Electroelastic properties of cracked piezoelectric materials under longitudinal shear

Analytical solutions are obtained to quantify the influence of cracks on electroelastic properties of piezoelectric materials containing doubly-periodic arrays of cracks. Both the rectangular and diamond-shaped arrays of cracks are considered. Solutions are obtained for the case of an antiplane shear load coupled with an in-plane electrical load. This study makes it possible to understand the multicrack interactions in piezoelectric solids and their effects on the fracture and electroelastic properties. The crack tip field intensity factors and the change in stored electroelastic energy due to the presence of many microcracks are calculated. These calculations enable the prediction of the effective elastic, piezoelectric and dielectric constants of a damaged piezoelectric material. The results of this work can be useful in developing a technique to determine the state of mechanical and electrical damage in piezoelectric materials.