Effect of Microgeometry on the Effective Dielectric Property of Anisotropic Composites

Composite Material is ubiquitous in both natural and engineered systems. Electromagnetic responses of these systems are determined by the effective properties of the composites, e.g. permittivity and conductivity. However, the relationship between such properties and composites' geometrical structure is largely unknown. For instance, the effective dielectric properties of isotropic or anisotropic composite materials are closely related to the inclusion shape, size, spatial orientation and the electrical properties of each component. By approximating the isotropicity of material, most models using scalars to quantify the dielectric property can hardly provide a meaningful insight when the material is highly anisotropic, e.g. natural formation contains fractures or engineered materials with directional properties. In this paper, the composite material containing ellipsoid inclusion is modeled and simulated by using a Finite-Element Method_(FEM) solver: COMSOL Multiphysics®. The constitutional relationship is taken as its original form with a full dielectric tensor and the effective values are determined by numerical experiments. To illustrate the influence of the micro-geometry, we tested different ellipsoid inclusions. The simulation shows that different ellipsoid inclusions result in vastly different dielectric tensor, although the inclusion volume of each case remains the same. Furthermore, it is shown that the principal components of dielectric permittivity tensor have a correlation with the projected area fraction of the inclusions in each corresponding direction, which provides a theoretical reference for the analysis of the electrical properties of anisotropic materials.