Analysis of Solids with Numerous Microcracks Using the Fast Multipole DBEM

The fast multipole method (FMM) is applied to the dual boundary element method (DBEM) for the analysis of finite solids with large numbers of microcracks. The application of FMM significantly enhances the run-time and memory storage efficiency. Combining multipole expansions with local expansions, computational complexity and memory requirement are both reduced to O(N), where N is the number of DOFs (degrees of freedom). This numerical scheme is used to compute the effective in-plane bulk modulus of 2D solids with thousands of randomly distributed microcracks. The results prove that the IDD method, the differential method, and the method proposed by Feng and Yu can give proper estimates. The effect of microcrack non-uniform distribution is evaluated, and the numerical results show that non-uniform distribution of microcracks increases the effective in-plane bulk modulus of the whole microcracked solid.