A weakly singular SGBEM for analysis of two-dimensional crack problems in multi-field media

A weakly singular symmetric Galerkin boundary element method (SGBEM) is developed for analysis of fractures in two-dimensional multi-field media. Specialization for the cases of anisotropic linear elasticity, piezoelectricity and magnetoelectroelasticity is considered. The basis for the method is a pair of weak-form integral equations for ‘generalized’ displacement and traction that involve only (at most) weakly singular kernels of order lnr. Standard CoCo elements are employed everywhere except at the crack tips. A special crack-tip element is developed to properly model the asymptotic behavior of the relative crack-face displacements. Extra degrees of freedom at the tip node are incorporated in the crack-tip element so that the ‘generalized’ stress intensity factors are directly obtained from the solution to the system of discretized equations. Various examples for cracks in both infinite and finite domains are examined. Highly accurate results are obtained with relatively coarse meshes.