  An extension of the two-step staggered time discretization of linear
elastodynamics in stress-velocity form to systems involving internal variables
subjected to a possibly non-linear dissipative evolution is proposed. The
original scheme is thus enhanced by another step for the internal variables
which, in general, is implicit, although even this step might be explicit if no
spatial gradients of the internal variables are involved. Using an abstract
Banach-space formulation, a-priori estimates and convergence are proved under a
CFL condition. The developed three-step scheme finds applications in various
problems of continuum mechanics at small strain. Here, we consider in
particular plasticity, viscoelasticity (creep), diffusion in poroelastic media,
and damage.
