Abstract In recent years the phase-field method and the coupled energy and stress-based criterion have attracted much attention due to their adaptability in modeling fractures. Both approaches have been successfully used to determine crack initiation and have compared well with real-life experiments. The phase-field method diffuses the crack surface into the volume of the solid, thus making the solution viable through variational techniques. The diffusion is controlled by an internal length scale, which is primarily considered to be a numerical aid without any real physical meaning. In this paper, we question the consideration that the internal length is only a numerical parameter, and assess its mechanical significance with the help of the coupled criterion. Through elaborate benchmark examples, the correlation between the two methods is demonstrated based on the critical loading, the crack topology, and the crack arrest length. We reveal that independently of the chosen aspect, the phase-field approach and the coupled criterion present excellent correspondence. We show that the correlation between tensile strength and length scale is unique for the standard phase-field formulation. Interestingly, we find that both stress and energy criteria are satisfied in the phase-field fracture, and this is explained by demonstrating the alteration in global energy release rate due to the regularization introduced by the smeared model.

中文翻译：

---

韧性还是强度？耦合判据解释的相场断裂正则化

摘要 近年来，相场法和基于能量与应力的耦合准则因其在模拟裂缝中的适应性而备受关注。这两种方法都已成功用于确定裂纹萌生，并与现实生活中的实验进行了很好的比较。相场法将裂纹表面扩散到固体体积中，从而通过变分技术使解决方案可行。扩散由内部长度标度控制，其主要被认为是没有任何实际物理意义的数字辅助。在本文中，我们质疑内部长度只是一个数值参数的考虑，并借助耦合准则评估其力学意义。通过详细的基准示例，基于临界载荷、裂纹拓扑和裂纹止裂长度证明了两种方法之间的相关性。我们揭示，独立于所选择的方面，相场方法和耦合标准呈现出极好的对应关系。我们表明，对于标准相场公式，拉伸强度和长度尺度之间的相关性是独一无二的。有趣的是，我们发现在相场断裂中应力和能量标准都得到满足，这可以通过证明由于涂抹模型引入的正则化导致全局能量释放速率的改变来解释。我们表明，对于标准相场公式，拉伸强度和长度尺度之间的相关性是独一无二的。有趣的是，我们发现在相场断裂中应力和能量标准都得到满足，这可以通过证明由于涂抹模型引入的正则化导致全局能量释放速率的改变来解释。我们表明，对于标准相场公式，拉伸强度和长度尺度之间的相关性是独一无二的。有趣的是，我们发现在相场断裂中应力和能量标准都得到满足，这可以通过证明由于涂抹模型引入的正则化导致全局能量释放速率的改变来解释。