  In this article we develop a fully discrete variational scheme that
approximates the equations of three dimensional elastodynamics with polyconvex
stored energy. The fully discrete scheme is based on a time-discrete
variational scheme developed by S.~Demoulini, D.~M.~A.~Stuart and
A.~E.~Tzavaras (2001). We show that the fully discrete scheme is
unconditionally stable. The proof of stability is based on a relative entropy
estimation for the fully discrete approximates.
