Inserted: 18 jul 2020
Last Updated: 4 aug 2021
Journal: Calculus of Variations and Partial Differential Equations
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