Interfacial Cracks in Piezoelectric Bimaterials: an approach based on Weight Functions and Boundary Integral Equations

TL;DR

This paper develops a mathematical framework using weight functions and boundary integral equations to analyze interfacial cracks in piezoelectric bimaterials, accounting for electrical and mechanical loadings and different poling directions.

Contribution

It introduces a novel approach combining extended Stroh formalism and Riemann-Hilbert problems to derive weight functions for piezoelectric interface cracks, including electrical effects.

Findings

Derived general expressions for weight functions in piezoelectric bimaterials.

Formulated singular integral equations relating loads to displacement and traction fields.

Analyzed effects of different poling directions on crack behavior.

Abstract

The focus of this paper is on the analysis of a semi-infinite crack lying along a perfect interface in a piezoelectric bimaterial with arbitrary loading on the crack faces. Making use of the extended Stroh formalism for piezoelectric materials combined with Riemann-Hilbert formulation, general expressions are obtained for both symmetric and skew-symmetric weight functions associate with plane crack problems at the interface between dissimilar anisotropic piezoelectric media. The effect of the coupled electrical fields is incorporated in the derived original expressions for the weight function matrices. These matrices are used together with Betti's reciprocity identity in order to obtain singular integral equations relating the extended displacement and traction fields to the loading acting on the crack faces. In order to study the variation of the piezoelectric effect, two different poling directions are considered. Examples are shown for both poling directions with a number of mechanical and electrical loadings applied to the crack faces.