ABSTRACT
Determination of temperature distribution in a heterogeneous material is important for a variety of coupled thermo-mechanical problems. Temperature fields are especially critical near the matrix-inclusion interface regions where high gradients are expected due to thermal property mismatch. In this chapter, the Voronoi cell finite element method (VCFEM) is developed for solving steady state heat conduction problems in homogeneous and heterogeneous materials. An assumed heat flux hybrid formulation is developed in this chapter for steady state heat conduction problems. The method has been developed in [277, 147], based on the assumed stress hybrid finite element method in [320, 321]. The effect of the second phase within each Voronoi cell element is accounted for by an eigen-temperature gradient method for heat conduction. The eigen-temperature gradient method [184, 409] follows the eigen-strain methods that have been developed in [282, 292] for treating heterogeneous solids. Numerical experiments are conducted and results are compared with those by conventional FEM and analytical solutions to validate the VCFEM model.
