We describe a model based on continuum mechanics that reduces the study of a significant
class of problems of discrete dislocation dynamics to questions of the modern theory of …

Shape-memory alloys exhibit a rich microstructure, characterized by large regions
containing relatively regular laminates mixing different martensitic variants. Macrointerfaces …

Minimization is a recurring theme in many mathematical disciplines ranging from pure to
applied. Of particular importance is the minimization of integral functionals, which is studied …

The ground state crystal structure of Fe, ferromagnetic body-centered cubic (bcc), undergoes
a stress-induced martensitic phase transformation to a hexagonally close-packed (hcp) …

A three-dimensional thermoviscoelastic system derived from the balance laws of momentum
and energy is considered. To describe structural phase transitions in solids, the stored …

The aim of this presentation is the development of a general approach for modelling the
global complex energy landscapes of phase transitions. For the sake of clarity and brevity …

A framework for modeling complex global energy landscapes in a piecewise manner is
presented. Specifically, a class of strain-dependent energy functions is derived for the triple …

This thesis consists of two parts. The first part explores a 2-d edge dislocation model to
demonstrate characteristics of Field Dislocation Mechanics (FDM) in modeling single and …

Many complex phenomena in nature exhibit multiple scales. The challenge is to understand
how the effects on one scale influence those on another. This review discusses some …

We determine locally minimizing functions that are invariant with respect to the action of a
finite linear group. This resolves a problem which is inverse to one discussed in a seminal …