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

Abstract

homogenization scheme for piezoelectric composites with arbitrarily-oriented spheroidal inhomogeneities.Abstract 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.

Effective Medium Theory for the Elastic Properties of Composite Materials with Various Percolation Thresholds

“…[1,2,15,16]) describes the behavior of the effective coefficients with the accuracy of the first power of concentration p. The Maxwell's approach can also be generalized to other physical properties, e.g. the piezoelectricity [24].…”

“…where c p is the preselected percolation threshold, while c p is the percolation threshold resulting from the EMT (24). It is easily seen that the solution of Equation ( 26) with respect to Taking into account (25), we find that at the percolation threshold (which we now defined ourselves)…”

“…where c p is the preselected percolation threshold, while c p is the percolation threshold resulting from the EMT (24). It is easily seen that the solution of Equation (26) with respect to c p is cc pp …”

“…Then, the multipliers in the large round brackets in (24) are equal to 1 and we obtain from (24), taking into account the expression for c ( , ) s p p (23),…”

A Mori–Tanaka Based Micromechanical Model for Predicting the Effective Electroelastic Properties of Orthotropic Piezoelectric Composites with Spherical Inclusions

“…Dunn and Taya [26], Huang et al [27,28], and Mikata [29,30] have extended Deeg's formulation to incorporate the results for transversely isotropic and orthotropic matrix with inclusion types such as elliptic, rod-shaped, penny-shaped, ribbonshaped and spheroid. Maxwell homogenization scheme has also been applied to find the effective electroelastic properties of piezoelectric composites with transversely isotropic matrix and reinforcement, with unidirectionally aligned spheroidal particles [31] and with randomly aligned spheroidal particles [32]. In addition, Odegard [2] and Kar-Gupta et al [33] have performed finite element analyses to evaluate the effective properties of orthotropic-matrix piezoelectric composites.…”