On the mechanical dissipation of solutions to the Riemann problem for impact involving a two-phase elastic material (Q1192730)

The author considers the longitudinal isothermal impact of a rod of elastic material on a target rod of different material exhibiting two stable phases. This gives rise to a class of initial value problems with piecewise constant initial data, for equations exhibiting a jump in the constitutive law. The solutions include shock waves, rarefaction waves and phase boundaries. The admissibility of the phase boundaries is decided on the basis of the maximum dissipation condition, which is equivalent to the entropy rate condition of Dafermos. The main result is that there is a solution of the problem for every impact velocity, but for impact velocities in a certain interval, the maximum dissipation condition is invoked to ensure uniqueness of the solution. There are certain technical restrictions on the constitutive behaviour in order for the argument to be carried out fully.