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.

A Comprehensive Evaluation of the Predictive Capabilities of Several Advanced Micromechanics Approaches

“…[1,[14][15][16][17] developed the variational asymptotic method for unit cell homogenization (VAMUCH), a general-purpose micromechanics approach, to handle the problems of heterogeneous materials. In fact, VAMUCH is not only capable of predicting the effective material properties and recovering the local fields but also has several unique features compared with other numerical methods.…”

Variational asymptotic homogenization of temperature-dependent heterogeneous materials under finite temperature changes

“…For a micromechanics model to be useful for practical material systems, it must be versatile enough to handle realistic microstructures as it could introduce unacceptable errors by approximating realistic complex microstructures using highly idealized mathematical models on which traditional micromechanics approaches are based. To this end, a general-purpose micromechanics modeling framework, VAMUCH (Variational Asymptotic Method for Unit Cell Homogenization), is developed for handling composites with arbitrary periodic microstructures (Yu and Tang, 2007b,a;Tang and Yu, 2007). As long as a unit cell (aka the building block) of the material can be identified and represented by a finite element mesh, VAMUCH can be used to predict not only the effective properties but also the local fields of the heterogeneous materials.…”

Micromechanics Modeling of High Temperature Materials with Temperature-dependent Constituents

“…To this end, a general-purpose micromechanics modeling framework, VAMUCH (Variational Asymptotic Method for Unit Cell Homogenization), is developed for handling composites with arbitrary microstructures. 5,8,9 As long as a unit cell (aka the building block) of the material can be identified and represented by a finite element mesh, VAMUCH can be used to predict not only the effective properties but also the local fields of the heterogeneous materials. A detailed explanation of the uniqueness of VAMUCH can be found in Ref.…”