The propagation of fractures in a solid undergoing cyclic loadings is known as the fatigue phenomenon. In this paper, we present a time continuous model for fatigue, in the special situation of the debonding of thin layers, coming from a time discretized version recently proposed by Jaubert and Marigo [C. R. Mecanique333 (2005) 550–556]. Under very general assumptions on the surface energy density and on the applied displacement, we discuss the well-posedness of our problem and we give the main...

We characterize quasi-static rate-independent evolutions, by means of their graph parametrization, in terms of a couple of equations: the first gives stationarity while the second provides the energy balance. An abstract existence result is given for functionals ℱ of class C1 in reflexive separable Banach spaces. We provide a couple of constructive proofs of existence which share common features with the theory of minimizing movements for gradient flows. Moreover, considering a sequence of functionals...