Abstract

In this paper, a new crack surface energy for the simulation of ductile fracture is proposed, which is based on the Allen–Cahn theory of diffuse interfaces. In contrast to existing fracture approaches, here, the crack surface energy density is a double-well potential based on a new interpretation of the crack surface. That is, the energy associated with the whole diffuse region between the fully cracked and intact regions is interpreted as crack surface energy. This kind of formulation, on the one hand, results in the balance of micromechanical forces and on the other hand, is a priori thermodynamically consistent. Furthermore, the proposed formulation is based on a gamma-convergent interface energy and it is in agreement with the classical solution of Irwin (Appl Mech Trans ASME E24:351–369, 1957). It is shown that in contrast to existing models, crack irreversibility is automatically fulfilled and no further constraints related to neither local nor global irreversibility are needed. To also account for potential plastic shear band localization, the approach is extended by a micromorphic plasticity model. By analyzing two different classical numerical benchmark problems, the proposed formulation is shown to enable mesh-independent results which are in agreement with the results of competing approaches.

中文翻译：

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基于 Allen-Cahn 理论的有限应变下延性断裂的先验不可逆相场公式：变分方法和有限元实现

摘要

本文基于扩散界面的 Allen-Cahn 理论，提出了一种用于模拟延性断裂的新裂纹表面能。与现有的断裂方法相比，这里的裂纹表面能量密度是基于对裂纹表面的新解释的双阱势。也就是说，与完全裂纹区域和完整区域之间的整个扩散区域相关的能量被解释为裂纹表面能。这种公式一方面导致微机械力的平衡，另一方面在热力学上是先验一致的。此外，所提出的公式基于伽玛收敛界面能，并且与 Irwin 的经典解决方案一致（Appl Mech Trans ASME E24:351–369, 1957）。结果表明，与现有模型相比，裂纹不可逆性是自动满足的，并且不需要与局部或全局不可逆性相关的进一步约束。为了也考虑潜在的塑性剪切带局部化，该方法通过微形态塑性模型进行了扩展。通过分析两个不同的经典数值基准问题，所提出的公式显示出能够实现与网格无关的结果，该结果与竞争方法的结果一致。