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 …

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 …

Functionals involving both volume and surface energies have a number of applications
ranging from Computer Vision to Fracture Mechanics. In order to tackle numerical and …

We propose a discrete time model for dynamic fracture based on crack regularization. The
advantages of our approach are threefold: first, our regularization of the crack set has been …

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 …

A phase field (PF) approximation of fracture for functionally graded materials (FGM) using a
diffusive crack approach incorporating the characteristic length scale as a material …

Abstract Recently, Francfort and Marigo (J. Mech. Phys. Solids 46, 1319–1342, 1998) have
proposed a novel approach to fracture mechanics based upon the global minimization of a …

The analysis of fracture phenomena of thin-walled structures has been a matter of intensive
research in the last decades. These phenomena notably restrict the applicability of slender …

A “special displacement with bounded deformation” is a function u: Ω⊂ RN→ RN whose
symmetrized gradient is a bounded measure which coincides, outside a (N− 1)-dimensional …

Existence and convergence results are proved for a regularized model of dynamic brittle
fracture based on the Ambrosio–Tortorelli approximation. We show that the sequence of …