Higher-order three-scale asymptotic model and efficient two-stage numerical algorithm for transient nonlinear thermal conduction problems of composite structures

Abstract

The accurate thermal analysis of composite structures remains a challenging issue due to complicated multiscale configurations and nonlinear temperature-dependent behaviors. This work offers a novel higher-order three-scale asymptotic (HOTSA) model and corresponding numerical algorithm for accurately and efficiently simulating transient nonlinear thermal conduction problems of heterogeneous structures with three-scale spatial hierarchy. Firstly, by recursively macro-meso and meso-micro two-scale asymptotic analysis, the macro-meso-micro correlative HOTSA model is established with higher-order cell functions and higher-order correction terms. Then, a rigorous error estimation of the HOTSA model is presented under some assumptions in the point-wise and integral sense. Furthermore, a two-stage numerical algorithm with offline micro-meso computation and online macro-multiscale computation is developed to implement efficient and high-accuracy thermal simulation for heterogeneous structures with three-level spatial scales. Finally, numerical experiments are conducted to assess the efficiency and accuracy of the proposed HOTSA model and two-stage algorithm. This study establishes a reliable higher-order three-scale computational framework, that has a great potential for accurately capturing the microscopic oscillatory information of composite structures along with a drastic reduction in the computation resource.