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.

我们为初始应力对称开发了一些类似 Gent 的有限可扩展模型。当硬化参数接近最大允许极限时，所提出的模型表现出明显的应变硬化特性。当该最大允许极限趋于无穷大时，这些模型将简化为其他一些现有的初始应力模型。我们进行了一项与提议的本构行为一致的微观机械调查。该研究还证实，残余应力会影响所提出模型所展示的有限弹性行为。我们应用所提出的扩展 Gent 模型和扩展的 Mooney-Rivlin 模型来研究残余应力厚球体和圆柱体的膨胀和不稳定性特征。检查残余应力对稳定性特性的影响。我们观察到，在扩展的 Mooney-Rivlin 球体的膨胀特性中，固定拐点是针对单个残余应力值获得的。另一方面，在扩展 Gent 球体的膨胀特性中，对于两个残余应力极限获得了固定拐点。当残余应力超过固定拐点的极限时，这些残余应力球体表现出稳定的膨胀特性。然而，在这些限制内，膨胀特性显示膨胀跳跃不稳定。在没有残余应力的情况下，一些提议的模型也表现出极限点不稳定性。我们接下来研究受约束和不受约束的轴向拉伸的残余应力厚圆柱的膨胀。