Stability of deformation of isotropic hyperelastic bodies

The equations relating stress rates to strain rates are formulated and conditions of stable deformation of isotropic hyperelastic bodies are described. Stress–strain relations are presented for pure shear and uniaxial and axisymmetric loading of a material with a constitutive function obtained by generalization of the constitutive function of Hooke's law. In the case of small strains, the diagrams virtually coincide with the linear diagrams following from Hooke's law. Ramification of solutions and transition to declining diagrams begin at the same time, irrespective of values of the constants of the material, when large stresses of the order of the shear modulus are reached.