The focus of this paper is to extend the variational asymptotic method for unit cell
homogenization (VAMUCH) to predict the effective thermal conductivity and local
temperature field distribution of heterogeneous materials. Starting from a variational
statement of the conduction problem of the heterogeneous continuum, we formulate
the micromechanics model as a constrained minimization problem using the
variational asymptotic method. To handle realistic microstructures in applications,
we implement this new model using the finite element method. For validation, a few
examples are used to demonstrate the application and accuracy of this theory
and companion code. Since heat conduction is mathematically analogous to
electrostatics, magnetostatics, and diffusion, the present model can also be used to
predict effective dielectric, magnetic, and diffusion properties of heterogeneous
materials.