Efficient higher-order multi-scale method and its convergence estimate for dynamic nonlinear hygro-thermo-mechanical coupling problems of heterogeneous structures

Abstract

This paper presents a novel higher-order multi-scale (HOMS) computational framework for efficient, high-accuracy, and low-cost simulation of nonlinear hygro-thermo-mechanical (H-T-M) coupling problems in heterogeneous structures. The inherent nonlinearity in the investigated model stems primarily from temperature- or moisture-dependent material properties, and this model also accounts for temperature-dependent internal heat source and moisture sink terms induced by exothermic, moisture-consuming chemical reactions (e.g., hydration). The main contributions of this work are as follows. First, a high-accuracy multi-scale asymptotic model incorporating higher-order correction terms is constructed for nonlinear H-T-M coupling problems in heterogeneous structures with highly spatial inhomogeneity, using the multi-scale asymptotic approach together with Taylor series expansions. Second, rigorous error estimates in both point-wise and integral senses are derived for the multi-scale asymptotic solutions, which theoretically demonstrate the necessity and superiority of the proposed HOMS method. Third, an efficient two-stage numerical algorithm with off-line and on-line stages is developed, based on finite difference and finite element methods, and its convergence is also proved rigorously. Finally, two- and three-dimensional numerical experiments are performed to assess the computational performance of the proposed HOMS approach, showing excellent numerical accuracy and robustness with low computational overhead.