Dynamics of deformation of an elastic medium with initial stresses

The constitutive equations of motion of an elastic medium with given initial stresses are formulated in the form of a hyperbolic system of differential equations of the first order. Equations describing the propagation of small perturbations in a prestressed isotropic medium with an arbitrary energy dependence of the elastic deformation in the strain tensor are derived, and equations for the quadratic dependence of elastic strain energy on the strain tensor are given.