Extended Gent models for residually stressed thick spheres and cylinders

摘要

We develop some Gent-like limited extensible models for initial stress symmetry. The proposed models exhibit sharp strain-stiffening characteristics when the stiffening parameter approaches the maximum allowable limit. When this maximum allowable limit tends to infinity, these models reduce to some other existing models for initial stress. We perform a micro-mechanical investigation which agree with the proposed constitutive behaviour. This investigation also affirms that the residual stress influences the limited elastic behaviour as exhibited by the proposed models. We apply the proposed extended Gent models and the extended Mooney-Rivlin model to investigate the inflation and instability characteristics of residually stressed thick spheres and cylinders. The influence of residual stress on the stability characteristics is examined. We observe that the stationary inflection point is obtained for a single value of residual stress, in the inflation characteristics for extended Mooney-Rivlin spheres. On the other hand, in the inflation characteristics of extended Gent spheres, stationary inflection points are obtained for two residual stress limits. These residually stressed spheres exhibit stable inflation characteristics when residual stress is beyond the limits of stationary inflection points. Within these limits, however, the inflation characteristics show inflation-jump instability. Limit point instability is also exhibited by some of the proposed models in absence of residual stress. We next study the inflation of residually stressed thick cylinders for both constrained and unconstrained axial stretch. The thick cylinder inflation characteristics with unconstrained axial stretch show both stability and inflation-jump instability based on the magnitude of residual stress.