Interface integral technique for the thermoelasticity of random structure matrix composites

Abstract

We consider linear thermoelastic composite media, which consist of a homogeneous matrix containing a statistically homogeneous random set of aligned homogeneous heterogeneities of non-canonical (i.e. non-ellipsoidal) shape. The representations of the effective properties (effective moduli, thermal expansion, and stored energy) are expressed through the statistical averages of the interface polarization tensors introduced apparently for the first time. The properties of the interface polarization tensors are described. The new general integral equations connecting the stress and strain fields in the point being considered with the stress and strain fields in the surrounding points are obtained for the random fields of heterogeneities. The method is based on a recently developed centering procedure where the notion of a perturbator is introduced in terms of boundary interface integrals estimated by the method of fundamental solution for a single inclusion inside the infinite matrix. This enables us to reconsider basic concepts of micromechanics such as effective field hypothesis, quasi-crystalline approximation, and the hypothesis of “ellipsoidal symmetry.” Effective properties (such as effective moduli, thermal expansion, and stored energy) as well as the first statistical moments of stresses in the phases are estimated for statistically homogeneous composites with the general case of the inclusion shape. The results of this reconsideration are quantitatively estimated for some modeled statistically homogeneous composites reinforced by aligned homogeneous heterogeneities of non-canonical shape. The explicit new representations of the effective thermoelastic properties and stress concentration factor are expressed through some building blocks ( perturbators) described by numerical solutions for one heterogeneity inside the infinite medium subjected to the homogeneous remote loading. Some new effects are detected that are impossible in the framework of a classical background of micromechanics.