Statistical evaluation of electric field distributions in 3D composites with a random spatial distribution of dielectric inclusions

Abstract

Electromagnetic applications of composites often impose constraints on the internal electric fields, such as an upper limit on the field strength to prevent local heating or dielectric breakthrough. However, owing to heterogeneity, the local fields in a composite differ from those in a homogeneous material. Moreover, they are accessible neither by experiment nor by effective medium theories, at least for arbitrary microstructures. In this work, we use numerical simulations to evaluate the electric field distribution and the effective permittivity for 3D systems of monodisperse impenetrable spheres dispersed in a continuous matrix phase. We restrict ourselves to loss-free dielectric materials and to a random spatial distribution of particles. Samples are placed in a parallel plate waveguide and exposed to a transverse electromagnetic wave. The local field amplitudes are calculated via the finite element method and are normalized to those of a homogeneous sample exhibiting the same effective permittivity and geometry. We analyze the distribution of the local electric field strength in both constituents, namely, particles and matrix. Thus, we evaluate mean values and standard deviations as well as the field strengths characterizing the highest and lowest percentiles. Increasing particle concentration or permittivity enhances heterogeneity, and so the local electric field strength in some domains can become much higher than its average value. The methods we apply here can also be used in further investigations of more complex systems, including lossy materials and agglomerating particles.