  We propose a variational scheme for the construction of isentropic processes
of the equations of adiabatic thermoelasticity with polyconvex internal energy.
The scheme hinges on the embedding of the equations of adiabatic polyconvex
thermoelasticity into a symmetrizable hyperbolic system. We establish existence
of minimizers for an associated minimization theorem and construct
measure-valued solutions that dissipate the total energy. We prove that the
scheme converges when the limiting solution is smooth.
