Plane strain dynamics of an incompressible nonlinear-elastic body

Nonlinear elasticity model in current state variables is used to study the plane strain dynamics of an incompressible body, and a system of nonlinear equations of displacement and pressure is obtained. In the absence of bulk forces and in the assumption of quadratic elastic potential, the resulting equations that describe plane waves, self-similar motions, and stress fields in these motions are solved and studied. It is shown that several solutions of a certain type are possible both in wave and self-similar cases.