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 …

This work constitutes an up-to-date and unified account of the contributions of the authors
and their collaborators to the field of asymptotic modelling of elastic rods and their …

Our work on rate-independent systems was stimulated by our search for evolutionary
material models for shape-memory alloys that are flexible enough to encompass nonlinear …

This book deals with a class of mathematical problems which involve the minimization of the
sum of a volume and a surface energy and have lately been refered to as' free discontinuity …

Following an idea of G. Nguetseng, the author defines a notion of “two-scale” convergence,
which is aimed at a better description of sequences of oscillating functions. Bounded …

At the risk of being unfair, we credit first and foremost AA Griffith for develo** the field of
brittle fracture. His views were that cracks are the macroscopic manifestation of putative …

Introduction Since the completion of this volume in 1986, there has been an enormous
amount of fundamental advances in the theory of three-dimensional elasticity (Chapters 6 …

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 …

In the context of shape optimization, we seek minimizers of the sum of the elastic compliance
and of the weight of a solid structure under specified loading. This problem is known not to …

This book is developed for the study of vectorial problems in the calculus of variations. The
subject is a very active one and almost half of the book consists of new material. This is a …