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

IGOR TSUKROV, BORYS DRACH, ANTON TROFIMOV and KOSTIANTYN VASYLEVSKYI

Abstract


We compare two approaches to homogenization of linearly elastic solids with irregularly shaped pores: direct finite element analysis (FEA) of periodic representative volume elements (RVEs) and micromechanical modeling using the elasticity solution for a single pore. To generate periodic RVEs for the direct FEA approach, a simplified algorithm of collective rearrangement type is utilized. Homogeneity and isotropy of the generated RVEs are confirmed using two-point statistics (also known as covariograms). The “single pore†micromechanical modeling approach is based on the cavity compliance contribution tensor (H-tensor), which is calculated for a pore in a large reference volume by an automated FEA procedure. The resulting H-tensors are then used in non-interaction, Mori-Tanaka, self-consistent and Maxwell homogenization schemes. Results are obtained for microstructures containing spherical, prolate spheroidal, cubical, and a specific case of irregular pore shape. They show good correspondence between direct FEA simulations of periodic RVEs and analytical micromechanical predictions of Mori-Tanaka and Maxwell schemes while self-consistent scheme significantly underpredicts the effective stiffness of porous materials.

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