English

Visco-Energetic solutions to one-dimensional rate-independent problems

Analysis of PDEs 2016-10-04 v1

Abstract

Visco-Energetic solutions of rate-independent systems are obtained by solving a modified time Incremental Minimization Scheme, where at each step the dissipation is reinforced by a viscous correction, typically a quadratic perturbation of the dissipation distance. Like Energetic and Balanced Viscosity solutions, they provide a variational characterization of rate-independent evolutions, with an accurate description of their jump behaviour. In the present paper we study Visco-Energetic solutions in the one-dimensional case and we obtain a full characterization for a broad class of energy functionals. In particular, we prove that they exhibit a sort of intermediate behaviour between Energetic and Balanced Viscosity solutions, which can be finely tuned according to the choice of the viscous correction.

Keywords

Cite

@article{arxiv.1610.00507,
  title  = {Visco-Energetic solutions to one-dimensional rate-independent problems},
  author = {Luca Minotti},
  journal= {arXiv preprint arXiv:1610.00507},
  year   = {2016}
}
R2 v1 2026-06-22T16:08:40.550Z