Fracture Analysis of Piezoelectric Materials by Boundary and Trefftz Finite Element Methods

This paper contains two main parts. First, applications of Trefftz finite element methods to mode III fracture problems are presented in this paper. Trial functions for electoelastic fields are presented for both regular element and cracked element. These functions are used in deriving Trefftz finite element formulation together with modified variational principle. The performance of the proposed element model is assessed by an example and comparison is made with those obtained by conventional finite element model or by other approaches. Second, boundary element formulation for analyzing fracture behaviour of thermopiezoelectric materials is presented. Based on the Green’s function of piezoelectric materials with various defects and total potential variational principle, a boundary element model for thermopiezoelectric solid with multiple cracks has been developed and can be used to calculate the stress intensity factors of the multiple crack problem.