scale material microstructure, and (ii) thermal actuation of heterogeneously patterned sheets. For the latter, we show that the theory, which comes in the form of a two dimensional metric constraint, admits two broad classes of designable actuation in nonisometric origami and lifted surface. For the former, we show that taut and appreciably stressed sheets of nematic elastomer are capable of suppressing wrinkling by modifying the expected state of stress through the formation of microstructure.</p>https://thesis.library.caltech.edu/id/eprint/10250Optimal Design of Materials for Energy Conversion
https://resolver.caltech.edu/CaltechTHESIS:06132017-164608976
Authors: {'items': [{'email': 'lincoln.n.collins@gmail.com', 'id': 'Collins-Lincoln-Nash', 'name': {'family': 'Collins', 'given': 'Lincoln Nash'}, 'show_email': 'NO'}]}
Year: 2017
DOI: 10.7907/Z9X928B7
<p>The efficiency of fuel cells, batteries and thermochemical energy conversion devices depends on inherent material characteristics that govern the complex chemistry and transport of multiple species as well as the spatial arrangement of the various materials. Therefore, optimization of the spatial arrangement is a recurrent theme in energy conversion devices. Traditional methods of synthesis offer limited control of the microstructure and there has been much work in advanced imaging for these uncontrolled microstructures and optimizing gross features. However, the growing ability for directed synthesis allows us to ask the question of what microgeometries are optimal for particular applications. Through this work, we study problems motivated by metal oxides used in solar-driven thermochemical conversion devices designed to split water or carbon dioxide into fuels. We seek to understand the arrangement of the solid and porous regions to maximize the transport given sources and sinks for the gaseous oxygen and vacancies. Three related problems are investigated with the common theme of understanding the role of microstructure design.</p>
<p>We derive the transport equations for electrons and oxygen vacancies through ceria under an externally-applied electric potential in an oxygen environment using various balance laws and constitutive equations. From this, we obtain various thermodynamic potentials that take into consideration the thermal, chemical, and mechanical state of the material. Accordingly, we obtain a system of partial differential equations describing ambipolar diffusion. We present the applicability of strain-engineering as a way to design systems to improve the behavior of thermochemical conversion devices. We look at an idealized thin film of mixed conductor attached to an inert substrate with a thermal mismatch as a way to induce strain into the film. The resulting impact on equilibrium non-stoichiometry is analyzed using data describing non-stoichiometry in ceria as a function of oxygen pressure and temperature.</p>
<p>The optimal design of material microstructure for thermochemical conversion is addressed from two standpoints: the mathematical homogenization of associated transport models, and from topology optimization. We present the homogenization of coupled transport through porous media consisting of linearized Stokes flow, convective diffusion, and diffusion in the solid phase with interface reaction. Depending on the strength of the interface chemistry, different forms of effective behavior are described at the macroscale, and we gain insight into the impact cell-design and pore shape has on the behavior.</p>
<p>The topology optimization of a model energy-conversion reactor is then presented. We express the problem of optimal design of the material arrangement as a saddle point problem and obtain an effective functional which shows that regions with very fine phase mixtures of the material arise naturally. To explore this further, we introduce a phase-field formulation of the optimal design problem, and numerically study selected examples. We find that zig-zag interfaces develop to balance mass transport and interface exchange. </p> https://thesis.library.caltech.edu/id/eprint/10336Effective Toughness of Heterogeneous Materials
https://resolver.caltech.edu/CaltechTHESIS:06042017-165228124
Authors: {'items': [{'email': 'renhsueh@gmail.com', 'id': 'Hsueh-Chun-Jen', 'name': {'family': 'Hsueh', 'given': 'Chun-Jen'}, 'orcid': '0000-0001-6522-4505', 'show_email': 'YES'}]}
Year: 2017
DOI: 10.7907/Z9HH6H49
<p>Composite materials are widely used because of their extraordinary performance. It is understood that the heterogeneity / microstructure can dramatically affect the effective behavior of materials. Although there is a well-developed theory for this relation in elasticity, there is no similar theory in fracture mechanics. Therefore, we use theoretical, numerical, and experimental approaches to study the relationship between heterogeneity / microstructure and the effective fracture behavior in this thesis.</p>
