On the estimation of the electromagnetic, elastodynamic and piezoelectric properties of homogenized composite materials
The work in this thesis concerns the estimation of the electromagnetic, elastodynamic and piezoelectric properties of homogenized composite materials (HCMs). A composite may be considered homogeneous if wavelengths are suficiently large in comparison to the size of the particles of each component material. This thesis examines HCMs constructed from two component materials and several methods of estimating the HCMs constitutive properties. Firstly, the Maxwell Garnett estimates and Bergman-Milton bounds on the electromagnetic properties of HCMs are examined. While both are widely used, we re-examine them, for isotropic dielectric HCMs, in light of recent advancements in material manufacture. Secondly, we examine the strong-property-fluctuation theory (SPFT). The SPFT estimate is calculated using iterations upon an initial ansatz, these iterations being dependent on statistical cumulants of the spatial distribution of the particles of the component materials. The zeroth-order SPFT estimate is identical to the first-order and both are taken to be identical to a comparison material. For the second-order estimate a two-point correlation function along with its associated correlation length are used to characterize the component materials' particle distribution. The general framework for the elastodynamic SPFT was established in 1999 by Zhuck and Lakhtakia. Here we further develop the elastodynamic SPFT for orthotropic HCMs, in order to undertake numerical studies. We simplify certain integrals in order to make them amenable to numerical computation. Also, we establish the piezoelectric SPFT for orthorhombic mm2 materials. The general theory is developed first in a manner analogous to the elastodynamic SPFT. We then implement a two-point covariance function, perform similar integral simplifications to those done in the elastodynamic SPFT and carry out numerical experiments. From the numerical studies it is clear that, for both the elastodynamic and piezoelectric HCMs, the lowest-order SPFT estimate is similar to that provided by the corresponding Mori-Tanaka formalism. It is also apparent that the second-order SPFT estimate provides a significant correction to the lowest-order estimate, which reflects dissipative losses due to scattering.