Error propagation from microstructure changes to apparent stiffness in 2D biphase matrix-inclusion composites

Abstract

The representation of material microstructure in most existing analytical homogenization models is condensed into a set of well-known “classical” microstructure descriptors, such as the volume fraction and morphology of the individual phases of a composite. This study considers an enriched set of micro descriptors, containing both those “classical” descriptors as well as “non-classical” descriptors which quantify the spatial correlations of any two given micro material points inside a random heterogeneous material. We focus on 2D composites consisting of a matrix with embedded inhomogeneities (or inclusions) of random spatial arrangement. Both phases are treated as homogeneous, linearly elastic and isotropic. Starting from a rich database of reference microstructures, new datasets of perturbed microstructures are created, by inducing changes emulating the physical processes of inclusion nucleation and growth. All microstructures are characterized using the enriched set of micro descriptors, while their apparent stiffness tensor is computed numerically with the finite element (FE) method. A sensitivity analysis between the changes of the micro descriptors and corresponding changes of the apparent stiffness tensor reveals that the “non-classical” descriptors are consistently highly important to the macroscopic behavior. This suggests that enhanced homogenization models, made dependent on the identified pertinent “non-classical” micro descriptors, could be of higher predictive capability than existing approaches.