A variational asymptotic micromechanics model for predicting conductivities of composite materials

Abstract

The focus of this paper is to extend the variational asymptotic method for unit cell homogenization (VA-MUCH) 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.