The Jacobian derivative method for three‐dimensional fracture mechanics

SUMMARY This paper presents a new algorithm to compute the distribution of the strain energy release rate along the crack front for three-dimensional cracks (e.g surface cracks). The algorithm is economical and accurate. The algorithm is illustrated via two-dimensional and three-dimensional examples including a surface crack in a cylinder under internal 'pressure and sieJe-grooved compact-test specimens. It is shown, via specific examples, that only a single, self-similar virtual crack extension is necessary to accurately compute the strain-energy release-rate distribution along the crackfront. Two main areas have received attention in fracture mechanics analyses: (i) to model accurately the singular behaviour near the crack front; (ii) to compute the stress intensity factor from the solution to the finite-element model of the problem. The present study deals with the second problem, with emphasis on the use of isoparametric elements. The method presented here has its origins in the virtual crack extension method of Hellen 4 and the stiffness derivative method of Parks. 5 But in contrast to the VCEM, the Jacobian derivative method presented herein does not require an arbitrary choice of a 'virtual' 6xtension that in the VCEM becomes an 'actual' extension. We take advantage of the isoparametric formulation to compute the strain energy release rates directly from the displacement field. The Jacobian derivative method is a tr,ue post-processor algorithm. In thiS method the stress intensity factors are computed from an independently obtained displacement solution. Therefore, the displacement solution can be obtained with a program without any fracture mechanics capability, although adequate representation 'of the singular behaviour near the crack front is necessary. The displacement field may even be obtained by experimental techniques. Furthermore, the proposed technique does not require computation of stresses,