Finite element analysis of quasistatic crack propagation in brittle media with voids or inclusions

A three-level finite element scheme is proposed for simulation of crack propagation in heterogeneous media including randomly distributed voids or inclusions. To reduce total degrees of freedom in the view of mesh gradation, the entire domain is categorized into three regions of different-level meshes: a region of coarse-level mesh, a region of intermediate-level mesh, and a region of fine-level mesh. The region of coarse-level mesh is chosen to be far from the crack to treat the material inhomogeneities in the sense of coarse-graining through homogenization, while the region near the crack is composed of the intermediate-level mesh to model the presence of inhomogeneities in detail. Furthermore, the region very near the crack tip is refined into the fine-level mesh to capture a steep gradient of elastic field due to the crack tip singularity. Variable-node finite elements are employed to satisfy the nodal connectivity and compatibility between the neighboring different-level meshes. Local remeshing is needed for readjustment of mesh near the crack tip in accordance with crack growth, and this is automatically made according to preset values of parameters determining the propagation step size of crack, and so the entire process is fully automatic. The effectiveness of the proposed scheme is demonstrated through several numerical examples. Meanwhile, the effect of voids and inclusions on the crack propagation is discussed in terms of T-stresses, with the aid of three-level adaptive scheme.