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 …

Phase-field approaches to fracture based on energy minimization principles have been
rapidly gaining popularity in recent years, and are particularly well-suited for simulating …

Phase-field models of brittle fracture can be regarded as gradient damage models including
an intrinsic internal length. This length determines the stability threshold of solutions with …

The present work is concerned with the verification and validation of a variant of the
eigenfracture scheme of Schmidt et al.(2009) based on element erosion, which we refer to …

In the nonconvex case, solutions of rate-independent systems may develop jumps as a
function of time. To model such jumps, we adopt the philosophy that rate-independence …

This paper is devoted to a numerical implementation of the Francfort–Marigo model of
damage evolution in brittle materials. This quasi-static model is based, at each time step, on …

In this work, we propose to succinctly review, in non technical terms, the current
mathematical state of brittle fracture first put forth by AA Griffith in his seminal work Griffith …

A recurrent question arising in several fields is the determination of sufficient conditions,
hopefully necessary as well, ensuring the convergence of sequences of minimum problems …

The aim of the present article is a description of the many phenomenological aspects of
fracture and of their relations with other inelastic phenomena, such as the formation of …

The present work is concerned with the verification and validation of an implementation of
the eigenfracture scheme of Schmidt et al.(SIAM J Multiscale Model Simul 7: 1237–1266 …