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

TL;DR

This paper analyzes how dynamic solutions of finite-dimensional rate-independent systems with time-dependent dissipation converge to quasistatic solutions, with applications to soft crawling robots.

Contribution

It introduces a vanishing inertia approach for systems with nonautonomous dissipation and demonstrates uniform convergence to quasistatic evolutions, extending previous models.

Findings

Proves uniform convergence of dynamic to quasistatic solutions

Handles time-dependent dissipation potentials in the analysis

Applies results to models of soft crawling locomotion

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.