Order and disorder in heterogeneous material microstructure: Electric and elastic characterisation of dispersions of pseudo-oriented spheroids

The paper deals with the electrical and elastic characterisation of dispersions of pseudo-oriented ellipsoids of rotation: it means that we are dealing with mixtures of inclusions of different eccentricities and arbitrary non-random orientational distributions. The analysis ranges from parallel spheroidal inclusions to completely random oriented inclusions. A unified theory covers all the orientational distributions between the random and the parallel ones. The electrical and micro-mechanical averaging inside the composite material is carried out by means of explicit results which allows us to obtain closed-form expressions for the macroscopic or equivalent dielectric constants or elastic moduli of the overall composite materials. In particular, this study allows us to affirm that the electrical behaviour of such a dispersion of pseudo-oriented particles is completely defined by one order parameter which depends on the given angular distribution. Moreover, the elastic characterisation of this heterogeneous material depends on two order parameters, which derive from the orientational distribution. The theory may be applied to characterise media with different shapes of the inclusions (i.e. spheres, cylinders or planar inhomogeneities) yielding a set of procedures describing several composite materials of great technological interest.