Interface corners in piezoelectric materials

Through proper arrangement, the constitutive law, strain-displacement relation and equilibrium equation of piezoelectric materials can be written in the same mathematical form as those of elastic materials and hence Stroh formalism can be extended for piezoelectric analysis. Based on this viewpoint, the authors’ previous works for fracture analysis of anisotropic elastic materials, e.g. the eigen-relation for determining singular orders, the near-tip solutions, and the unified definition of stress intensity factors for interface corners, can also be applied to piezoelectric materials. In this paper, the theoretical framework of our previous works is briefly introduced, and then an efficient and accurate computing method (H-integral) and its required auxiliary solutions are derived for extracting the stress/electric intensity factors of interface corners made up of piezoelectric materials. This theoretical framework and H-integral form a universal solution technique that is valid for the fracture analysis of cracks, corners, interface cracks, and interface corners. Besides, the special cases that suggest how we simulate elastic insulators/conductors from piezoelectric materials are discussed. Several numerical examples are dealt with to display the feasibility and applicability of the proposed approaches, and finally, a numerical example which exhibits how the electric load influences the fracture behavior is also studied.