  This paper revolves around a newly introduced weak solvability concept for
rate-independent systems, alternative to the notions of Energetic and Balanced
Viscosity solutions. Visco-Energetic solutions have been recently obtained by
passing to the time-continuous limit in a time-incremental scheme, akin to that
for Energetic solutions, but perturbed by a `viscous' correction term, as in
the case of Balanced Viscosity solutions. However, for Visco-Energetic
solutions this viscous correction is tuned by a fixed parameter. The resulting
solution notion turns out to describe a kind of evolution in between Energetic
and Balanced Viscosity evolution.
  In this paper we aim to investigate the application of Visco-Energetic
solutions to the paradigmatic example of perfect plasticity, and to nonsmooth
rate-independent processes in solid mechanics such as damage and plasticity at
finite strains. With the limit passage from adhesive contact to brittle
delamination, we also provide a first result of Evolutionary Gamma-convergence
for Visco-Energetic solutions. The analysis of these applications reveals the
wide applicability of this solution concept and confirms its intermediate
character.
