A local moving extended phase field method (LMXPFM) for failure analysis of brittle materials

In this work, a local moving extended phase field method (LMXPFM) is proposed for the failure analysis of brittle materials. In this approach, nonlinear phase field crack evolution equations are solved in an adaptively refined small region (which is prone to crack nucleation or propagation). In the proposed LMXPFM, phase field method (PFM), extended finite element method (XFEM) and multiscale finite element method (MsFEM) are combined together such that the MsFEM acts as a medium to couple coarse mesh with fine mesh, and the XFEM is used to represent a discontinuity (such as crack) outside the phase field region. Thus, the LMXPFM not only provides an adaptively refined mesh in a small region near the smeared discontinuity but also fulfills the prerequisite of refined mesh for solving phase field crack evolution equations. This local approach provides a huge saving in the computational efforts as compared to PFM applied in the entire domain. The efficiency and accuracy of the LMXPFM are verified by solving and comparing the results with standard PFM and literature solutions.