On the thermo-elastostatics of heterogeneous materials. I. General integral equation

TL;DR

This paper develops general integral equations for the stress and strain fields in heterogeneous thermoelastic composites with functionally graded inclusions, using a statistical averaging method that avoids auxiliary assumptions.

Contribution

It introduces a new integral equation approach for analyzing thermoelastic composites with inhomogeneous inclusions, emphasizing locality and statistical averaging without effective field hypotheses.

Findings

Derived general integral equations for stress and strain fields.

Applied the method to functionally graded materials with inhomogeneous inclusions.

Ensured locality principle in the integral equations.

Abstract

We consider a linearly thermoelastic composite medium,which consists of a homogeneous matrix containing a statistically inhomogeneous random set of inclusions, when the concentration of the inclusions is a function of the coordinates (so-called Functionally Graded Materials). The composite medium is subjected to essentially inhomogeneous loading by the fields of the stresses, temperature and body forces (e.g. for a centrifugal load). The general integral equations connecting the stress and strain fields in the point being considered and the surrounding points are obtained for the random fields of inclusions. The method is based on a centering procedure of subtraction from both sides of a known initial integral equation their statistical averages obtained without any auxiliary assumptions such as, e.g., effective field hypothesis implicitly exploited in the known centering methods. In so doing the size of a region including the inclusions acting on a separate one is finite, i.e. the locality principle takes place.