Approximation and characterization of quasi-static \(H^1\)-evolutions for a cohesive interface with different loading-unloading regimes (Q1650257)

In this paper, the quasi-static evolution of a prescribed cohesive interface dissipative under loading and elastic under unloading is considered. The existence in terms of parametrized BV-evolutions is provided, employing a discrete scheme based on local minimization, with respect to the \( H^1\)-norm, of a regularized energy. 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 viscoelastic type.