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

摘要

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 n the outside boundary (no-crack boundary) of the problem and on one side of the crack surface, respectively. The Green's functions for the anisotropy zoelectric 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., K_I, K_II, K_III and K_IV. For a finite crack in an infinite anisotropy piezoelectric solid, the extended SIFs obtained with the current numeric formulation were found to be very close to the exact solutions. For a central and inclined crack in a finite and anisotropy piezoelectric solid, we found that both the coupled and uncoupled (i.e., the piezoelectric coefficient e_ijk=0) cases predict very similar stress intensity factors K_I and K_II when a uniform tension σ_yy is applied, and very similar electric displacement intensity factor K_IV when a uniform electrical displacement D_y is applied. However, the relative crack displacement and electrical potential along the crack surface are quite different for the coupled fna uncoupled cases. Furthermove, for a inclined crack within a finite domain, we found that wh