Effective elastic isotropic moduli of highly filled particulate composites with arbitrarily shaped inhomogeneities

Abstract

The purpose of present work is three-fold: (i) to model thin binding interphases within highly filled particulate composites (HFPCs) as equivalent spring-type interfaces of zero-thickness; (ii) to develop a computational approach for calculating the effective elastic moduli of HFPCs containing arbitrarily shaped inhomogeneities; (iii) to establish a numerical scheme which generates simplified models for substitution of real representative volume elements of HFPCs while ensuring linear isotropic elasticity at the macroscopic scale. At first, a spring-type interface model with explicit physical background is derived to replace the soft interphases in HFPCs, and the macroscopic quantities and effective moduli accounting for the interfacial discontinuities are reformulated. Then, the strong and weak formulations of the boundary value problems of HFPCs are constructed, and a computational approach is developed by using the extended finite element and level set methods so as to determine the effective moduli of HFPCs. A numerical procedure is further elaborated to generate macroscopically isotropic RVEs by dividing a cubic model into differently shaped subdomains, and the minimal number of cutting planes is obtained based on the necessary and sufficient conditions in He (2004). Finally, discussions are made on the inclusion size and shape effects on the overall isotropic moduli of HFPCs.