Abstract. 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 BV evolutions, employing a discrete scheme based on local minimization, with respect to the Hnorm, 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.

中文翻译：

---

具有不同加载-卸载机制的粘性界面的准静态 $H^1$-演化的近似和表征

摘要。我们考虑规定内聚界面的准静态演变：加载下耗散和卸载下弹性。我们在参数化 BV 演化方面提供存在性，采用基于局部最小化的离散方案，相对于正则化能量的 Hnorm。从技术上讲，演化完全具有以下特征：内部变量的平衡、能量平衡和 Karush-Kuhn-Tucker 条件。灾难性状态（时间上的不连续性）由粘弹性类型的梯度流描述。