Construction of Models for Elastic Media with the Restricted Normal Components of the Stress Vector

Аннотация

It is shown that the medium exhibiting the property of boundedness for normal stresses is hyperelastic, and the constitutive equation of the medium model is a nonlinear relation between the Piola–Kirchhoff and Green–Saint–Venant tensors. For an isotropic medium, it is shown that the stress and strain tensors are coaxial, and a representation of the relation between the stress and strain tensors in the form of elementary functions of a tensor argument is obtained. A geometric proof of the uniqueness of the obtained representation is given.