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We consider the quasi-static evolution of a prescribed cohesive interface: dissipative under loading and elastic under unloading. We provide existence in terms of parametrized -evolutions, employing a discrete scheme based on local minimization, with respect to the -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 visco-elastic type.
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Matteo Negri, Enrico Vitali, Approximation and characterization of quasi-static -evolutions for a cohesive interface with different loading-unloading regimes. Interfaces Free Bound. 20 (2018), no. 1, pp. 25–67DOI 10.4171/IFB/396