The embedding of the equations of polyconvex elastodynamics to an augmented
symmetric hyperbolic system provides in conjunction with the relative entropy method
a robust stability framework for approximate solutions \cite{LT06}.
We devise here a model of stress relaxation motivated by the
format of the enlargement process which formally approximates
the equations of polyconvex elastodynamics. The model is endowed with
an entropy function which is not convex but rather of polyconvex type.
Using the relative entropy we prove a stability estimate and convergence
of the stress relaxation model to polyconvex elastodynamics in the
smooth regime. As an application, we show that models of pressure relaxation for
real gases in Eulerian coordinates fit into the proposed framework
