2016/02/10 by Paolo Gidoni, Antonio DeSimone · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Adhesion, Friction, and Surface Interactions #Brake Systems and Friction Analysis #Bristle #Convergence (economics) #Element (criminal law) #Force Microscopy Techniques and Applications #Microscale chemistry #Product (mathematics) #Property (philosophy) #Surface (topology) #math-ph #math.MP
paper · pdf · doi:10.1051/cocv/2017030
published as ESAIM: Control, Optimization and Calculus of Variations 23 (2017), pp. 1023-1046
arxiv created 2016/02/10 · openalex created_date 2016/06/24 · openalex publication_date 2017/03/28 · arxiv updated 2018/04/06 · openalex updated_date 2026/08/05
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.