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 …

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

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 …

This work uses the energetic formulation of rate-independent systems that is based on the
stored-energy functionals E and the dissipation distance D. For sequences (E _k) _ k ∈ N …

We analyze a rate-independent model for damage evolution in elastic bodies. The central
quantities are a stored energy functional and a dissipation functional, which is assumed 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 …

We study the evolution of a single crack in an elastic body and assume that the crack path is
known in advance. The motion of the crack tip is modeled as a rate-independent process on …

Rate-independent systems allow for solutions with jumps that need additional modeling.
Here we suggest a formulation that arises as limit of viscous regularization of the solutions in …

In these notes we want to give an overview of the recently developed theory for rate-
independent systems. Such systems are used to model hysteresis, dry friction …

The celebrated Brezis–Ekeland principle [CR Acad. Sci. Paris Ser. AB, 282 (1976), pp. Ai,
A1197–A1198, Aii, and A971–A974] characterizes trajectories of nonautonomous gradient …