Abstract :
A weakly singular, symmetric Galerkin boundary element method (SGBEM)
is established to compute stress and electric intensity factors for isolated cracks in threedimensional,
generally anisotropic, piezoelectric media. The method is based upon a weakform
integral equation, for the surface traction and the surface electric charge, which is
established by means of a systematic regularization procedure; the integral equation is in a
symmetric form and is completely regularized in the sense that its integrand contains only
weakly singular kernels ofO(1/r ) (hence allowing continuous interpolations to be employed
in the numerical approximation). The weakly singular kernelswhich appear in theweak-form
integral equation are expressed explicitly, for general anisotropy, in terms of a line integral
over a unit circle. In the numerical implementation, a special crack-tip element is adopted to
discretize the region near the crack front while the remainder of the crack surface is discretized
by standard continuous elements. The special crack-tip element allows the relative crack-face
displacement and electric potential in the vicinity of the crack front to be captured to high
accuracy (even with relatively large elements), and it has the important feature that the mixedmode
intensity factors can be directly and independently extracted from the crack front nodal
data. To enhance the computational efficiency of the method, special integration quadratures
are adopted to treat both singular and nearly singular integrals, and an interpolation strategy is
developed to approximate theweakly singular kernels. As demonstrated by various numerical
examples for both planar and non-planar fractures, the method gives rise to highly accurate
intensity factors with only a weak dependence on mesh refinement
