Calculation of J₂-integral for 2-D cracks in rubbery materials

A numerical scheme, incorporated with the finite element method, is developed for calculation of the J₂-integral for 2-D cracks appearing in rubbery fields under large deformation. The scheme is formulated based on the concept of the generalized version of the domain integral method. Due to the nature of J₂ the method is shown to be "patch-independent" in a modified sense, and so the neartip region is always included in the calculation. The proposed technique is therefore particularly addressed to appropriate modeling of the near-tip singular mechanical behavior in order to circumvent the unavoidable imprecision aisociated with the finite element approximations in the vicinity of the crack tip. The numerical results show that no a priori information on the asymptotic singular behavior is required in order to achieve an acceptable value of J₂. The computation procedure is generally feasible for different rubbery material models.