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We report a detailed numerical investigation of a recently introduced two dimensional model for square-to-rectangle martensitic transformation that explains several unusual features of the martensitic transformation. This model includes…
We consider the Ginzburg-Landau functional with a variable applied magnetic field in a bounded and smooth two dimensional domain. The applied magnetic field varies smoothly and is allowed to vanish non-degenerately along a curve. Assuming…
A model for a MEMS device, consisting of a fixed bottom plate and an elastic plate, is studied. It was derived in a previous work as a reinforced limit when the thickness of the insulating layer covering the bottom plate tends to zero. This…
Minimizing the so-called "Dirichlet energy" with respect to the domain under a volume constraint is a standard problem in shape optimization which is now well understood. This article is devoted to a prototypal non-linear version of the…
We study dislocation networks in the plane using the vectorial phase-field model introduced by Ortiz and coworkers, in the limit of small lattice spacing. We show that, in a scaling regime where the total length of the dislocations is…
We developed a micromagnetic method for modeling magnetic systems with periodic boundary conditions along an arbitrary number of dimensions. The main feature is an adaptation of the Ewald summation technique for evaluation of long-range…
We investigate a variational theory for magnetoelastic solids under the incompressibility constraint. The state of the system is described by deformation and magnetization. While the former is classically related to the reference…
A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane…
A diffuse-interface model for microstructure with an arbitrary number of components and phases was developed from basic thermodynamic and kinetic principles and formalized within a variational framework. The model includes a composition…
This paper is motivated by the complex blister patterns sometimes seen in thin elastic films on thick, compliant substrates. These patterns are often induced by an elastic misfit which compresses the film. Blistering permits the film to…
Wrinkles are often observed on the surfaces of compressed soft materials in nature. In the past few decades, the fascinating surface patterns have been studied extensively by using the linear bifurcation analysis under plane strain. The…
A novel energy minimization formulation of electrostatics that allows computation of the electrostatic energy and forces to any desired accuracy in a system with arbitrary dielectric properties is presented. An integral equation for the…
A thermodynamically consistent multiphase phase-field approach for stress and temperature-induced martensitic phase transformation at the nanoscale and under large strains is developed. A total of N independent order parameters are…
A body $\Theta$ containing two phases, which may form a periodic composite with microstructure much smaller that the body, or which may have structure on a length scale comparable to the body, is subjected to slowly time varying boundary…
In this paper, we extend a micromechanics-based phase-field framework for fatigue fracture to incorporate cyclic plasticity with ratcheting. This mechanism is particularly relevant for low-cycle fatigue, where the accumulation of inelastic…
We use phase field simulations to study composites made of two different ferroelastics (e.g., two types of martensite). The deformation of one material due to a phase transformation can elastically affect the other constituent and induce it…
Martensites are metastable phases, possessing a characteristic morphology, usually formed during a fast quench accross a structural transition. We attempt to understand these morphological features using a coarsegrained free energy…
We consider a nonlinear, frame indifferent Griffith model for nonsimple brittle materials where the elastic energy also depends on the second gradient of the deformations. In the framework of free discontinuity and gradient discontinuity…
Using a variational model based on non-linear elasticity we investigate whether in a cubic-to-tetragonal phase transformation it is energetically preferable to nucleate martensite within austenite. Under minimal growth assumptions on the…
We study the linearized Fopl - von Karman theory of a long, thin rectangular elastic membrane that is bent through an angle $2 \alpha$. We prove rigorous bounds for the minimum energy of this configuration in terms of the plate thickness…