Slip Morphology of Elastic Strips on Frictional Rigid Substrates

Physical Review Letters
Tomohiko G SanoHirofumi Wada

Abstract

The morphology of an elastic strip subject to vertical compressive stress on a frictional rigid substrate is investigated by a combination of theory and experiment. We find a rich variety of morphologies, which-when the bending elasticity dominates over the effect of gravity-are classified into three distinct types of states: pinned, partially slipped, and completely slipped, depending on the magnitude of the vertical strain and the coefficient of static friction. We develop a theory of elastica under mixed clamped-hinged boundary conditions combined with the Coulomb-Amontons friction law and find excellent quantitative agreement with simulations and controlled physical experiments. We also discuss the effect of gravity in order to bridge the difference in the qualitative behaviors of stiff strips and flexible strings or ropes. Our study thus complements recent work on elastic rope coiling and takes a significant step towards establishing a unified understanding of how a thin elastic object interacts vertically with a solid surface.

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Citations

Jan 31, 2020·Soft Matter·David J SchunterDouglas P Holmes
Feb 20, 2020·Physical Review. E·Kui PanSheldon Green
Feb 17, 2018·Physical Review. E·Tomohiko G Sano, Hirofumi Wada
Feb 29, 2020·Physical Review Letters·Tetsuo YamaguchiYoshinori Sawae
Nov 21, 2020·Physical Review Letters·Keisuke Yoshida, Hirofumi Wada
Apr 21, 2021·Proceedings of the National Academy of Sciences of the United States of America·Paul GrandgeorgePedro M Reis
May 29, 2021·The European Physical Journal. E, Soft Matter·Raphaelle TaubFrédéric Restagno

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