For the purpose of these lectures, a microstructure is any structure on a scale between the
macroscopic scale (on which we usually make observations) and the atomic scale. Such …

Microstructure is a feature of crystals with multiple symmetry-related energy-minimizing
states. Continuum models have been developed explaining microstructure as the mixture of …

The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

This second edition takes advantage of several comments received by colleagues and
students. With respect to the first edition (published by SIAM in 2006) several new sections …

Predictions are made based on an analysis of a new nonlinear theory of martensitic
transformations introduced by the authors. The crystal is modelled as a nonlinear elastic …

Weak convergence is a basic tool of modern nonlinear analysis because it enjoys the same
compactness properties that finite dimensional spaces do: basically, bounded sequences …

The relaxation method has enjoyed an intensive development during many decades and
this new edition of this comprehensive text reflects in particular the main achievements in the …

(1) Vu (x) EK ae in Q, where u is a (Lipschitz) mapping of an open set QC gradient (ie the
matrix oui (x)/oxj, 1< i< m, 1< j every x EQ), and K is a subset of the set MmXn o In addition to …

Continuum Models for Phase Transitions and Twinning in Crystals presents the
fundamentals of a remarkably successful approach to crystal thermomechanics. Developed …

The calculus of variations has its roots in the first problems of optimality studied in classical
antiquity by Archimedes (ca. 287–212 BC in Syracuse, Magna Graecia) and Zenodorus (ca …