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 analysis, the extended displacement (elastic displacement and electrical potential) and extended traction (elastic traction and electrical displacement) integral equations are collocated on the outside boundary (no-crack boundary) of the problem and on one side of the crack surface, respectively. The Green's functions for the anisotropic piezoelectric solids in an infinite plane, a half plane, and two joined dissimilar half-planes are also derived using the complex variable function method. The extrapolation of the extended relative crack displacement is employed to calculate the extended `stress intensity factors' (SIFs), i.e., KI, KII, KIII and KIV. For a finite crack in an infinite anisotropic piezoelectric solid, the extended SIFs obtained with the current numerical formulation were found to be very close to the exact solutions. For a central and inclined crack in a finite and anisotropic piezoelectric solid, we found that both the coupled and uncoupled (i.e., the piezoelectric coefficient eijk=0) cases predict very similar stress intensity factors KI and KII when a uniform tension ?yy is applied, and very similar electric displacement intensity factor KIV when a uniform electrical displacement Dy is applied. However, the relative crack displacement and electrical potential along the crack surface are quite different for the coupled and uncoupled cases. Furthermore, for a inclined crack within a finite domain, we found that while a uniform ?yy (=1Nm?2) induces only a very small electrical displacement intensity factor (in the unit of Cm?3/2), a uniform Dy (=1Cm?2) can produce very large stress intensity factors (in the unit of Nm?3/2).
fracture mechanics anisotropic piezoelectric solid boundary element method dual bem general green's functions