Lisbon WADE — Webinar in Analysis and Differential Equations  

18/02/2021, 14:00 — 15:00 — Online
Paolo Gidoni, Czech Academy of Sciences

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

The quasistatic limit is a convenient approximation in the modelling of several (suitable) mechanical systems, when the evolution occurs at a sufficiently slow time-scale. In this talk we discuss the validity of the quasistatic approximation in finite-dimensional rate-independent systems via a vanishing-inertia asymptotic analysis of dynamic evolutions. More precisely, we show the uniform convergence of dynamic solutions to the quasistatic one, employing the concept of energetic solution. Our work is motivated by the application to a family of models for biological and bio-inspired crawling locomotion. Hence a part of the seminar will focus on modelling: we will discuss how soft crawlers can be effectively described in our theoretical framework and briefly survey the relevance, or lack thereof, of inertia in some locomotion strategies. By a technical point of view, our application requires time-dependence of the dissipation potential and translation invariance of the potential energy.

Joint work with Filippo Riva.