Slip Morphology of Elastic Strips on Frictional Rigid Substrates

TL;DR

This study explores the diverse morphologies of elastic strips on frictional substrates through theory and experiments, classifying states based on stress and friction, and providing a unified understanding of elastic-object interactions with surfaces.

Contribution

It introduces a comprehensive theoretical framework for elastic strips on frictional surfaces, validated by experiments, and clarifies the effects of gravity and elasticity on morphology.

Findings

Identified three distinct morphological states: pinned, partially slipped, and completely slipped.

Developed a theory combining elastica with Coulomb-Amontons friction law, showing excellent agreement with experiments.

Analyzed the influence of gravity, bridging behaviors between stiff and flexible elastic objects.

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.