One-period stability analysis of polygonal sweeping processes with application to an elastoplastic model
Mathematical modelling of natural phenomena, Tome 15 (2020), article no. 25.

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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.
DOI : 10.1051/mmnp/2019030

Ivan Gudoshnikov 1 ; Mikhail Kamenskii 2 ; Oleg Makarenkov 1 ; Natalia Voskovskaia 2

1 Department of Mathematical Sciences, University of Texas at Dallas, 75080 Richardson, USA.
2 Department of Mathematics, Voronezh State University, Voronezh, Russia.
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Ivan Gudoshnikov; Mikhail Kamenskii; Oleg Makarenkov; Natalia Voskovskaia. One-period stability analysis of polygonal sweeping processes with application to an elastoplastic model. Mathematical modelling of natural phenomena, Tome 15 (2020), article  no. 25. doi : 10.1051/mmnp/2019030. https://geodesic-test.mathdoc.fr/articles/10.1051/mmnp/2019030/

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