New RVE concept in thermoelasticity of periodic composites subjected to compact support loading

TL;DR

The work addresses predicting nonlocal thermoelastic responses of periodic composites subject to localized excitations by replacing traditional RVEs and Green-function-based homogenization with a compact-support loading strategy that defines a learning-friendly RVE (Definition 4.2). It introduces Additive General Integral Equations (AGIE) and centering-based General Integral Equations (GIE) to capture multi-inclusion interactions while decoupling from the effective-field hypothesis. A structured, translation-averaged dataset $\mathcal{D}^T$ (and $\mathcal{D}^{dT}$) is built from DNS within a finite RVE under BFCS/TCCS, enabling surrogate nonlocal operators learned via ML/NN (CAMNN) that generalize to infinite media and arbitrary loadings. By eliminating boundary-layer and finite-size effects at the data generation stage, the framework offers a scalable, physics-informed path to nonlocal micromechanics for both periodic and deterministic microstructures, with potential extensions to nonlinear processes such as fracture and plasticity.

Abstract

This paper introduces an advanced Computational Analytical Micromechanics (CAM) framework for linear thermoelastic composites (CMs) with periodic microstructures. The approach is based on an exact new Additive General Integral Equation (AGIE), formulated for compactly supported loading conditions, such as body forces and localized thermal effects (for example laser heating). In addition, new general integral equations (GIEs) are established for arbitrary mechanical and thermal loading. A unified iterative scheme is developed for solving the static AGIEs, where the compact support of loading serves as a new fundamental training parameter. At the core of the methodology lies a generalized Representative Volume Element (RVE) concept that extends Hill classical definition of the RVE. Unlike conventional RVEs, this generalized RVE is not fixed geometrically but emerges naturally from the characteristic scale of localized loading, thereby reducing the analysis of an infinite periodic medium to a finite, data-driven domain. This formulation automatically filters out nonrepresentative subsets of effective parameters while eliminating boundary effects, edge artifacts, and finite-size sample dependencies. Furthermore, the AGIE-based CAM framework integrates seamlessly with machine learning (ML) and neural network (NN) architectures, supporting the development of accurate, physics-informed surrogate nonlocal operators.