Comparative analysis of the two-constant generalizations of Hooke's law for isotropic elastic materials at finite strains

For ten models of the isothermal behavior of materials, the solutions of boundary-value problems are studied for five types of the experimentally reproducible uniform stress–strain state with unchanged directions of the principal axes. It is found that, for three models, the governing equations are similar to the relations of Hooke's law and valid within the same range of the ratio between the shear and bulk moduli. In these models, the specific strain energy can be represented as a sum of the energies due to changes in volume and shape. The ranges where the other three known models exhibit incorrect behavior are determined.