  The 2-step staggered (also called leap-frog) time discretisation of linear
2nd-order Hamiltonian systems (typically linear elastodynamics in a
stress-velocity form) is extended for a 3-step staggered discretisation
applicable for systems involving some internal variables subjected to a
dissipative evolution. After spatial discretisation, a-priori estimates and
convergence is proved under the usual CFL-condition. Applications to specific
problems in continuum mechanics of solids at small stains are considered, in
particular linearized plasticity, diffusion in poroelastic media, damage, or
adhesive contact. Numerical implementation and some computational 2-dimensional
simulation of waves emitted by a rupture (delamination) of an adhesive contact
illustrate the abstract theory and efficiency of the explicit method.
