Adaptive Tetrahedral Mesh Generation of 3D Heterogeneous Objects

Abstract

In recent years, heterogeneous materials have attracted a lot of attention for their superior properties over homogeneous materials. To design, analyze, and optimize the behavior of heterogeneous materials, the finite element method (FEM) as an effective numerical method has been immensely utilized. Although tremendous efforts are devoted to finite element analysis (FEA) of heterogeneous materials in the past two decades, little attention has been focused on mesh generation, which is an essential part of the FEA procedure. For the sake of simplicity, classic mesh generation methods targeted on homogeneous objects are often directly applied into the domain of heterogeneous objects. The meshes generated by these traditional methods, however, either result in poor simulation accuracies (as they fail to characterize the material heterogeneities), or introduce denser elements than desired, significantly degrading the computational efficiency. To solve such problems, specific mesh generation methods for efficient and robust FEA of heterogeneous objects are called for. Zhang et al proposed an automatic 3D mesh generation method for heterogeneous objects. Unfortunately, only multiple material objects, which are very primitive in terms of material heterogeneities, are taken into account. Functionally graded materials (FGMs), whose material heterogeneities vary gradually within the domain of interest, usually outperform multiple materials. Therefore, meshing strategies that concentrate on these objects warrant further exploration.