Basic relationships for nonlinear elastic systems with regard for interaction of deformation process and translational motion (Q2771583)

A methodology of derivation of basic relationships for potential description of nonlinear elastic solids is suggested. Neglecting effects of elastic displacement of mass-center with respect to geometric center of small subsystems (principle of substantionality) and under isothermic conditions, the basic relationship is represented by the differential 1-form. Different approximations of the Hamilton function are considered. In the isotropic case the Hamiltonian can be represented as a function of scalar invariants of state parameters. In a more general nonlinear case, it is represented by a third-order polynomial of scalar invariants. Derived governing equations can be used for study of parameters of resonance and self-organization phenomena in physically nonlinear elastic solids.