Inserted: 20 oct 2016
Last Updated: 21 oct 2016
We consider the quasi-static evolution of a prescribed cohesive interface: dissipative under loading and elastic under unloading. We provide existence, by energy approximation and time discretization, in terms of parametrized $BV$-evolutions with respect to the $H^1$-norm. Technically, the evolution is fully characterized by: equilibrium, energy balance and Karush-Kuhn-Tucker conditions for the internal variable. Catastrophic regimes (discontinuities in time) are described by gradient flows of visco-elastic type.