On the genesis of directional friction through bristle-like mediating elements

TL;DR

This paper explains how directional dry friction can emerge from oscillations in a bristle-like element interacting with surface fluctuations, combining mathematical analysis and mechanical modeling.

Contribution

It extends a convergence result for Prandtl-Tomlinson systems to include non-homothetic scalings, applying it to model directional friction from surface interactions.

Findings

Friction depends on bristle angle and surface fluctuation profile.

Friction is proportional to the normal force on the bristle.

The model explains asymmetry in friction with respect to nap direction.

Abstract

We propose an explanation of the genesis of directional dry friction, as emergent property of the oscillations produced in a bristle-like mediating element by the interaction with microscale fluctuations on the surface. Mathematically, we extend a convergence result by Mielke, for Prandtl-Tomlinson-like systems, considering also non-homothetic scalings of a wiggly potential. This allows us to apply the result to some simple mechanical models, that exemplify the interaction of a bristle with a surface having small fluctuations. We find that the resulting friction is the product of two factors: a geometric one, depending on the bristle angle and on the fluctuation profile, and a energetic one, proportional to the normal force exchanged between the bristle-like element and the surface. Finally, we apply our result to discuss the with the nap/against the nap asymmetry.