A hybrid complex-variable solution for piezoelectric/isotropic elastic interfacial cracks

In many practical applications, piezoelectric ceramics are bonded to non-piezoelectric and insulating isotropic elastic materials such as polymer. Since the conventional form of Stroh’s formulation, on which almost all of existing works on interfacial cracks in piezoelectric media have been based, breaks down or becomes complicated for isotropic elastic materials, many solutions available in the literature cannot be directly applied to interfacial cracks between a piezoelectric material and an isotropic elastic material. The present paper is devoted to a hybrid complex-variable method which combines the Stroh’s method of piezoelectric materials with the well-known Muskhelishvili’s method of isotropic elastic materials. This method is illustrated in detail for an insulating interfacial crack between a piezoelectric half-plane and an isotropic elastic half-plane, although interface cracks between piezoelectric and isotropic elastic conductor can be analyzed in a similar way. The solution obtained generally exhibits oscillatory singularity, in agreement with a previous known result based on the Stroh’s formulation. A simple explicit condition is obtained for the bimaterial constants under which the oscillatory singularity disappears. It is expected that the hybrid complex-variable method could more conveniently handle other possible complications (such as a hole or an inclusion) inside the isotropic elastic material, because it offers explicit solutions of a single complex variable rather than several different complex-variables associated with the Stroh’s formulation.