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An abstract 2nd-order evolution equation or inclusion is discretised in timein such a way that the energy is conserved at least in qualified cases,typically in the cases when the governing energy is component-wise quadratic or"slightly-perturbed" quadratic. Specific applications in continuum mechanics ofsolids possibly with various internal variables cover vibrations or waves inlinear viscoelastic materials at small strains, coupled with some inelasticprocesses as plasticity, damage, or phase transformations, and also somesurface variants related to contact mechanics. The applicability is illustratedby numerical simulations of vibrations interacting with a frictional contact orwaves emitted by an adhesive contact of a 2-dimensional viscoelastic body.

Energy-conserving time-discretisation of abstract dynamic problems with applications in continuum mechanics of solids