This paper combines energy decomposition and an extended gradient damage (EGD) model to develop an anisotropic fracture framework with decoupling of tensile and shear cohesive laws. By introducing the shear-normal decomposition in the energy form, the driving force of the damage variable is established within the framework of the EGD model, which is then capable of capturing the traction-separation of potential crack surfaces in both shear and normal directions. The intrinsic correspondence between the cohesive law and the damage evolution enables the accurate prediction of anisotropic fracture behavior in the mixed form of Mode I and Mode II. Furthermore, the proposed model also addresses the damage unloading issue, which still remains a challenge in classic phase field theory or non-local damage theory. A number of numerical examples are presented as validation. Some cutting-edge benchmarks, such as complex mixed-mode fracture and perfect shear fracture, are well reproduced.

中文翻译：

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各向异性断裂的扩展梯度损伤模型


本文结合能量分解和扩展梯度损伤（EGD）模型，开发了一种具有拉伸和剪切粘聚定律解耦的各向异性断裂框架。通过引入能量形式的剪切法线分解，在EGD模型的框架内建立了损伤变量的驱动力，从而能够捕获剪切和法线方向上潜在裂纹表面的牵引分离。内聚定律与损伤演化之间的内在对应关系使得能够准确预测模式 I 和模式 II 混合形式的各向异性断裂行为。此外，所提出的模型还解决了损伤卸载问题，这仍然是经典相场理论或非局部损伤理论中的一个挑战。提供了许多数值示例作为验证。一些尖端基准，例如复杂混合模式断裂和完美剪切断裂，得到了很好的再现。