<p>We use the surfing boundary condition, a boundary condition that ensures the macroscopic steady crack growth, and then define the effective toughness of heterogeneous materials as the peak energy release rate during crack propagation. We also use the homogenization theory to prove that the effective J-integral in heterogeneous materials is well defined, and that it can be calculated by the homogenized stress and strain field.</p>
<p>In order to study the relationship between heterogeneities and effective toughness, we first use the semi-analytical method under the assumption of small elastic contrast to study selected examples. For strong heterogeneities, we use the phase field fracture method to study the crack propagation numerically. We then optimize the microstructure with respect to effective stiffness and effective toughness in a certain class of microgeometries. We show that it is possible to significantly enhance toughness without significant loss of stiffness. We also design materials with asymmetric toughness.</p>
<p>We develop a new experimental configuration that can measure the effective toughness of specimens with arbitrary heterogeneities. We confirm through preliminary tests that the heterogeneities can enhance the effective toughness.</p>
<p>Besides study the effective toughness of heterogeneous materials, we also study a model problem of peeling a thin sheet from a heterogeneous substrate. We develop a methodology to systematically optimize microstructure.</p>https://thesis.library.caltech.edu/id/eprint/10266Proliferation 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/10365Controlling the Buckling Behavior of Bilayered Systems
https://resolver.caltech.edu/CaltechTHESIS:09272018-211547049
Authors: {'items': [{'email': 'paul.mazur@gadz.org', 'id': 'Mazur-Paul-Antoine-Benoit', 'name': {'family': 'Mazur', 'given': 'Paul Antoine Benoit'}, 'orcid': '0000-0002-2837-9716', 'show_email': 'NO'}]}
Year: 2019
DOI: 10.7907/C70B-K221
<p>A bilayered system is an assembly of two different materials and has the form of flat and thin layers. The two materials are attached to each other at the surface. The attachment method varies depending on the materials properties. Bilayered systems made of materials with different dimensions and stiffness have been widely studied and used for different applications. The characteristic scale of this kind of system can go from hundreds of km in the case of geological layers on the Earth surface to some µm in the case of very small electronic systems or microlenses.</p>
<p>The behavior of a bilayered system, when submitted to a stimulus, is characterized by the conflict between the preferred response of each material and the constraint that one imposes on the other. As a result, the deformation of the bilayered system will be different from that which could be obtained when the materials are taken separately. Of particular interest is the buckling of such systems: when submitted to a particular stress distribution, one material will expand significantly more than the other, but as the two materials are attached at the interface surface, the material displacements must be continuous through this interface. The conflict between the continuity of displacement and the need to expand differently may result in nonlinear patterns at this interface. Those unstable situations can be used to define a limit of constraint for the materials or can be used as actuators for a desired surface pattern. Many studies have focused on characterizing homogeneous buckling within an entire surface due to homogeneous strain distribution within the top surface. This characterization was performed theoretically, numerically, and experimentally. But, some studies have shown different possibilities of evolution of the buckling patterns known today. As a consequence, we can pose two questions: 1) Is there a possibility to modify non-linear patterns regardless of what is imposed by mechanical properties and dimensions? 2) What happens in the case of a non-uniform state of constraints within the bilayered system?</p>
