| Issue |
Math. Model. Nat. Phenom.
Volume 15, 2020
Systems with Hysteresis and Switching
|
|
|---|---|---|
| Article Number | 25 | |
| Number of page(s) | 18 | |
| DOI | https://doi.org/10.1051/mmnp/2019030 | |
| Published online | 10 April 2020 | |
One-period stability analysis of polygonal sweeping processes with application to an elastoplastic model
1
Department of Mathematical Sciences, University of Texas at Dallas,
75080
Richardson, USA.
2
Department of Mathematics, Voronezh State University,
Voronezh, Russia.
* Corresponding author: makarenkov@utdallas.edu
Received:
23
January
2019
Accepted:
25
June
2019
We offer a finite-time stability result for Moreau sweeping processes on the plane with periodically moving polyhedron. The result is used to establish the convergence of stress evolution of a simple network of elastoplastic springs to a unique cyclic response in just one cycle of the external displacement-controlled cyclic loading. The paper concludes with an example showing that smoothing the vertices of the polyhedron makes finite-time stability impossible.
Mathematics Subject Classification: 74C05 / 37J25
Key words: Moreau’s sweeping process / elastoplasticity / displacement-controlled loading / one-period stability
© The authors. Published by EDP Sciences, 2020
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