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.
Accepté le :
DOI : 10.1051/cocv/2017030
Keywords: Directional dry friction, rate-independent systems, wiggly energy landscape, with the nap/against the nap asymmetry, energy-dissipation principle
Gidoni, Paolo 1, 2 ; DeSimone, Antonio 2, 3
@article{COCV_2017__23_3_1023_0,
author = {Gidoni, Paolo and DeSimone, Antonio},
title = {On the genesis of directional friction through bristle-like mediating elements},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1023--1046},
year = {2017},
publisher = {EDP Sciences},
volume = {23},
number = {3},
doi = {10.1051/cocv/2017030},
zbl = {1365.74021},
mrnumber = {3660458},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2017030/}
}
TY - JOUR AU - Gidoni, Paolo AU - DeSimone, Antonio TI - On the genesis of directional friction through bristle-like mediating elements JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 1023 EP - 1046 VL - 23 IS - 3 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2017030/ DO - 10.1051/cocv/2017030 LA - en ID - COCV_2017__23_3_1023_0 ER -
%0 Journal Article %A Gidoni, Paolo %A DeSimone, Antonio %T On the genesis of directional friction through bristle-like mediating elements %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 1023-1046 %V 23 %N 3 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2017030/ %R 10.1051/cocv/2017030 %G en %F COCV_2017__23_3_1023_0
Gidoni, Paolo; DeSimone, Antonio. On the genesis of directional friction through bristle-like mediating elements. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 3, pp. 1023-1046. doi: 10.1051/cocv/2017030
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