Isogeometric boundary element method for calculating effective property of steady state thermal conduction in 2D heterogeneities with a homogeneous interphase

Based on the generalized self-consistent scheme (GSCS), the isogeometric boundary element method (IGABEM) is used to calculate the effective thermal conductivity of two dimensional (2D) steady state heat conduction heterogeneities with a homogeneous interphase. The heat energy formulation and the boundary integral equations adopted in this paper only contain the temperatures from the inclusion–interphase and interphase–matrix interfaces, respectively, so that the effective thermal conductivity from the generalized self-consistent model with a homogeneous interphase can be conveniently calculated. In numerical implementation, the Non-Uniform Rational B-Splines (NURBS) are employed not only to construct the exact interface shapes but also to approximate the interface temperatures. The results show that the conductivity and the thickness of the homogeneous interphase have great influence on the effective thermal conductivity. Higher interphase thermal conductivity enhances the effective thermal conductivity, whereas thinner thickness of the interphase results in the reduction of the effective thermal conductivity. Numerical examples show that the proposed method works well compared with the conventional quadratic isoparametric boundary element method.