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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.
When a flat elastic strip is compressed along its axis, it is bent in one of two possible directions via spontaneous symmetry breaking and forms a cylindrical arc, a phenomenon well known as Euler buckling. When this cylindrical section is pushed in
The temperature dependence of the hydrodynamic boundary condition between a PDMS melt and two different non-attractive surfaces made of either an OTS (octadecyltrichlorosilane) self-assembled monolayer (SAM) or a grafted layer of short PDMS chains ha
A theory is presented which quantitatively accounts for the cooperative adsorption of cationic surfactants to anionic polyelectrolytes. For high salt concentration we find that the critical adsorption concentration (CAC) is a bilinear function of the
Frictional forces affect the rheology of hard-sphere colloids, at high shear rate. Here we demonstrate, via numerical simulations, that they also affect the dynamics of active Brownian particles, and their motility induced phase separation. Frictiona
Hydrodynamic slip of a liquid at a solid surface represents a fundamental phenomenon in fluid dynamics that governs liquid transport at small scales. For polymeric liquids, de Gennes predicted that the Navier boundary condition together with the theo