High-Order Multi-Scale Method and Its Convergence Analysis for Nonlinear Thermo-Electro-Mechanical Coupling Problems of Composite Structures

TL;DR

This paper introduces a high-order multi-scale method for nonlinear thermo-electro-mechanical problems in composite structures, achieving high accuracy and efficiency through novel asymptotic modeling and error analysis.

Contribution

It develops a new high-order multi-scale asymptotic model with correction terms and provides convergence analysis for complex nonlinear coupled problems.

Findings

The method achieves high numerical accuracy in simulations.

It reduces computational cost compared to traditional methods.

Numerical experiments validate the method's effectiveness for complex structures.

Abstract

This study proposes a high-order multi-scale method tailored for time-dependent nonlinear thermo-electro-mechanical coupling problems of composite structures with highly spatial heterogeneity, which incorporate temperature-dependent material properties and Joule heating effect. By employing the multi-scale asymptotic approach and the Taylor series technique, a high-accuracy multi-scale asymptotic model featuring novel high-order correction terms is established for nonlinear multi-physics simulation of periodic solid structures. A local point-wise error analysis is derived to theoretically and physically illustrate the local balance preserving of heat quantity, electric charge and stress,thereby enabling high-accuracy multi-scale computation. Moreover, a global error estimation is obtained that provides an explicit convergence rate for high-order multi-scale solutions. Furthermore, an efficient numerical algorithm featuring with off-line and on-line stages is presented meticulously, accompanied by a corresponding error analysis. Numerical experiments are conducted to showcase the competitive advantages of the proposed method for simulating the time-dependent nonlinear thermo-electro-mechanical coupling problems with highly oscillatory and discontinuous coefficients, demonstrating superior numerical accuracy and reduced computational cost.