On singularities in composite piezoelectric wedges and junctions

Abstract

The plane problems of piezoelectric wedges and multi-material wedges/junctions involving piezoelectrics are studied in this paper. The study is focused on the singular behaviour of electroelastic fields at the corner of wedges and junctions. The polarization orientation of the piezoelectric medium may be arbitrary. The problem is formulated by extending Lekhnitskii’s complex potential functions. In the homogeneous piezoelectric cases of a half plane and a semi-infinite crack, it is shown that the singularity is invariant with respect to the direction of polarization and explicit solutions are derived for homogeneous boundary condition combinations. In general cases involving multi-material systems, the order of singularity is determined by solving a transcendental characteristic equation derived on the basis of boundary conditions and geometry. The accuracy of the numerical algorithm is verified by comparing with the existing results for pure elastic wedges. Numerical results of homogeneous piezoelectric wedges indicate that electric boundary conditions have a significant effect on the order of singularities. A selected set of practically useful wedges and junctions involving piezoelectrics are studied to examine the influence of wedge angle, polarization orientation, material types, and boundary and interface conditions on the order of singularity of electroelastic fields.