Multi-region Trefftz boundary element method for fracture analysis in plane piezoelectricity

This paper presents a multi-region Trefftz boundary element method for fracture analysis in plane piezoelectricity. To model the sub-region that contains the crack, a special set of Trefftz functions that satisfy the traction-free and charge-free conditions along the crack faces are constructed. To model the remaining sub-regions, the basic set of Trefftz functions co-derived previously by the authors are employed. With the two sets of Trefftz functions, the multi-region Trefftz boundary element method is formulated by point collocation. The special set of Trefftz functions exempts all the boundary treatment of the crack faces and enables the direct determination of the electromechanical intensity factors. Numerical examples are presented to illustrate the efficacy of the formulation.