A unified representation of plane solutions for anisotropic piezoelectric elasticity

This paper investigates the generalized two-dimensional deformation of an anisotropic piezoelectric solid. A unified piezoelectric formalism for a general representation of elastic and electric fields in the anisotropic piezoelectric material is developed based on a transformed function method. This unified piezoelectric formalism is valid for degenerate anisotropic piezoelectric materials with multiple roots as well as for anisotropic piezoelectric materials with distinct roots. Closed-form solutions of elastic and electric fields for degenerate anisotropic piezoelectric materials are obtained by taking the limits in the piezoelectric formalism. Special attention is paid to a piezoelectric material with a plane of material property symmetry. Decoupled in-plane and anti-plane fields for this material are explicitly expressed. The usefulness of the unified piezoelectric formalism is discussed for the interface crack problem.