Application of the reciprocity principle for the determination of planar cracks in piezoelectric material

Piezoelectricity is a coupling between the electrical and the mechanical behaviour of certain materials, which is exploited in a wide range of transducer applications. By far most of the piezoelectric devices nowadays consist of ceramics, which are known as brittle material. Therefore, the detection of cracks in piezoelectric ceramics from external measurements in the sense of nondestructive testing is a task which is of high practical interest. This paper is a further extension of a method using the reciprocity principle, which has been introduced by Andrieux, Ben Abda et. al in the context of linear [2] isotropic electrostatics, and in the case of isotropic linear elasticity [1]. As preliminary work we use a first extension of the method concerning crack plane determination in anisotropic linear elasticity [14], especially including the case of transversal isotropy like in the elastic part of the piezoelectric material tensor. Our extension of [2] and [14] provides a method which is applicable for crack plane determination in piezoelectrics, using only data from the outer boundary. Also a 2D-implementation in an existing FEM-software has been carried out to test the method on some numerical examples.