A piezoelectric-inhomogeneity system with imperfect interface

Abstract

This paper examines the electro-mechanical fields for a circular anisotropic piezoelectric fiber sensor inside an anisotropic piezoelectric or non-piezoelectric elastic matrix with imperfect interface under remote in-plane uniform tension. The interface imperfection is posed on the mechanical fields only. The present formulation admits different boundary value problems in a unified manner, so various fiber–matrix interface conditions are considered: (1) perfect bonding; (2) pure debonding; (3) in-plane pure sliding; (4) out-of-plane pure sliding; (5) full debonding; and (6) partial debonding. An interface condition is modeled by a specific layer of mechanical springs with vanishing thickness, namely k sd for normal debonding, k st for in-plane sliding, and k sv for out-of-plane sliding. Partial debonding is the one that allows to represent intermediate states between cases (1)–(5) above, for which the spring constants can take on any arbitrary values. An accurate three-dimensional approach in conjunction with an energy formulation based on linear theory of piezoelectricity is presented. The generalized displacement field is expressed in terms of series involving some appropriate amending functions. In the context of the present study the nature of the solution satisfies the necessary continuity in the electric potential across the fiber–matrix interface, while accounting for possible discontinuity in its derivative at the interface. This consideration accelerates the convergence rate significantly.