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

Abstract

This paper revolves around a newly introduced weak solvability concept for rate-independent systems, alternative to the notions of Energetic ([Formula: see text]) and Balanced Viscosity ([Formula: see text]) solutions. Visco-Energetic ([Formula: see text]) solutions have been recently obtained by passing to the time-continuous limit in a time-incremental scheme, akin to that for [Formula: see text] solutions, but perturbed by a “viscous” correction term, as in the case of [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] solutions are not available, and confirms its intermediate character between the [Formula: see text] and [Formula: see text] notions.