Plane crack propagation in a hyperelastic incompressible material

We propose a crack propagation criterion for hyperelastic materials (rubber type material) within the framework of plane elasticity in finite deformation. The criterion is based on the examination of the asymptotic elastic field near the crack tip prior to propagation. According to this criterion, the propagation will take place for a critical value of the strain energy density intensity factor. The kink angle, obtained by applying the criterion of maximum opening stress, will depend on the fracture tensile stress of the actual material. We propose to use a local iterative finite element method to compute the asymptotic quantities involved in the criterion at a reasonable cost. Examples of computation for some hyperelastic laws simulating the behavior of vulcanized rubber are presented.