Calculus of Variations and Geometric Measure Theory

R. Rossi

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

created by rossi on 09 Mar 2018
modified on 09 Feb 2019


Accepted Paper

Inserted: 9 mar 2018
Last Updated: 9 feb 2019

Journal: Mathematical Models and Methods in the Applied Sciences
Year: 2019

In press.


This paper revolves around a newly introduced weak solvability concept for rate-independent systems, alternative to the notions of \emph{Energetic} (E) and \emph{Balanced Viscosity} (BV) solutions. \emph{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 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. \par 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.