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

Stability of fully discrete variational schemes for elastodynamics with a polyconvex stored energy