Visco-energetic solutions to some rate-independent systems in damage, delamination, and plasticity

This paper revolves around a newly introduced weak solvability concept for rate-independent systems, alternative to the notions of Energetic (E) and Balanced Viscosity (BV) solutions. Visco-Energetic (VE) solutions have been recently obtained by passing to the time-continuous limit in a time-incremental scheme, akin to that for E solutions, but perturbed by a "viscous" correction term, as in the case of BV solutions. However, for VE 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 BV evolution. In this paper we aim to investigate the application of VE solutions to nonsmooth rate-independent processes in solid mechanics such as damage and plasticity at finite strains. We also address the limit passage, in the VE formulation, from an adhesive contact to a brittle delamination system. The analysis of these applications reveals the wide applicability of this solution concept, in particular to processes for which BV solutions are not available, and confirms its intermediate character between the E and BV notions.