Numerical evaluation on the effective thermal conductivity of the composites with discontinuous inclusions: Periodic boundary condition and its numerical algorithm

Boundary condition plays an important role in prediction of the effective thermal conductivity of composites. In this research, the periodic boundary condition and the representative volume element (RVE) based finite element (FE) homogenization method are adopted to evaluate the effective thermal conductivities of the composites reinforced by the spherical, ellipsoidal and cylindrical inclusions, and the emphases are on the numerical implementation algorithm and validation of the periodic boundary condition. The heat flux continuity of the node pairs on the opposite surfaces of the RVEs of the composites is analyzed and the effective thermal conductivity of the composites are homogenized. The results show that the heat flux continuity of the node pairs on the opposite surfaces of the RVEs of the composites can be guaranteed by the proposed numerical implementation algorithm for the periodic boundary condition, and that the predicted effective thermal conductivities of the composites agree well with those determined by the Lewis-Nielsen model and the experimental tests. Therefore, the RVE based FE homogenization method with the periodic boundary condition can accurately evaluate the effective thermal conductivity of the composites with discontinuous inclusions.