A BEM analysis of fracture mechanics in 2D anisotropic piezoelectric solids

This paper presents a single-domain boundary element method (BEM) analysis of fracture mechanics in 2D anisotropic piezoelectric solids. In this analy sis, the extended displacement (elastic displacement and electrical potenti al) and extended traction (elastic traction and electrical displacement) in tegral equations are collocated on the outside boundary (no-crack boundary) of the problem and on one side of the crack surface, respectively. The Gre en's functions for the anisotropic piezoelectric solids in an infinite plan e, a half plane, and two joined dissimilar half-planes are also derived usi ng the complex variable function method. The extrapolation of the extended relative crack displacement is employed to calculate the extended 'stress i ntensity factors' (SIFs), i.e., K-I, K-II, K-III and K-IV. For a finite cra ck in an infinite anisotropic piezoelectric solid, the extended SIFs obtain ed with the current numerical formulation were found to be very close to th e exact solutions. For a central and inclined crack in a finite and anisotr opic piezoelectric solid, we found that both the coupled and uncoupled (i.e ., the piezoelectric coefficient e(ijk) = 0) cases predict very similar str ess intensity factors K-I and K-II when a uniform tension sigma(yy) is appl ied, and very similar electric displacement intensity factor K-IV when a un iform electrical displacement D-y is applied. However, the relative crack d isplacement and electrical potential along the crack surface are quite diff erent for the coupled and uncoupled cases. Furthermore, for a inclined crac k within a finite domain, we found that while a uniform sigma(yy) (=1N m(-2 )) induces only a very small electrical displacement intensity factor tin t he unit of Cm-3/2), a uniform D-y (=1 C m(-2)) can produce very large stres s intensity factors tin the unit of Nm(-3/2)). (C) 1998 Elsevier Science Lt d. All rights reserved.