Volume 23, Number 3, July-September 2017
|Page(s)||1023 - 1046|
|Published online||03 May 2017|
On the genesis of directional friction through bristle-like mediating elements
1 CMAF-CIO – Centro de Matemática, Aplicações Fundamentais e Investigação Operacional, Faculdade de Ciências da Universidade de Lisboa, Campo Grande, Edificio C6, 1749-016 Lisboa, Portugal.
2 SISSA – International School for Advanced Studies, Trieste, Italy.
3 GSSI – Gran Sasso Science Institute, L’ Aquila, Italy.
Received: 10 February 2016
Revised: 14 February 2017
Accepted: 26 March 2017
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.
Mathematics Subject Classification: 74A55 / 74M10 / 74N30
Key words: Directional dry friction / rate-independent systems / wiggly energy landscape / with the nap/against the nap asymmetry / energy-dissipation principle
© EDP Sciences, SMAI 2017
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