In this paper, based on the stability criteria described by the B–E inequality, E-inequality and T–C inequality, the region of stability is evaluated for common compressible isotropic hyper-elastic models by using the deformation modes of simple shear and volumetric change. For models with three model constants, the region of stability will be that of deformation induced by the inequalities due to the normalization conditions. For the models with four constants, for example, the region of stability will be two-folded. For the case in which the free constant is given, the region of deformation will be restricted. For the case in which the limiting deformation is given, the region of the free constant will be restricted. The current work describes how the region of deformation and/or free constant is determined when a compressible hyper-elastic model is utilized in practical engineering.

在本文中，基于由B–E不等式，E不等式和T–C不等式描述的稳定性标准，通过使用简单剪切和体积变形模式来评估常见可压缩各向同性超弹性模型的稳定性区域更改。对于具有三个模型常数的模型，稳定性区域将是归一化条件导致的不等式引起的变形。例如，对于具有四个常数的模型，稳定性区域将是两倍的。对于给出自由常数的情况，变形区域将受到限制。对于给出极限变形的情况，自由常数的区域将受到限制。