Inflation and rupture of rubber membrane

Inflation and rupture of a circular rubber membrane is modeled in the present work. It is the first time when a failure description is incorporated in the stress analysis of the rubber membrane. The failure description is enforced by the concept of the energy limiter that provides the saturation value for the strain energy indicating the maximal energy which may be dissipated by an infinitesimal material volume. The energy limiter is a material constant that can be calibrated via macroscopic experiments. Particularly, two constitutive theories for Natural and Styrene-Butadiene Rubbers enhanced with the energy limiters calibrated in experiments are used for modeling the membrane inflation and failure. It is found based on the finite element simulations and in a good correspondence with the experimental data that rupture occurs in the center of the membrane when the stretches reach the critical magnitude of ~ 5. It is interesting also that the stresses at the point of rupture are essentially smaller than the rubber strength-the critical stress in the uniaxial tension tests. The latter notion questions the applicability of the concept of the material strength defined in uniaxial tests to the multiaxial strain-stress states.