Estimation of local field statistics in highly filled composites based on an incremental mean-field homogenization scheme

Abstract

This article addresses the estimation of local field statistics and effective properties of highly filled particulate composites. With this aim in view, use is made of the differential scheme in its incremental form. In this framework, accounting for the successive homogenization steps characteristic of the incremental process, we derive the expressions of first- and second-order moments of intraphase strain fields. For first-order moments, this involves the calculation of the localization tensors for each phase at each step. For the second-order moments, the approach relies on the application of the chain derivation rule throughout the process, making it possible to express the derivatives of the final effective properties as a function of the initial properties of the phases. These expressions have been validated by comparison with available analytical solution for isotropic porous media. Besides, more general microstructures have been considered with phases exhibiting high mechanical contrasts and for a wide range of volume fractions. The numerical results on local field statistics have been compared to other mean-field homogenization schemes, such as the Mori–Tanaka and Lielens models, as well as to full-field simulations on representative microstructures. These comparisons confirm the relevance of the proposed approach in the context of highly inclusionary media.