FE calculation of contour integrals in plane anisotropic elastic media with crack surface tractions

The application of the J_k, M, and L integrals is extended for fracture analysis with consideration of crack surface tractions. The study is considered to be feasible for problems with generally linearly anisotropic elastic materials. With the presence of crack surface tractions in anisotropic fields, the concept of path independence of these contour integrals needs to be modified by additionally including extra domain and line integrals, where the near-tip region is inevitably included in their evaluations. A numerical procedure, based on the finite element solutions, is therefore presented for calculation of these integrals, with special attention addressed to modeling of the portion of integration around the near-tip area, where singular mechanical behavior dominates. No particular singular elements are used in the study.