An adaptive multiscale phase field method for brittle fracture

In the present work, a multiscale finite element method (MsFEM) is coupled with hybrid phase field method to simulate brittle fracture problems. This approach along with adaptive meshing, known as adaptive multiscale phase field method (AMPFM), is quite useful for local mesh refinement. During mesh refinement, the degrees of freedom of coarse-mesh and fine-mesh are linked together using multiscale basis functions. The proposed mesh refinement approach automatically tracks a propagating crack and refines the domain in the vicinity of the crack by utilizing the values of the current phase field variable and its increment. This approach when applied to simulate fracture behaviour of heterogeneous structures containing uniformly distributed small-size discontinuities (voids/inclusions) leads to a significant reduction in the memory and CPU time. Various numerical problems are solved using the proposed AMPFM, and results are compared with the standard PFM and available literature results.