On the Constitutive Relation of Isotropic Hyperelastic Materials in Terms of the Hencky Strain

The constitutive relation of isotropic hyperelastic materials is studied in terms of the Hencky strain. Firstly, the theory for establishing the constitutive relation of hyperelastic materials is briefed from the viewpoint of the Hencky strain, and a set of new strain invariants with an extra factor is proposed and their characteristics are then thoroughly analyzed. Next, experimental data from three essential deformation modes are divided into three deformation regimes, namely, small to moderate regime, large regime, and extra large regime. The strain energy function is accordingly individually constructed for each regime together with the parameter identification. The predictions to Treloar's data are made as compared with three other widely used models. The results show that the present model is overall more accurate than the others. Particularly, the present model can be reduced via the truncation analysis. The results indicate that, within the limited strain ranges, the reduced models with fewer parameters are robust and more accurate as well.