Variational principles and size-dependent bounds for piezoelectric inhomogeneous materials with piezoelectric spring–layer imperfect interfaces

Abstract

The piezoelectric spring–layer interface model is widely used in describing some imperfect interfaces frequently involved in piezoelectric inhomogeneous materials. Typically, it is appropriate for modeling a thin, soft and low conducting interface between two bulk phases. This model stipulates that, across an interface, the displacement and electric potential are discontinuous while the traction and normal electric displacement are continuous and proportional to the displacement and electric potential jumps, respectively. In this work, the classical minimum potential principles of linear piezoelectricity are extended to piezoelectric inhomogeneous materials with piezoelectric spring–layer imperfect interfaces, and to investigating the interface effects on their effective properties. By choosing simple admissible displacement–electric displacement and stress–electric potential coupling fields, the extended Voigt and Reuss bounds can explicitly be derived for the corresponding effective properties of a transversely isotropic fiber reinforced composite which is subjected to remotely uniform in-plane electric loading and anti-plane mechanical loading. Numerical results are provided to illustrate the size-dependent features of the obtained Voigt and Reuss bounds.