MsFEM Upscaling for the Coupled Thermo-Mechanical Problem

In this paper, we present the framework for the multiscale thermoelastic analysis of composites. Asphalt concrete (AC) was selected to demonstrate the applicability of the proposed approach. It is due to the observed high dependence of this material performance on the thermal effects. The insight into the microscale behavior is upscaled to the macroresolution by the multiscale finite element method (MsFEM) that has not been used so far for coupled problems. In the paper, we present a brief description of this approach together with its new application to coupled thermoelastic numerical modeling. The upscaled results are compared with the reference ones and the error analysis is presented. A very good agreement between these two solutions was obtained. Simultaneously, a large reduction of the degrees of freedom can be observed for the MsFEM solution. The number of degrees of freedom was reduced by 3 orders of magnitude introducing an additional approximation error of only about 6%. We also present the convergence of the method with the increasing approximation order at the macroresolution. Finally, we demonstrate the impact of the thermal effects on the displacements in the analyzed asphalt concrete sample.