A finite element approach for J₂ calculation in anisotropic materials

A numerical scheme, based on the concept of domain integral method, is developed for evaluation of J₂ in two-dimensional anisotropic linear elastic solids. The scheme is designed to be in conjunction with finite element solutions. Although the method is verified to be patch-independent, in a modified sense, the near tip region is always included in the calculation due to the nature of J₂. Special attention is addressed on appropriate modelling of the singular behavior around the crack tip area. The numerical examples show that J₂ can be calculated with good accuracy without using any particular singular elements. The order of singularity of the strain energy density jump along the crack surfaces in the near tip region is also properly estimated.