A Vanishing inertia analysis for finite dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlers
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Date
2020-07-21
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SISSA
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.
Description
Contents: 1. Introduction and motivation. 2. Setting of the problem and main result.
3. Existence of solutions for the dynamic problem. 4. R-absolutely continuous functions and functions of bounded R-variation. 5. Differential and energetic solutions for the quasistatic problem. 6. Quasistatic limit. 7. Applications and examples. References.
Keywords
Quasistatic limit, Vanishing inertia, Rate-independent systems, Energetic solutions, Soft crawlers