Material stability consideration for common compressible isotropic hyper-elastic models

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.