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 Prandtlâ€“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.

%B ESAIM: COCV %V 23 %P 1023-1046 %G eng %U https://doi.org/10.1051/cocv/2017030 %R 10.1051/cocv/2017030 %0 Journal Article %J Continuum. Mech. Therm. %D 2011 %T Gamma-convergence of energies for nematic elastomers in the small strain limit %A Virginia Agostiniani %A Antonio DeSimone %K Liquid crystals %XWe study two variational models recently proposed in the literature to describe the mechanical behaviour of nematic elastomers either in the fully nonlinear regime or in the framework of a geometrically linear theory. We show that, in the small strain limit, the energy functional of the first one I\\\"-converges to the relaxation of the second one, a functional for which an explicit representation formula is available.

%B Continuum. Mech. Therm. %I Springer %V 23 %G en %U http://hdl.handle.net/1963/4141 %1 3882 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-15T13:10:38Z\\nNo. of bitstreams: 1\\nAgost_DeSim07M.pdf: 348761 bytes, checksum: b9b69eb7da7ca6962e4a46e904646a6b (MD5) %& 257 %R 10.1007/s00161-011-0180-2 %0 Journal Article %J Netw. Heterog. Media 3 (2008) 567-614 %D 2008 %T Globally stable quasistatic evolution in plasticity with softening %A Gianni Dal Maso %A Antonio DeSimone %A Maria Giovanna Mora %A Massimiliano Morini %X We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is characterized by the following properties: global stability at each time and energy balance on each\\ntime interval. An example developed in detail compares the solutions obtained by this method with the ones provided by a vanishing viscosity approximation, and shows that only the latter capture a decreasing branch in the stress-strain response. %B Netw. Heterog. Media 3 (2008) 567-614 %G en_US %U http://hdl.handle.net/1963/1965 %1 2228 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-05-15T11:03:21Z\\nNo. of bitstreams: 1\\nDM-DeS-Mor-Mor-05-3-final.pdf: 395475 bytes, checksum: 5789494df44986207d416d5d1ea15d22 (MD5)