The goal of the current work is to explore direction-dependent damage initiation and propagation within an arbitrary anisotropic solid. In particular, we aim at developing anisotropic cohesive phase-field (PF) damage models by extending the idea introduced in \cite{REZAEI2021a} for direction-dependent fracture energy and also anisotropic PF damage models based on structural tensors. The cohesive PF damage formulation used in the current contribution is motivated by the works of \cite{LORENTZ201120, wu2018, GEELEN2019}. The results of the latter models are shown to be insensitive with respect to the length scale parameter for the isotropic case. This is because they manage to formulate the fracture energy as a function of diffuse displacement jumps in the localized damaged zone. In the present paper, we discuss numerical examples and details on finite element implementations where the fracture energy, as well as the material strength, are introduced as an arbitrary function of the crack direction. Using the current formulation for anisotropic cohesive fracture, the obtained results are almost insensitive with respect to the length scale parameter. The latter is achieved by including the direction-dependent strength of the material in addition to its fracture energy. Utilizing the current formulation, one can increase the mesh size which reduces the computational time significantly without any severe change in the predicted crack path and overall obtained load-displacement curves. We also argue that these models still lack to capture mode-dependent fracture properties. Open issues and possible remedies for future developments are finally discussed as well.

中文翻译：

---

各向异性内聚断裂模型：长度尺度不敏感相场损伤模型的优点和局限性

当前工作的目标是探索任意各向异性固体内与方向相关的损伤的发生和传播。特别是，我们的目标是通过扩展 \cite{REZAEI2021a} 中引入的思想来开发各向异性内聚相场 (PF) 损伤模型，以获得方向相关的断裂能以及基于结构张量的各向异性 PF 损伤模型。当前贡献中使用的内聚 PF 损伤公式是由 \cite{LORENTZ201120, wu2018, GEELEN2019} 的作品激发的。后一种模型的结果表明对各向同性情况的长度尺度参数不敏感。这是因为他们设法将断裂能公式化为局部损坏区域中扩散位移跳跃的函数。在本文中，我们讨论了有限元实现的数值示例和细节，其中断裂能以及材料强度被引入为裂纹方向的任意函数。使用当前的各向异性粘性断裂公式，获得的结果对长度尺度参数几乎不敏感。后者是通过除断裂能外还包括材料的方向相关强度来实现的。利用当前的公式，可以增加网格尺寸，从而显着减少计算时间，而不会对预测的裂纹路径和整体获得的载荷-位移曲线产生任何重大变化。我们还认为这些模型仍然缺乏捕捉依赖于模式的断裂特性。