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Microscopic voids can irreversibly grow into the macroscopic ones under hydrostatic tension. To explain this phenomenon, it was suggested in the literature to use the asymptotic value of the hydrostatic tension in the plateau yieldlike region on the stress–stretch curve obtained for the neo-Hookean model. Such an explanation has two limitations: (a) it relies on analysis of only one material model and (b) the hyperelasticity theory is used for the explanation of the failure phenomenon. In view of the mentioned limitations, the objective of the present note is twofold. First, we simulate the cavity expansion in rubber by using various experimentally calibrated hyperelastic models in order to check whether the stress–stretch curves have the plateau yieldlike regions independently of the constitutive law. Second, we repeat simulations via these same models enhanced with a failure description. We find (and that was not reported in the literature) that the process of cavity expansion simulated via hyperelastic constitutive models exhibiting stiffening, due to unfolding of long molecules, is completely stable and there are no plateau yieldlike regions on the stress–stretch curves associated with cavitation. In addition, we find that the instability in the form of yielding observed in experiments does appear in all simulations when the constitutive laws incorporate failure description with energy limiters.

Phase-field or gradient-damage approaches offer elegant ways to model cracks. Material stiffness decreases in the cracked region with the evolution of the phase-field or damage variable. This variable and, consequently, the decreased stiffness are spatially diffused, which essentially means the loss of the internal links and the bearing capacity of the material in a finite region. Considering the loss of material stiffness without the loss of inertial mass seems to be an incomplete idea when dynamic fracture is considered. Loss of the inertial mass in the damaged material region may have significant effect on the dynamic failure processes. In the present work, dynamic fracture is analyzed using a theory, which takes into account the local loss of both material stiffness and inertia. Numerical formulation for brittle fracture at large deformations is based on the Cosserat point method, which allows suppressing the hourglass type deformation modes in simulations. Based on the developed algorithms, the effect of the material inertia around a crack tip is studied. Two different problems with single and multiple cracks are considered. Results suggest that in dynamic fracture the localized loss of mass plays an important role at the crack tip. It is found, particularly, that the loss of inertia leads to lower stresses at the crack tip and, because of that, to narrower cracks as compared to the case in which no inertia loss is considered. It is also found that the regularized problem formulation provides global convergence in energy under the mesh refinement. At the same time, the local crack pattern might still depend on the geometry of the unstructured mesh.