Computation of the Effective Conductivity of Fibrous Composites with Imperfect Thermal Contact by Combination of Asymptotic Homogenization, Domain Decomposition and Finite Elements Methods

Abstract

The methods of asymptotic homogenization, domain decomposition and finite elements are combined for the computation of the effective thermal conductivity of periodic biphasic fibrous composites with interfacial thermal resistance. The asymptotic homogenization method is used to obtain the so-called local problems on the periodic cell whose solution allows the calculation of the effective conductivity tensor. The numerical solution of the local problems requires a special treatment because of the temperature discontinuity on the interfaces due to the thermal barrier. In the present work these problems are decomposed into two, one for each phase, linked via a coupling condition. The finite element method, implemented in the software FreeFEM++, is employed to solve the resulting problems on each phase. FreeFEM++, which is based on the variational formulation of the problems, potentially allows to consider arbitrary shapes for both the fiber and the periodic cell cross sections. Numerical results for a square periodic cell with fibers of circular cross-section are presented and compared with results from other reported approaches.