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.
