Numerical Modelling of Two-Phase Piezocomposites with Interface Mechanical Anisotropic Effects

Abstract

The present paper considers the homogenization problems for two-phase piezocomposite materials with random inclusions and with taking into account the mechanical imperfect interface boundaries. The accepted constitutive equations on the interface correspond to the Gurtin–Murdoch model for surface stresses and give a significant effect only for nanosized inclusions. To find the effective material properties, an integrated approach was used, based on the effective moduli method, on the modelling of representative volume element and on the finite element method. A set of boundary value problems was presented, which allow one to determine a complete collection of effective stiffness moduli, piezomoduli, and dielectric permittivities for a piezocomposite of arbitrary anisotropy class. The numerical realization was carried out in the ANSYS finite element package, which was used for representative volume modelling and for computation of the effective properties for piezocomposite material. The representative volume consisted of a regular mesh of cubic piezoelectric finite elements with the material properties of two phases. The interphase boundaries were covered with anisotropic elastic membrane elements that simulated surface stresses. As an example, the homogenization problem for one ceramomatrix piezocomposite with nanosized inclusions was solved numerically. It was noted that the interface stresses can essentially increase the effective stiffness moduli. However, the mechanical interface had a small influence on the effective piezomoduli and on the dielectric permittivities.