Modeling of cracks in 3D piezoelectric finite media by weakly singular SGBEM

This paper presents the first weakly singular, symmetric Galerkin boundary element method (SGBEM) that is capable of modeling cracks in three-dimensional, generally anisotropic, linear piezoelectric finite media. The proposed numerical procedure is a generalization of the work by Rungamornrat and Mear [15] to treat piezoelectric media and that by Rungamornrat and Mear [16] to allow the treatment of cracks in a finite domain. The symmetric formulation is obtained via the proper use of a pair of weak-form boundary integral equations: one for the generalized displacement (i.e. the displacement and the electric potential) and the other for the generalized traction (i.e. the traction and the surface electric charge). The distinct feature of this pair of integral equations is that they are completely regularized to contain only weakly singular kernels of O(1/r)O(1/r). This desirable property renders continuous basis functions to be employed in the construction of an approximate solution by Galerkin strategy. To further enhance the efficiency and accuracy of the current technique, the local field in the neighborhood of the crack front is approximated by special interpolation functions. This properly enriched approximate field can capture the exact local field up to sufficiently high order terms and, with the incorporation of extra degrees of freedom along the crack front, the stress and electric intensity factors can be accurately obtained with the use of relatively coarse meshes. The proposed technique was tested by performing numerical experiments for various crack problems and it was found that the technique is robust and promising. In particular, it yields highly accurate numerical solutions for the stress and electric intensity factors along the crack front with only weak dependence on the level of mesh refinement.