Voronoi cell finite element method for heat conduction analysis of composite materials

Abstract In this paper, Voronoi cell finite element method (VCFEM) based on assumed flux hybrid formulation has been presented for heat conduction problem of particle reinforced composites material. The heat fluxes satisfying a priori internal thermal balance are directly approximated independently in the matrix and the inclusion respectively. The temperatures on element boundary and matrix-inclusion interface are interpolated by nodal temperature. The thermal balance on the interelement boundary and matrix-inclusion interface is relaxed and introduced into the functional by taking the temperature as Lagrange multiplier. In this way, a functional containing two variables of heat flux and temperature is proposed. Full field heat flux and effective thermal conductivity are obtained. Feasibility and effectiveness of the proposed approach are verified through several numerical examples.