A multiscale reduced‐order‐model strategy for transient thermoelasticity with variable microstructure

Abstract

AbstractThis article deals with thermoelastic computation of heterogeneous structures containing quasi‐periodic microstructures having variable properties (geometric and/or material) using reduced‐order modeling. Such heterogeneous structure is extremely expensive to simulate using classical finite element methods, as the level of discretization required to capture the microstructural effects, is too fine. Based on the asymptotic homogenization theory, the multiscale technique explores the micro–macro behavior for thermoelasticity. Considering each integration point of the macrostructure consists of an underlying locally periodic microstructure, the overall problem is basically separated into a homogeneous problem defined over the macrostructure and a heterogeneous problem defined over each microstructure. Even though the usage of multiscale strategy helps in the reduction of numerical expense, it still deals with a full‐order finite element solution for the macroproblem and each microproblem. Using a twofold reduced‐order modeling further accentuates the cost reduction and provides a robust solution in a reduced space: (i) as an offline precomputation stage for the microstructural problem, and (ii) as an online process that can embed adaptivity for the macroscopic problem.