In this paper we propose a notion of irreversibility for the evolution of cracks in presence of cohesive forces, which allows for different responses in the loading and unloading processes, motivated by a variational approximation with damage models. We investigate its applicability to the construction of a quasi-static evolution in a simple one-dimensional model. The cohesive fracture model arises naturally via Gamma-convergence from a phase-field model of the generalized Ambrosio-Tortorelli type, which may be used as regularization for numerical simulations.

中文翻译：

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一维内聚断裂：静态相场模型的准静态演化和推导

在本文中，我们提出了存在内聚力时裂纹演变的不可逆性概念，它允许在加载和卸载过程中产生不同的响应，这是由损伤模型的变分近似驱动的。我们研究了它在简单一维模型中构建准静态演化的适用性。内聚断裂模型通过伽玛收敛从广义 Ambrosio-Tortorelli 类型的相场模型自然产生，可用作数值模拟的正则化。