Homogenization of Linearly Elastic Materials with Pores of Irregular Shapes Via Direct FEA and Single Pore Approaches

摘要

We compare two approaches to homogenization of linearly elastic solids withirregularly shaped pores: direct finite element analysis (FEA) of periodicrepresentative volume elements (RVEs) and micromechanical modeling using theelasticity solution for a single pore. To generate periodic RVEs for the direct FEAapproach, a simplified algorithm of collective rearrangement type is utilized.Homogeneity and isotropy of the generated RVEs are confirmed using two-pointstatistics (also known as covariograms). The “single pore” micromechanical modelingapproach is based on the cavity compliance contribution tensor (H-tensor), which iscalculated for a pore in a large reference volume by an automated FEA procedure. Theresulting H-tensors are then used in non-interaction, Mori-Tanaka, self-consistent andMaxwell homogenization schemes. Results are obtained for microstructurescontaining spherical, prolate spheroidal, cubical, and a specific case of irregular poreshape. They show good correspondence between direct FEA simulations of periodicRVEs and analytical micromechanical predictions of Mori-Tanaka and Maxwellschemes while self-consistent scheme significantly underpredicts the effectivestiffness of porous materials.