A new approach to irreversible quasistatic fracture growth is given, by means of Young measures.The study concerns a cohesive zone model with prescribed crack path, when the material gives different responses to loading and unloading phases.In the particular situation of constant unloading response,the result contained in [G. Dal Maso and C. Zanini,Proc. Roy. Soc. Edinburgh Sect. A137 (2007) 253–279] is recovered.In this case, the convergence of the discrete time approximationsis improved.

Rate-independent evolution for material models with nonconvexelastic energies is studied without any spatial regularization ofthe inner variable; due to lack of convexity, the model is developedin the framework of Young measures. An existence result for thequasistatic evolution is obtained in terms of compatible systems ofYoung measures. We also show as this result can be equivalentlyreformulated with probabilistic language and leads to thedescription of the quasistatic evolution in terms of stochasticprocesses on a suitable probability space.

The propagation of fractures in a solid undergoing cyclic loadingsis known as the fatigue phenomenon. In this paper, we present a time continuousmodel for fatigue, in the special situation of the debonding of thin layers,coming from a time discretized version recently proposed byJaubert and Marigo [C. R. Mecanique333 (2005) 550–556].Under very general assumptions on the surface energy density andon the applied displacement, we discuss the well-posedness of ourproblem and we give the main properties of the evolution process.