Multiscale simulation of major crack/minor cracks interplay with the corrected XFEM

The present work aims at saving computational cost of multiscale simulation on major crack/minor crack interaction problems. The multiscale extended finite element method (MsXFEM) used for the numerical simulation is developed on multiscale projection technique which enables different scale decomposition, and transition of field variables between different scales. Both macroscale and microscale problems are solved independently and alternatively, in the framework of XFEM. The improvement made in this paper is to employ corrected XFEM on the macroscale level, so that a more accurate boundary condition can be obtained for the microscale problem. The modification leads to a reduced necessary microscale domain size, meanwhile a solution of higher accuracy and enhanced convergence rate can be achieved. The numerical examples of minor cracks near a major one are studied, which show that the effect of minor cracks on major crack can be efficiently captured.