A quasi-static evolution generated by local energy minimizers for an elastic material with a cohesive interface. (December 2017) - Negri, M.; Scala, R.
Abstract: We deal with a model for an elastic material with a cohesive crack along a prescribed fracture set. We consider two n -dimensional elastic bodies and a cohesive law, on their common interface, with incompenetrability constraint and general loading–unloading regimes. We first provide a time-discrete evolution by means of local minimizers of the energy with respect to the L 2 -norm of the crack opening displacement. The choice of this norm is due to technical reasons (the λ -convexity of the energy) and is in analogy with the classical approach in quasi-static brittle fracture, where the evolution of the system is condensed into the evolution of the crack. In the "time-continuous" limit we obtain a B V -evolution, in parametrized form, characterized by Karush–Kuhn–Tucker conditions, for the internal variable, equilibrium and energy identity.