Statistical higher-order multi-scale method for nonlinear thermo-mechanical simulation of random composite materials with temperature-dependent properties

TL;DR

This paper introduces a statistical higher-order multi-scale method for efficient and accurate nonlinear thermo-mechanical simulation of random composite materials with complex microstructures, addressing computational challenges.

Contribution

The paper develops a novel SHOMS approach combining asymptotic analysis and Taylor series to improve simulation accuracy and efficiency for complex composite materials.

Findings

SHOMS accurately predicts nonlinear thermo-mechanical responses.

The method maintains local energy and momentum conservation.

Numerical experiments demonstrate high efficiency and precision.

Abstract

Stochastic multi-scale modeling and simulation for nonlinear thermo-mechanical problems of composite materials with complicated random microstructures remains a challenging issue. In this paper, we develop a novel statistical higher-order multi-scale (SHOMS) method for nonlinear thermo-mechanical simulation of random composite materials, which is designed to overcome limitations of prohibitive computation involving the macro-scale and micro-scale. By virtue of statistical multi-scale asymptotic analysis and Taylor series method, the SHOMS computational model is rigorously derived for accurately analyzing nonlinear thermo-mechanical responses of random composite materials both in the macro-scale and micro-scale. Moreover, the local error analysis of SHOMS solutions in the point-wise sense clearly illustrates the crucial indispensability of establishing the higher-order asymptotic corrected terms in SHOMS computational model for keeping the conservation of local energy and momentum. Then, the corresponding space-time multi-scale numerical algorithm with off-line and on-line stages is designed to efficiently simulate nonlinear thermo-mechanical behaviors of random composite materials. Finally, extensive numerical experiments are presented to gauge the efficiency and accuracy of the proposed SHOMS approach.