Multiscale Method and Convergence Analysis for Coupled Nonlinear Thermomechanical Problems in Heterogeneous Shells
Hao Dong, Xiaofei Guan, Yufeng Nie · SIAM Journal on Scientific Computing · 2025
Abstract. This paper discusses the multiscale computations for nonlinear dynamic coupled thermomechanical problems in heterogeneous shells, which possess temperature-dependent material properties and orthogonal periodic configurations. The new contributions in this study are the novel coupled formulation with the higher-order correction terms for orthogonal periodic configurations and the global error estimation with an explicit rate for higher-order multiscale solutions in the integral norm sense. By combining the multiscale asymptotic technique and the Taylor series approach, the multiscale method is developed for nonlinear time-dependent thermomechanical problems, which can keep the conservation of local energy and momentum for multiscale simulation. Moreover, an efficient space-time numerical algorithm with off-line and on-line stages is presented in detail. Numerical results show that the proposed method has competitive advantages for solving the dynamic thermomechanical problem in heterogeneous shells, which has exceptional numerical accuracy and less computational cost. Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and data available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://github.com/mathguan/Nonlinear-material-structure and in the supplementary materials ( Nonlinear-material-structure-main.zip [186MB]). [Formula: see text]