View article

We prove a stability result for a large class of unilateral minimality properties which arise naturally in the theory of crack propagation proposed by Francfort & Marigo in [14]. Then we give an application to the quasistatic evolution of cracks in composite materials. The main tool in the analysis is a Γ-convergence result for energies of the form where S(u) is the jump set of u and is a sequence of rectifiable sets with We prove that no interaction occurs in the Γ-limit process between the bulk and the surface part of the energy. Relying on this result, we introduce a new notion of convergence for (N−1)-rectifiable sets called σ-convergence, which is useful in the study of the stability of unilateral minimality properties.