A new analytical generalization of the J and G-theta integrals for planar cracks in a three-dimensional medium

This paper focuses on the theoretical and numerical development of the J-integral concept for three-dimensional problems. A new integral parameter, developed for the real three-dimensional case, computes the combined energy release rate for an arbitrary crack front. A path-independent integral is verified in both the static and crack propagation cases. Generalization of the J3D-integral toward its Gθ3D implementation form is performed. The efficiency of this proposed integral is then compared with a number of J integrals available in the literature. Lastly, the paper offers a finite element implementation along with its numerical validation.