Anti-plane problems of piezoelectric material with a micro-void or micro-inclusion based on micromorphic electroelastic theory

The linear theory of micromorphic electroelasticity, which incorporate the coupled electromechanical behavior into the framework of micromorphic continuum theory, is used to solve the anti-plane problems of piezoelectric media with a micro-void or micro-inclusion in this paper. The electromechanical field solutions for a transversely isotropic piezoelectric medium are derived in the context of micromorphic electroelasticity and a generalized characteristic length is introduced to describe the size effect. Anti-plane problems of an infinite piezoelectric medium containing a micro-void or micro-inclusion are analyzed. Numerical results reveal that the mechanical and electric fields predicted by the present model highly depend on the relative size of the micro-void or micro-inclusion with respect to the generalized characteristic length, which is obviously different from the classical prediction.