Title: A variational phase-field model for anisotropic fracture accounting for multiple cohesive lengths Show Chinese title

Title: 一种考虑多个粘聚长度的各向异性断裂变分相场模型

Abstract: We propose a novel variational phase-field model for fracture in anisotropic materials. The model is specifically designed to allow a more flexible calibration of crack nucleation than existing anisotropic fracture formulations, while avoiding the introduction of multiple damage variables. In addition to the classical components of anisotropic phase-field models based on a single damage variable -- namely, anisotropic elasticity and the extension of the fracture energy density via a second-order structural tensor -- the proposed approach introduces fracture anisotropy through a cohesive degradation function with potentially distinct cohesive lengths along the principal material directions. For this reason, we refer to it as multi-cohesive model. This feature enables independent control of the critical stresses governing crack nucleation in each material direction. We analyze the homogeneous solution and its second-order stability, and we compare the resulting strength surfaces with those of two representative anisotropic phase-field models available in the literature. Finally, numerical simulations in two and three dimensions demonstrate the capability of the proposed model to independently control crack nucleation and propagation in anisotropic fracture problems of increasing complexity. Show Chinese abstract

Abstract: 我们提出了一种新颖的变分相场模型，用于各向异性材料中的断裂。 该模型专门设计为允许比现有各向异性断裂公式更灵活的裂纹萌生校准，同时避免引入多个损伤变量。 除了基于单个损伤变量的各向异性相场模型的经典组成部分——即各向异性弹性以及通过二阶结构张量扩展断裂能密度之外，所提出的方法通过一个可能在主材料方向上具有不同粘聚长度的粘聚退化函数来引入断裂各向异性。 因此，我们将其称为多粘聚模型。 这一特性使得能够独立控制每个材料方向上决定裂纹萌生的关键应力。 我们分析了均匀解及其二阶稳定性，并将所得强度曲面与文献中两种代表性各向异性相场模型的结果进行了比较。 最后，二维和三维的数值模拟展示了所提出模型在独立控制日益复杂的各向异性断裂问题中裂纹萌生和扩展方面的能力。