Thermo-mechanical analysis of periodic porous materials with microscale heat transfer by multiscale asymptotic expansion method

A novel multiscale asymptotic method used to simulate thermo-mechanical analysis of periodic porous materials with microscale heat transfer is systematically studied. In these materials, heat radiation and heat convection that account for the scale effect of unit cells have an important impact on the macroscopic temperature and stress fields, which is our particular interest in this study. The scale effect is thought to be the result of microscopic heat transfer, the amount of which depends on the microscale pore size of porous materials. The higher-order multiscale formulations for computing the dynamic thermo-mechanical coupling problem with the inertia term, coupling term, convection term and radiation term are given successively. Then, the corresponding numerical algorithm based on the finite element-difference method is brought forward in details. Finally, numerical examples are given to demonstrate the efficiency and validity of the proposed method. The results indicate the disadvantages of classical finite element method.