On some background of micromechanics of random structure matrix composites

TL;DR

This paper develops a new integral equation approach for linearly elastic composite media with random heterogeneities, removing classical assumptions and revealing new effects in micromechanics.

Contribution

It introduces a general integral equation that does not rely on traditional hypotheses like the effective field hypothesis or ellipsoidal symmetry.

Findings

New integral equation derived without classical assumptions

Detection of fundamentally new effects in micromechanics

Method applicable to statistically inhomogeneous composites

Abstract

We consider a linearly elastic composite medium, which consists of a homogeneous matrix containing statistically inhomogeneous random set of heterogeneities and loaded by inhomogeneous remote loading. The new general integral equation is obtained by a centering procedure without any auxiliary assumptions such as, e.g., effective field hypothesis implicitly exploited in the known centering methods. The method makes it possible to abandon the basic concepts of classical micromechanics such as effective field hypothesis, and the hypothesis of "ellipsoidal symmetry". The results of this abandonment leads to detection of some fundamentally new effects that is impossible in the framework of a classical background of micromechanics.