  In this paper, we study a second-order, nonlinear evolution equation with
damping arising in elastodynamics. The nonlinear term is monotone and possesses
a convex potential but exhibits anisotropic and nonpolynomial growth. The
appropriate setting for such equations is that of monotone operators in Orlicz
spaces. Global existence of solutions in the sense of distributions is shown
via convergence of the backward Euler scheme combined with an internal
approximation. Moreover, we show uniqueness in a class of sufficiently smooth
solutions and provide an a priori error estimate for the temporal
semidiscretization.
