Slip Morphology of Elastic Strips on Frictional Rigid Substrates

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 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 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.

arXiv comment10 pages, 10 figures

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• On/off switching of adhesion in gecko-inspired adhesives
• A mechanical model of bacteriophage DNA ejection
• Indentation of an elastic arch on a frictional substrate: Pinning, unfolding and snapping
• Asymmetric Ground States in La${}_{0.67}$Sr${}_{0.33}$MnO${}_3$/BaTiO${}_3$ heterostructures Induced by Flexoelectric Bending
• Anchoring-mediated stick-slip winding of cholesteric liquid crystals
• Wrinkles, rucks, and folds formed in a heavy sheet on a frictional surface