Dynamic thermo-mechanical coupled simulation of statistically inhomogeneous materials by statistical second-order two-scale method

In this paper, a statistical second-order two-scale (SSOTS) method is developed to simulate the dynamic thermo-mechanical performances of the statistically inhomogeneous materials. For this kind of composite material, the random distribution characteristics of particles, including the shape, size, orientation, spatial location, and volume fractions, are all considered. Firstly, the representation for the microscopic configuration of the statistically inhomogeneous materials is described. Secondly, the SSOTS formulation for the dynamic thermo-mechanical coupled problem is proposed in a constructive way, including the cell problems, effective thermal and mechanical parameters, homogenized problems, and the SSOTS formulas of the temperatures, displacements, heat flux densities and stresses. And then the algorithm procedure corresponding to the SSOTS method is brought forward. The numerical results obtained by using the SSOTS algorithm are compared with those by classical methods. In addition, the thermo-mechanical coupling effect is studied by comparing the results of coupled case with those of uncoupled case. It demonstrates that the coupling effect on the temperatures, heat flux densities, displacements, and stresses is very distinct. The results show that the SSOTS method is valid to predict the dynamic thermo-mechanical coupled performances of statistically inhomogeneous materials.