computational homogenization for the thermo-mechanical analysis of heterogeneous solids

This paper presents a two-scale thermo-mechanical analysis framework for heterogeneous solids based on a computational homogenization technique. The evolution of the mechanical and thermal fields at the macroscopic level is resolved through the incorporation of the microstructural response. Within the proposed multi-scale approach, the temperature dependent non-linear thermo-mechanical response is accounted by solving a boundary value problem at the micro-scale, the results of which are properly averaged and transferred to the macro level in a consistent way. The framework does not require explicitly determined homogenized material properties (e.g. macroscopic thermal expansion coefficients) since no constitutive equations are required for the macroscopic stresses and heat fluxes at the macro level. A nested finite element solution procedure with an operator-split implementation is outlined and the effectiveness of the approach is demonstrated by illustrative key examples.