<p>This thesis explores those questions for the case of a thin stiff film attached to a compliant thick substrate. The first part of this thesis serves to describe the initial buckling theory in the case of uniform strain and explains how to define the loading threshold resulting in uniform buckling at the surface characterized by a finite number of spatial frequencies. The second part of the thesis studies the consequences of a non-uniform loading within the surface. A numerical method based on the theory of the first part is implemented to show the emergence of new frequencies due to the discontinuous loading distribution. The third part focuses on the possibility of tuning a uniform buckling by including an electromechanical coupling into the bilayered system. This coupling makes the materials sensitive to electric fields, thus creating a new energy term to interfere with the mechanical energy of deformation, thereby modifying the resulting spatial frequency of the buckling. This study is done theoretically and numerically by finite element modeling.</p>https://thesis.library.caltech.edu/id/eprint/11207Fast Adaptive Augmented Lagrangian Digital Image Correlation
https://resolver.caltech.edu/CaltechTHESIS:10162018-093212227
Authors: {'items': [{'email': 'yangjin2009010843@gmail.com', 'id': 'Yang-Jin', 'name': {'family': 'Yang', 'given': 'Jin'}, 'orcid': '0000-0002-5967-980X', 'show_email': 'YES'}]}
Year: 2019
DOI: 10.7907/MZ5G-PS98
<p>Digital image correlation (DIC) is a powerful experimental technique for measuring full-field displacement and strain. The basic idea of the method is to compare images of an object decorated with a speckle pattern before and after deformation in order to compute the displacement and strain fields. Local Subset DIC and finite element-based Global DIC are two widely used image matching methods; however there are some drawbacks to these methods. In Local Subset DIC, the computed displacement field may not satisfy compatibility, and the deformation gradient may be noisy, especially when the subset size is small. Global DIC incorporates displacement compatibility, but can be computationally expensive. In this thesis, we propose a new method, the augmented-Lagrangian digital image correlation (ALDIC), that combines the advantages of both the local (fast and in parallel) and global (compatible) methods. We demonstrate that ALDIC has higher accuracy and behaves more robustly compared to both Local Subset DIC and Global DIC.</p>
<p>DIC requires a large number of high resolution images, which imposes significant needs on data storage and transmission. We combined DIC algorithms with image compression techniques and show that it is possible to obtain accurate displace- ment and strain fields with only 5 % of the original image size. We studied two compression techniques – discrete cosine transform (DCT) and wavelet transform, and three DIC algorithms – Local Subset DIC, Global DIC and our newly proposed augmented Lagrangian DIC (ALDIC). We found the Local Subset DIC leads to the largest errors and ALDIC to the smallest when compressed images are used. We also found wavelet-based image compression introduces less error compared to DCT image compression.</p>
<p>To further speed up and improve the accuracy of DIC algorithms, especially in the study of complex heterogeneous strain fields at various length scales, we apply an adaptive finite element mesh to DIC methods. We develop a new h-adaptive technique and apply it to ALDIC. We show that this adaptive mesh ALDIC algorithm significantly decreases computation time with no loss (and some gain) in accuracy.</p>https://thesis.library.caltech.edu/id/eprint/11233Theoretical, Computational, and Experimental Characterization of Nematic Elastomers
https://resolver.caltech.edu/CaltechTHESIS:06042021-213808812
Authors: {'items': [{'email': 'victoriajlee2@gmail.com', 'id': 'Lee-Victoria-Jin-Young', 'name': {'family': 'Lee', 'given': 'Victoria Jin-Young'}, 'orcid': '0000-0002-2748-0089', 'show_email': 'YES'}]}
Year: 2021
DOI: 10.7907/f2hp-qe09
<p>Nematic elastomers are programmable soft materials that display large, reversible, and predictable deformation under an external stimulus such as a change in temperature or light. They are composed of a lightly crosslinked polymer network with stiff, rod-like liquid crystal molecules incorporated within the polymer chains. In thermotropic nematic elastomers, the liquid crystals undergo a continuous and reversible phase transition between the randomly oriented isotropic state and the highly oriented nematic state. Further, there is a direct thermo-mechanical coupling between the underlying temperature-responsive orientational order of the liquid crystal molecules and the macroscopic shape change of the surrounding elastomer chains. Finally, these materials display an unusually soft behavior. These remarkable properties make them promising materials for applications in aerospace as deployable structures and skins, in biomedical engineering as a soft pump, and in communications as the actuation mechanism in a reconfigurable antenna. Motivated by these applications, this thesis discusses the theoretical, computational, and experimental characterization of nematic elastomers.</p>
