MULTISCALE FINITE ELEMENT METHOD FOR HETEROGENEOUS MEDIA WITH MICROSTRUCTURES: CRACK PROPAGATION IN A POROUS MEDIUM

A novel multiscale FE scheme is proposed for simulation of crack propagation in heterogeneous media. A fine scale mesh is constructed to model the crack tip and the microstructures around the near-tip field, while a coarse scale mesh is introduced to model the far field, wherein the effect of the microstructures is averaged through the homogenization theory to yield the average macroscopic constitutive relationship. The so-called variable node elements are subsequently employed to connect the fine scale zone in a seamless way to the coarse scale zone. The moving crack tip is modeled in a straightforward manner with the conventional quarter-point singular element. Several numerical examples are presented to demonstrate the scheme as an effective tool for multiscale simulation of crack propagation in consideration of the microstructures in a heterogeneous body.