Abstract
This review paper deals with the dielectric and elastic characterization of composite materials constituted by dispersions of nonlinear inclusions embedded in a linear matrix. The dielectric theory deals with pseudo-oriented particles shaped as ellipsoids of revolution: it means that we are dealing with mixtures of inclusions of arbitrary aspect ratio and arbitrary non-random orientational distributions. The analysis ranges from parallel spheroidal inclusions to completely random oriented inclusions. Each ellipsoidal inclusion is made of an isotropic dielectric material described by means of the so-called Kerr nonlinear relation. On the other hand, the nonlinear elastic characterization takes into consideration a dispersion of nonlinear (spherical or cylindrical) inhomogeneities. Both phases are considered isotropic (actually it means polycrystalline or amorphous solids). Under the simplifying hypotheses of small deformation for the material body and of small volume fraction of the embedded phase, we describe a theory for obtaining the linear and nonlinear elastic properties (bulk and shear moduli and Landau coefficients) of the overall material.
Highlights
The central problem of considerable technological importance is to evaluate the effective physical properties governing the behavior of a composite material on the macroscopic scale, taking into account the actual microscale material features [1, 2]
The most important properties are the classical Hashin-Shtrikman variational bounds [3, 4], which provide an upper and lower bound for composite materials properties, and the expansions of Brown [5] and Torquato [6, 7] which take into account the spatial correlation function of the constituents
The nonlinear elastic characterization takes into consideration a dispersion of nonlinear inhomogeneities
Summary
The central problem of considerable technological importance is to evaluate the effective physical properties (dielectric or elastic) governing the behavior of a composite material on the macroscopic scale, taking into account the actual microscale material features [1, 2]. It is well known that it does not exist a universal mixing formula giving the effective properties of the heterogeneous materials (permittivity or elastic moduli) as some sort of average of the properties of the constituents. The primary aim in the study of materials is to understand and classify the relationship between the internal micro-structure and the physical properties. Such a relationship may be used for designing and improving materials or, for interpreting experimental data in terms of micro-structural features. In [8], a functional unifying approach has been applied to better understand the intrinsic mathematical properties of a general mixing formula
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