Additive general integral equations in thermoelastic micromechanics of composites

TL;DR

The paper advances thermoelastic micromechanics by replacing classical remote boundary conditions with compact-support loading, yielding an Additive General Integral Equation (AGIE) that defines a data-driven, finite-domain Representative Volume Element (RVE). It unifies exact GIE formulations with CAM and introduces a path to surrogate nonlocal operators that are trained on compressed datasets ${\cal D}^T$ derived from BFCS and TCCS loadings, avoiding edge effects and finite-size biases. The AGIE-CAMNN framework enables model-agnostic ML integration, including peridynamic-like operators and physics-informed networks, while accommodating imperfect interfaces and nonlocal interactions. This leads to a unified, scalable approach for generating physically constrained, nonlocal surrogate operators applicable to a broad class of random and deterministic microstructures, with potential impact on design, optimization, and real-time prediction of thermoelastic composites.

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.