A multiscale framework based on phase field method and XFEM to simulate fracture in highly heterogeneous materials

In the present work, the phase field method (PFM) is integrated with multiscale extended finite element method (MsXFEM) to simulate crack growth in highly heterogeneous materials i.e. matrix with periodically distributed voids and particles. To reduce total degrees of freedom, the entire domain is partitioned into two regions of distinct meshes: region of coarse mesh and region of fine mesh. The heterogeneous region away from the crack is discretized with coarse mesh using MsXFEM, on the other hand, the region near the crack is discretized with fine mesh using standard finite elements. To save the computational time, the region away from the crack is homogenized with the help of MsXFEM whereas, in the region of fine mesh near the crack, actual heterogeneities are modelled to incorporate the local physics of the material. To further reduce the computational effort, the phase field crack evolution equations are evaluated in the region of fine mesh only. The periodically distributed heterogeneities in the region of coarse and fine mesh are modelled using XFEM. The numerical simulations are performed by considering three different types of heterogeneities (voids, particles with a perfect interface, particles with a finite interface). The effectiveness of the proposed method is validated through various numerical experiments.