Loss of ellipticity in elasticity with energy limiters

This work addresses two practically interesting calculations concerning the onset of material instability via the loss of ellipticity. First, we consider simple shear of natural rubber. We find the direction of failure localization, which is in perfect qualitative correspondence with fracture observations in rubber bearings after earthquakes. Interestingly, the direction of failure localization is different from the one predicted by the criterion of maximum tension stress or stretch. Second, we consider equibiaxial tension of a sheet of aneurysm material. We find that the isotropic aneurysm material exhibits infinitely many possible directions of failure localization in equibiaxial tension. The latter means that the random direction of cracks in equibiaxial tension experiment, e.g. membrane inflation, can be an indicator of material isotropy. Accordingly, a preferable direction of the crack alignment can be interpreted as an indicator of the aneurysm anisotropy.