  A weak-strong uniqueness result is proved for measure-valued solutions to the
system of conservation laws arising in elastodynamics. The main novelty brought
forward by the present work is that the underlying stored-energy function of
the material is assumed strongly quasiconvex. The proof employs tools from the
calculus of variations to establish general convexity-type bounds on
quasiconvex functions and recasts them in order to adapt the relative entropy
method to quasiconvex elastodynamics.
