New Approach to Modeling Failure In Rubber

Nonlinear theories of elasticity describe rubber deformation but not failure; however, in reality rubbers do fail. In the present work we review a new approach of energy limiters that allows for unifying hyperelasticity theories with failure descriptions and we discuss results of this unification. First, we introduce the energy limiter concept, which allows the enforcement of failure descriptions in elasticity theories. The limiter provides the saturation value for the strain energy, hence indicating the maximal energy which may be stored and dissipated by an infinitesimal material volume. The limiter is a material constant that can be calibrated via macroscopic experiments. Second, we illustrate the new approach with examples where failure initiation is predicted but its propagation is not tracked. Examples include the problems of the crack initiation; cavity instability; and rupture of inflating membranes. Also the traditional strength-of-materials criteria are reassessed. Third, the theory is used for 3D explicit finite element simulations of a high-velocity penetration of a stiff elastic body into a rubber plate. These simulations show that a high-velocity penetration of a flat projectile leads to a diffused non-local failure, which does not trigger the mesh sensitivity. To the contrary, a low-velocity penetration of a sharp projectile leads to a highly localized crack-like failure, which does trigger the mesh sensitivity. Calculation of the characteristic length of failure localization allows for setting the mesh size that provides regularization of the simulations. The fact that the calculation is based on results of solely macroscopic experiments is noteworthy.