Calculus of Variations and Geometric Measure Theory
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P. Gidoni - F. Riva

A vanishing inertia analysis for finite dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlers

created by riva on 18 Jul 2020
modified on 04 Aug 2021

[BibTeX]

Published Paper

Inserted: 18 jul 2020
Last Updated: 4 aug 2021

Journal: Calculus of Variations and Partial Differential Equations
Volume: 60
Year: 2021
Doi: https://doi.org/10.1007/s00526-021-02067-6

ArXiv: 2007.09069 PDF
Links: Online version

Abstract:

We study the approximation of quasistatic evolutions, formulated as abstract finite-dimensional rate-independent systems, via a vanishing-inertia asymptotic analysis of dynamic evolutions. We prove the uniform convergence of dynamical solutions to the quasistatic one, employing the concept of energetic solution. Motivated by applications in soft locomotion, we allow time-dependence of the dissipation potential, and translation invariance of the potential energy.

Keywords: rate-independent systems, energetic solutions, Vanishing inertia, quasistatic limit, Soft crawlers


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