Extended Voronoi cell finite element method for multiple crack propagation in brittle materials

This paper introduces a new extended Voronoi cell finite-element method (X-VCFEM) for modelling the propagation of multiple cracks in brittle materials. The direction of the crack propagation is adaptively determined in terms of the maximum energy release rate near the crack tip, and we apply a remeshing strategy that a node at a last incremental crack tip in the crack advance process is replaced by a node pairs to realize the gradual crack propagation. In order to accurately capture crack-tip stress concentrations, some singular stress terms of Williams expansion in the vicinity of crack tips are introduced in the assumed stress hybrid formulation which also includes the polynomial terms and the reciprocal terms. Then several numerical examples are used to demonstrate the effectiveness and accuracy of X-VCFEM enriched by some singular stress terms of Williams expansion by comparing X-VCFEM results with those computed by the commercial finite element package ABAQUS or established results in the literature. At last, two numerical examples are given to simulate multiple crack propagation in brittle media. The effects of morphological distributions such as length, orientation and dispersion on the crack propagation are studied. It is obvious that the X-VCFEM has great advantage of analyzing large regions of the microstructure with multiple growing and interacting cracks.