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 …

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 …

We develop a method which permits the analysis of problems requiring the simultaneous
resolution of continuum and atomistic length scales-and associated deformation processes …

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 …

Plastically deformed crystals are often observed to develop intricate dislocation patterns
such as the labyrinth, mosaic, fence and carpet structures. In this paper, such dislocation …

Some outstanding open problems of nonlinear elasticity are described. The problems range
from questions of existence, uniqueness, regularity and stability of solutions in statics and …

The notion of \calA-quasiconvexity is introduced as a necessary and sufficient condition for
(sequential) lower semicontinuity of (u, v) ↦ Ω f (x, u (x), v (x))\, dx whenever …

This paper studies coherent, energy-minimizing mixtures of two linearly elastic phases with
identical elastic moduli. We derive a formula for the “relaxed” or “macroscopic” energy of the …

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

Oscillatory properties of a weak convergent sequence of functions bounded in L p, 1≤
p≤∞, may be summarized by the parametrized measure it generates. When such a …