Computing the effective crack energy of heterogeneous and anisotropic microstructures via anisotropic minimal surfaces

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.