Maxwell homogenization scheme for piezoelectric composites with arbitrarily-oriented spheroidal inhomogeneities

In this work, the effective electro-elastic properties of piezoelectric composites are computed using the Maxwell homogenization method (MHM). The composites are made by several families of spheroidal inhomogeneities embedded in a homogeneous infinite medium (matrix). Each family of spheroidal inhomogeneities is made of the same material, and all the inhomogeneities have identical size and shape and are randomly oriented. The inhomogeneities and matrix materials exhibit piezoelectric transversely isotropic symmetry. It is shown that the shape of the "effective inclusion" substantially affects the effective piezoelectric properties. A new and simple form to calculate the aspect ratio of effective inclusion is presented. The effect on the overall piezoelectric properties due to the orientation of the inhomogeneities and different families of piezoelectric inhomogeneities is discussed. The MHM approach is applied in two examples, material with inhomogeneities having scatter orientation and composites with two different families of spheroidal inhomogeneities.