<p>We begin by investigating an example of actuation that takes advantage of the programmable, soft nature of these materials as well as instabilities associated with large deformation. We outline the multi-stable equilibrium solutions to a cylindrical balloon subjected to internal inflation, the material's microstructure formation due to this deformation, and its use as a soft pump with large ejection fraction, which involves a snap-through instability. Then we extend the Agostiniani-DeSimone-Dolzmann relaxed energy to a generalized Mooney-Rivlin constitutive relation and study four examples of Ericksen's universal deformations -- the inflation of cylindrical and spherical balloons, the cavitation of a disk, and the bending of a block.</p>
<p>We then move beyond the modeling of ideal materials and present a new constitutive relation for isotropic-genesis polydomain nematic elastomers. It is based on internal variables that describe the fine-scale domain patterns and evolve according to a kinetic process with dissipation. We discuss the model's implementation in the commercial finite-element software, ABAQUS, and study the problem of torsion of a cylinder. We identify an interesting instability at large torsional strains as a result of the Poynting effect. Finally, we present the design of a thermo-mechanical tensile setup and the experimental results for strain-rate dependence and temperature-dependence of samples that we synthesize in-house.</p>https://thesis.library.caltech.edu/id/eprint/14243Multi-Functional Metamaterials
https://resolver.caltech.edu/CaltechTHESIS:05062021-023201965
Authors: {'items': [{'email': 'ssharaninjeti@gmail.com', 'id': 'Injeti-Sai-Sharan', 'name': {'family': 'Injeti', 'given': 'Sai Sharan'}, 'orcid': '0000-0003-1941-9752', 'show_email': 'YES'}]}
Year: 2021
DOI: 10.7907/3rfm-1x78
<p>Optimally designing interdependent mechanical properties in a structure allows for it to be used in application where an arbitrary combination of properties is desired. Architected materials have proven to be an effective way of attaining mechanical behaviors that are unattainable using their constituent materials alone, such as unusual static mechanical properties, unusual wave propagation behavior, and shape morphing. The advent of 3-D printing has allowed for fabricating metamaterials with complex topologies that display engineered mechanics. However, much of the current efforts have focused on optimally designing simple mechanical behaviors such as designing for stiffness and weight, particular frequency bandgaps, or bi-stability. In this work, we study two metamaterial systems where we control and optimize a wide set of static and dynamic properties, and one complex multi-stable structure.</p>
<p>Most studies on the optimal design of static properties have focused on engineering stiffness and weight, and much remains unknown about ways to decouple the critical load to failure from stiffness and weight. This is the focus of the first part of our work. We show that the addition of local internal pre-stress in selected regions of architected materials enables the design of materials where the critical load to failure can be optimized independently from the density and/or quasistatic stiffness. We propose a method to optimize the specific load to failure and specific stiffness using sensitivity analysis, and derive the maximum bounds on the attainable properties. We demonstrate the method in a 2-D triangular lattice and a 3-D octahedral truss, showing excellent agreement between experimental and theoretical results. The method can be used to design materials with predetermined fracture load, failure location and fracture paths.</p>
<p>For the second part of our work, we focus on designing acoustically transparent structures, by engineering the acoustic impedance -- a combination of wave speed and density, to match that of the surroundings. Owing to the strong correlation between acoustic wave speed and static stiffness, it is challenging to design acoustically transparent materials in a fluid, while maintaining their high structural rigidity. We provide a sensitivity analysis to optimize these properties with respect to design parameters of the structure, that include localized masses at specific positions. We demonstrate the method on five different periodic, three dimensional lattices, to calculate bounds on the longitudinal wave speed as a function of their density and stiffness. We then perform experiments on 3-D printed structures, to validate our numerical simulations. Further, using the sensitivity analysis together with a data-driven approach, we design and demonstrate a mode demultiplexer, that is capable of splitting arbitrarily mixed modes. The tools developed in this work allow for designing structures in a plethora of applications, including ultrasound imaging, wave filtering, and waveguiding.</p>
