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.

VL - 23 UR - https://doi.org/10.1051/cocv/2017030 ER - TY - JOUR T1 - Gamma-convergence of energies for nematic elastomers in the small strain limit JF - Continuum. Mech. Therm. Y1 - 2011 A1 - Virginia Agostiniani A1 - Antonio DeSimone KW - Liquid crystals AB -We 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.

PB - Springer VL - 23 UR - http://hdl.handle.net/1963/4141 U1 - 3882 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Globally stable quasistatic evolution in plasticity with softening JF - Netw. Heterog. Media 3 (2008) 567-614 Y1 - 2008 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Maria Giovanna Mora A1 - Massimiliano Morini AB - 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. UR - http://hdl.handle.net/1963/1965 U1 - 2228 U2 - Mathematics U3 - Functional Analysis and Applications ER -