Micromechanics-based homogenization of the effective physical properties of reinforced composites

Abstract

Micromechanics-based homogenization has been employed extensively to predict the effective properties of technologically important composites. In this dissertation, I address its application to various physical phenomena, including elasticity, thermal and electrical conduction, electric, and magnetic polarization, as well as multi-physics phenomena governed by coupled equations such as piezoelectricity and thermoelectricity. I begin with a brief review of the concept of the Eshelby tensor with regard to the elasticity and mean-field homogenization of the effective stiffness tensor of a composite with a perfect interface between the matrix and inhomogeneities. I then discuss the extension of the theory in two aspects. First, I discuss the mathematical analogy among steady-state equations describing the aforementioned physical phenomena and explain how the Eshelby tensor can be used to obtain various effective properties. Afterwards, I describe how the anisotropy of the matrix and interfacial imperfections, which exist in actual composites, can be accounted for and derive more correct formulas than previous results, which can be applicable for more general case. In the last section, I provide a summary and outlook considering future challenges.