Nonzero depolarization volumes in electromagnetic homogenization studies
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The work of this thesis concerns depolarization regions in the homogenization of random, particulate composites. In conventional approaches to homogenization, the depolarization dyadics which represent the component phase particles are provided by the singularity of the corresponding dyadic Green function. Thereby, the component particles are effectively treated as vanishingly small, point-like entities. However, through neglecting the spatial extent of the depolarization region, important information may be lost, particularly relating to coherent scattering losses. In this thesis, depolarization regions of nonzero volume are considered. In order to estimate the constitutive parameters of homogenized composite materials (HCMs), the strong-property-fluctuation theory (SPFT) is implemented. This is done through a standard procedure involving the calculation of successive corrections to a preliminary ansatz, in terms of statistical cumulants of the spatial distribution of the component phase particles. The influence of depolarization regions of nonzero volume on the zeroth (and first), second and third order SPFT estimates of HCM constitutive parameters is investigated. Both linear and weakly nonlinear HCMs are considered.