Periodic mesh generation and homogenization of inclusion-reinforced composites using an element-carving technique with local mesh refinement

An efficient periodic mesh generation scheme for representative volume elements (RVEs) of inclusion-reinforced composites is proposed with the aid of an element-carving technique. A background mesh with regular hexahedral elements is cut and split to fit periodic configurations of inclusions. The split hexahedral elements around the inclusion-matrix interfaces correspond to polyhedral elements, while the background hexahedral elements remain inside the inclusions and matrices. To further achieve an accurate and efficient RVE modeling, local refinement for the background mesh is introduced near the inclusion-matrix interfaces. Polyhedral elements that have arbitrary numbers of polygonal faces and nodes are also used to connect the refined and original background hexahedral elements. The generated meshes automatically have periodic boundary configurations, and no special treatment is thus required to impose periodic boundary conditions in a computational homogenization. In this paper, the cell-based smoothed finite element method is adopted to reduce the effort involved in explicitly defining shape functions and in accurately conducting numerical integration for polyhedral elements. The effectiveness of the proposed scheme is demonstrated in the numerical examples of generating RVEs, including spherical, ellipsoidal, or cylinder-shaped inclusions. Furthermore, the influences of inclusion configurations on estimating the effective elastic moduli are investigated with the generated meshes.