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

TL;DR

This paper introduces and explores Visco-Energetic solutions, a new weak solvability concept for rate-independent systems, demonstrating its applicability to damage, delamination, and plasticity in solid mechanics.

Contribution

It applies the Visco-Energetic solution framework to plasticity, damage, and delamination, and establishes evolutionary Gamma-convergence results.

Findings

Visco-Energetic solutions effectively model complex rate-independent processes.

The approach bridges Energetic and Balanced Viscosity solutions.

Evolutionary Gamma-convergence is established for delamination models.

Abstract

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.