Additive general integral equations in thermoelastic micromechanics of composites

TL;DR

This paper introduces an advanced computational framework for analyzing thermoelastic composites using additive integral equations, a generalized RVE concept, and compatibility with machine learning for improved micromechanical modeling.

Contribution

It develops new integral equations for thermoelastic composites, introduces a generalized RVE concept based on localized loading, and integrates ML techniques for surrogate modeling.

Findings

Unified integral equations for thermal and mechanical loading

Generalized RVE reduces analysis complexity

Framework compatible with ML and neural networks

Abstract

This work presents an enhanced Computational Analytical Micromechanics (CAM) framework for the analysis of linear thermoelastic composite materials (CMs) with random microstructure. The proposed approach is grounded in an exact Additive General Integral Equation (AGIE), specifically formulated for compactly supported loading, including both body forces and localized thermal changes (such as those from laser heating). New general integral equations (GIEs) for arbitrary mechanical and thermal loading are proposed. A unified iterative solution strategy is developed for the static AGIE, applicable to CMs with both perfectly and imperfectly bonded interfaces, where the compact support of loading is introduced as a new fundamental training parameter. Central to this methodology is a generalized Representative Volume Element (RVE) concept, which extends Hill classical definition. The resulting RVE is not predefined geometrically, but rather emerges from the characteristic scale of the localized loading, effectively reducing the analysis of an infinite, randomly heterogeneous medium to a finite, data-driven domain. This generalized RVE approach enables automatic exclusion of unrepresentative subsets of effective parameters, while inherently eliminating boundary effects, edge artifacts, and finite size limitations. Moreover, the AGIE-based CAM framework is naturally compatible with machine learning (ML) and neural network (NN) architectures, facilitating the construction of accurate and physically informed surrogate nonlocal operators.