A new multiscale XFEM with projection method for interaction between macrocrack and microcracks

Abstract

Crack develops through the accumulation and development of microcracks near its crack tip. In the present study, a new multiscale XFEM was proposed to simulate the interaction between macrocrack and microcracks. In the proposed method, a multiscale projection method is used to construct the discontinuous multiscale base functions, since the enrichment schemes at macroscale and microscale differ. These multiscale base functions can correctly and conveniently deliver the discontinuous information between the macroscale and microscale. The strategy provides a new approach to address the deficiency that the traditional coarse elements in multiscale finite element method (MsFEM) cannot well characterize the displacement jump on the boundary of the unit cell, therefore enables extended finite element method (XFEM) to be employed at both scales. The feasibility of the proposed method is demonstrated using three numerical examples: a bending beam containing a mixed mode crack, a macro crack interacting with two symmetrical micro cracks, and a macrocrack interacting with multiple micro cracks. The proposed method can provide detailed displacement field and accurate stress intensity factor results with high computational efficiency.