DYNAMIC CAVITATION WITH SHOCKS IN NONLINEAR ELASTICITY

The hyperbolic system of conservation laws that govern the motion of a homogeneous isotropic, nonlinearly elastic body is shown to have a di scontinuous solution for a class of stored-energy functions of slow gr owth. This solution is admissible by the usual entropy criterion and i s in fact preferred by the entropy-rate criterion over the smooth equi librium solution to the same problem. The existence of such a dissipat ive solution shows that the equilibrium solution is dynamically unstab le. This instability cannot be ascertained by linearisation.