Optimal lower bounds on the local stress inside random thermoelastic composites

TL;DR

This paper develops explicit bounds on the maximum and higher moments of local hydrostatic stress in random thermoelastic composites, linking microscopic stress fields to macroscopic loads and material properties.

Contribution

It introduces a methodology for deriving optimal lower bounds on local stresses in thermoelastic composites, attained by Hashin-Shtrikman coated sphere models.

Findings

Explicit formulas for optimal bounds are derived.

Bounds are attained by Hashin-Shtrikman coated sphere assemblages.

The bounds relate local stress excursions to applied loads and material parameters.

Abstract

A methodology is presented for bounding all higher moments of the local hydrostatic stress field inside random two phase linear thermoelastic media undergoing macroscopic thermomechanical loading. The method also provides a lower bound on the maximum local stress. Explicit formulas for the optimal lower bounds are found that are expressed in terms of the applied macro- scopic thermal and mechanical loading, coefficients of thermal expansion, elastic properties, and volume fractions. These bounds provide a means to measure load transfer across length scales relating the excursions of the local fields to the applied loads and the thermal stresses inside each phase. These bounds are shown to be the best possible in that they are attained by the Hashin-Shtrikman coated sphere assemblage.