Numerical evaluation of J₂-integral for rubbery materials under dynamic loads with finite element method

The J₂-integral for rubbery material problems with a stationary crack under dynamic large deformation is calculated with finite element solutions. General 2-D problems, including plane stress, plane strain, and axisymmetric cases, are considered in the formulation. The numerical procedure is verified to be path-independent in a generalized sense, and the near-tip region is hence always included in the calculation. A numerical treatment for simulation of the integration around the near-tip area is therefore proposed. It is demonstrated numerically that, with this treatment, the calculation is very insensitive to the crack tip finite element grid. In fact, no detailed information on the complicated asymptotic dynamic singular behavior for rubbery materials is required in the calculation.