A variety of materials, such as polycrystalline ceramics or carbon fiber reinforced polymers, show a pronounced anisotropy in their local crack resistance. We introduce an FFT-based method to compute the effective crack energy of heterogeneous, locally anisotropic materials. Recent theoretical works ensure the existence of representative volume elements for fracture mechanics described by the Francfort–Marigo model. Based on these formulae, FFT-based algorithms for computing the effective crack energy of random heterogeneous media were proposed, and subsequently improved in terms of discretization and solution methods. In this work, we propose a maximum-flow solver for computing the effective crack energy of heterogeneous materials with local anisotropy in the material parameters. We apply this method to polycrystalline ceramics with an intergranular weak plane and fiber structures with transversely isotropic crack resistance.

多种材料，例如多晶陶瓷或碳纤维增强聚合物，在其局部抗裂性方面表现出明显的各向异性。我们引入了一种基于 FFT 的方法来计算异质、局部各向异性材料的有效裂纹能量。最近的理论工作确保了 Francfort-Marigo 模型描述的断裂力学具有代表性的体积元素的存在。基于这些公式，提出了基于FFT的随机异构介质有效裂纹能量计算算法，并在离散化和求解方法方面进行了改进。在这项工作中，我们提出了一种最大流求解器，用于计算材料参数具有局部各向异性的异质材料的有效裂纹能。