On the thermo-elastostatics of heterogeneous materials. II. Analyze and generalization of some basic hypotheses

TL;DR

This paper develops a generalized approach to analyze the thermo-elastostatic behavior of heterogeneous composite materials, removing traditional micromechanical assumptions and revealing new effects in inhomogeneous fiber-reinforced composites.

Contribution

It introduces a new integral equation framework that generalizes classical micromechanics, enabling more accurate modeling of thermoelastic properties without relying on basic hypotheses.

Findings

Explicit representations of effective properties derived

Quantitative estimates for inhomogeneous fiber composites

Discovery of new effects beyond classical micromechanics

Abstract

One considers linearly thermoelastic composite media, which consist of a homogeneous matrix containing a statistically homogeneous random set of ellipsoidal uncoated or coated inclusions. Effective properties (such as compliance and thermal expansion) as well as the first statistical moments of stresses in the phases are estimated for the general case of nonhomogeneity of the thermoelastic inclusion properties. At first, one shortly reproduces both the basic assumptions and propositions of micromechanics used in most popular methods, namely: effective field hypothesis, quasi-crystallite approximation, and the hypothesis of "ellipsoidal symmetry". The explicit new representations of the effective thermoelastic properties and stress concentration factor are expressed through some building blocks described by numerical solutions for both the one and two inclusions inside the infinite medium subjected to both the homogeneous and inhomogeneous remote loading. The method uses as a background the new general integral equation proposed in the accompanied paper and makes it possible to abandon the basic concepts of micromechanics mentioned above. The results of this abandonment are quantitatively estimated for some modeled composite reinforced by aligned continously inhomogeneous fibers. Some new effects are detected that are impossible in the framework of a classical background of micromechanics.