Geodesic
On the genesis of directional friction through bristle-like mediating elements
Gidoni, Paolo1, 2 ; DeSimone, Antonio2, 3
1CMAF-CIO – Centro de Matemática, Aplicações Fundamentais e Investigação Operacional, Faculdade de Ciências da Universidade de Lisboa, Campo Grande, Edificio C6, 1749-016 Lisboa, Portugal.
2SISSA – International School for Advanced Studies, Trieste, Italy.
3GSSI – Gran Sasso Science Institute, L’Aquila, Italy.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 3, pp. 1023-1046

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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.

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Accepté le :
DOI : 10.1051/cocv/2017030
Classification : 74A55, 74M10, 74N30
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

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. 
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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