<p>Finally, most multi-stable structures are limited by bi-stability either at the macroscopic or the unit cell level owing to the difficulty in engineering a highly non-linear energy landscape using just elements that display convex energy landscapes. We demonstrate a method to design arbitrarily complex multi-stable shape morphing structures, by introducing rigid kinematic constraints together with disengaging energy storing elements. We present the idea on a kagome lattice configuration, producing a quadri-stable unit cell and complex stable topologies with larger tessellations, validated by demonstrations on 3-D printed structures. Most designs that use passive actuation address one-way shape morphing along the direction of least resistance. We demonstrate reversible, thermally actuated shape morphing between stable open and closed topologies using shape memory springs. The designs can be extended to non-planar structures and fabricated at vastly different length scales.</p>https://thesis.library.caltech.edu/id/eprint/14134Understanding 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/14513Modeling 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/14984Optimal 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/15274Physics-Based and Data-Driven Computational Models of Inelastic Deformations
https://resolver.caltech.edu/CaltechTHESIS:05312023-212652388
Authors: {'items': [{'email': 'ericocegueda@berkeley.edu', 'id': 'Ocegueda-Eric', 'name': {'family': 'Ocegueda', 'given': 'Eric'}, 'orcid': '0000-0001-7845-6890', 'show_email': 'NO'}]}
Year: 2023
DOI: 10.7907/3gqd-zp93
<p>Crystalline materials inevitably exhibit inelastic deformation when applied to large enough loads. The behavior in this inelastic regime is a coupling of physics across several length scales: from initiating as defects at the atomic scale, interacting with crystal defects, and finally spanning multiple grains and influencing macroscopic stress behavior. These length-scale interactions make predicting material response an open challenge and an avenue for leveraging microscale physics for material design. This thesis examines developing physics-based and data-driven computational models to capture complex inelastic behavior at appropriate length scales.</p>
<p>First, we present a mesoscale model for capturing deformation twinning physics at the polycrystal scale. Mechanical twinning is a form of inelastic deformation observed in low-symmetry crystals, such as magnesium and other hexagonal close-packed (hcp) metals. Twinning, unlike slip, forms as bands collectively across grains with complex local morphology propagating into bulk behavior, drastically affecting strength and ductility. We, thus, propose a model where twinning is treated using a phase-field approach, while dislocation slip is considered using crystal plasticity. Lattice reorientation, length-scale effects, interactions between dislocations and twin boundaries, and twin and slip interactions with grain boundaries are all carefully considered. We first outline the model and its implementation using a novel approach of accelerated computational micromechanics in a two-dimensional, single twin-slip system, polycrystal case to demonstrate its capabilities. Finally, we consider multiple twin-slip systems and conduct three-dimensional simulations of polycrystalline magnesium. We summarize the insights gained from these studies and the implications on the macroscale behavior of hcp materials.</p>
<p>The second part of the thesis focuses on data-driven models for capturing microscopic history-dependent phenomena for multiscale modeling applications. The multiscale modeling framework has seen increased usage over the last few decades for its ability to capture complex material behavior over a range of time/length scales by solving a macroscale problem directly with a constitutive relation defined implicitly by the solution of a microscale problem. However, this implementation is computationally expensive -- needing to solve a microscale problem at each point and time of the macroscopic calculation. In this study, we examine the use of machine learning by utilizing data generated through repeated solutions of a microscale problem to: (i) gain insights into the history dependent macroscopic internal variables that govern the response and (ii) create a computationally efficient surrogate. We do so by introducing a recurrent neural operator, which can provide accurate approximations of the stress response and insights into the physics of the macroscopic problem. We illustrate these capabilities on a laminate composite and polycrystal made of elasto-viscoplastic materials, summarize insights on the learned internal variables, and accuracy of stress predictions.</p>https://thesis.library.caltech.edu/id/eprint/15246