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Caltech Authors (142.336 recursos)
Repository of works by Caltech published authors.
Group = Solid Mechanics Research Group
Repository of works by Caltech published authors.
Group = Solid Mechanics Research Group
Bhattacharya, Kaushik; Schlömerkemper, Anja
Shape-memory alloys undergo a solid-to-solid phase transformation involving a change of crystal structure. We examine model problems in the scalar setting motivated by the situation when this transformation is induced by the application of stress in a polycrystalline material made of numerous grains of the same crystalline solid with varying orientations. We show that the onset of transformation in a granular polycrystal with homogeneous elasticity is in fact predicted accurately by the so-called Sachs bound based on the ansatz of uniform stress. We also present a simple example where the onset of phase transformation is given by the Sachs bound,...
Biggins, J. S.; Bhattacharya, K.
The neo-classical model of SmC (and SmC*) elastomers developed by Warner and Adams predicts a class of "soft" (zero energy) deformations. We find and describe the full set of stripe-domains – laminate structures in which the laminates alternate between two different deformations – that can form between pairs of these soft deformations. All the stripe-domains fall into two classes, one in which the smectic layers are not bent at the interfaces, but for which, in the SmC* case, the interfaces are charged, and one in which the smectic layers are bent but the interfaces are never charged. Striped deformations significantly...
Dondl, Patrick W.; Bhattacharya, Kaushik
A model for the quasistatic evolution of martensitic phase boundaries is presented. The model is essentially the gradient flow of an energy that can contains elastic energy due to the underlying change in crystal structure in the course of the phase transformation and surface energy penalizing the area of the phase boundary. This leads to a free boundary problem with a nonlocal velocity that arises from the coupling to the elasticity equation. We show existence of solutions under a technical convergence condition using an implicit time-discretization.
Givli, Sefi; Bhattacharya, Kaushik
A theoretical framework for predicting the macroscopic behavior of a muscle myofibril based on the collective behavior of sarcomeres is presented. The analysis is accomplished by rigorously transforming the nonlinear dynamics of an assemblage of sarcomeres into a partial differential equation for the probability distribution function of sarcomere lengths in the presence of stochastic temporal fluctuations and biological variability. This enables the study of biologically relevant specimens with reasonable computational effort. The model is validated by a comparison to quantitative experimental results. Further, it reproduces experimental observations that can not be explained by standard single sarcomere models, and provides new...
Kaneko, Y.; Lapusta, N.; Ampuero, J.-P.
We develop a spectral-element methodology (SEM) for simulating dynamic rupture on rate and state faults and use it to study how the rupture is affected by a shallow fault region of steady-state velocity-strengthening friction. Our comparison of the developed SEM and a spectral boundary-integral method (BIM) for an anti-plane (two-dimensional) test problem shows that the two methods produce virtually identical solutions for the finest resolution we use and that the convergence with grid reduction of the developed SEM methodology is comparable to that of BIM. We also use the test problem to compare numerical resolution required for different state evolution...
Porter, Mason A.; Daraio, Chiara; Herbold, Eric B.; Szelengowicz, Ivan; Kevrekidis, P. G.
We report the propagation of highly nonlinear solitary waves in heterogeneous, periodic granular media using experiments, numerical simulations, and theoretical analysis. We examine periodic arrangements of particles in experiments in which stiffer/heavier beads (stainless steel) are alternated with softer/lighter ones (polytetrafluoroethylene beads). We find excellent agreement between experiments and numerics in a model with Hertzian interactions between adjacent beads, which in turn agrees very well with a theoretical analysis of the model in the long-wavelength regime that we derive for heterogeneous environments and general bead interactions. Our analysis encompasses previously-studied examples as special cases and also provides key insights on...
Liu, Liping
We present solutions to the Eshelby conjectures based on a variational inequality. We first discuss the meanings of the original Eshelby's statement. By Fourier analysis, we establish the connection between the homogeneous Eshelby inclusion problem and the classic Newtonian potential problem. We then proceed to the solutions of the Eshelby conjectures. Under some hypothesis on the material properties and restricted to connected inclusions with Lipschitz boundary, we show that one version of the Eshelby conjectures is valid in all dimensions and the other version is valid in two dimensions. We also show the existence of multiply-connected inclusions in all dimensions...