A Computational Homogenization Method for Modeling the Kapitza Thermal Resistance in Heterogeneous Materials

In this paper, a multi-scale method is presented for homogenization of heterogeneous solid conductivity. Principle of the two scale computational homogenization is applied successfully in heat conduction problem. The technique is presented by employing the interfacial effect of constituent material, i.e. the Kapitza thermal resistance, in the framework of extended finite element method (XFEM) in order to capture a realistic response of materials. A heterogeneous domain is first generated with arbitrary inclusion shapes. The homogenized conduction tensor is then extracted for the variational formulation of micro-scale governing equation by using a Robin constraint type for material interfaces. The versatility of the homogenized conduction tensor is finally examined in a transient problem by comparing the temperature distribution between the multi-scale model and the direct numerical simulation (DNS).