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

TL;DR

This paper presents a novel RVE concept and an advanced computational framework for analyzing thermoelastic composites with localized loading, improving accuracy and efficiency by integrating micromechanics, integral equations, and machine learning.

Contribution

It introduces a generalized RVE concept based on localized loading scales and develops an AGIE-based computational framework for thermoelastic composites.

Findings

Generalized RVE reduces analysis domain to finite, data-driven size.

New integral equations accurately model localized thermal and mechanical loads.

Framework supports integration with machine learning for surrogate modeling.

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.