On the genesis of directional friction through bristle-like mediating elements

@article{Gidoni2016OnTG,
  title={On the genesis of directional friction through bristle-like mediating elements},
  author={Paolo Gidoni and Antonio DeSimone},
  journal={arXiv: Mathematical Physics},
  year={2016}
}
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… 

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References

SHOWING 1-10 OF 48 REFERENCES
Crawling on directional surfaces
Stasis domains and slip surfaces in the locomotion of a bio-inspired two-segment crawler
TLDR
By focusing on the tensions in the elastic segments, this work shows that the evolution laws for the system are entirely analogous to the flow rules of elasto-plasticity, and shows that specific choices of the actuation strategy can lead to net displacements also in the direction of higher friction.
A sudden-release bristle model that exhibits hysteresis and stick-slip friction
In this paper we introduce a bristle model for stick-slip friction. The friction force of the bristle model is generated by frictionless contact between a body and an infinite row of bristles. Each
Characterization of friction force dynamics
TLDR
This article presents an example of comprehensive model building, which, starting from the generic mechanisms behind friction, leads to the construction of a model that explains observed macroscopic friction behavior.
Crawling motility through the analysis of model locomotors: Two case studies
TLDR
The main conclusion is that there is no snail theorem, which means that the crawling analog of the scallop theorem of low Reynolds number hydrodynamics does not hold for snail-like crawlers.
Contact compliance effects in the frictional response of bioinspired fibrillar adhesives
TLDR
The shear failure and friction mechanisms of bioinspired adhesives consisting of elastomer arrays of microfibres terminated by mushroom-shaped tips are investigated in contact with a rigid lens and the extent of these mechanisms and their implications regarding static friction forces is found to depend on the crosstalk between the normal and lateral loading directions.
Biomimetic ratcheting motion of a soft, slender, sessile gel
TLDR
The simple theory and experiments provide a unified view of the creeping, undulating, and inchworming gaits observed in limbless locomotion on land, all of which originate as symmetry-breaking bifurcation of a simple base state associated with periodic longitudinal oscillations of a slender gel.
Adhesion and friction in gecko toe attachment and detachment
TLDR
Both the adhesion and friction forces of geckos can be changed over three orders of magnitude, allowing for the swift attachment and detachment during gecko motion, and have obvious implications for the fabrication of dry adhesives and robotic systems inspired by the gecko's locomotion mechanism.
Kinetics of materials with wiggly energies: Theory and application to the evolution of twinning microstructures in a Cu-Al-Ni shape memory alloy
We analyse the kinetics of the transition between two variants of martensite during biaxial dead loading. The volume fraction of one martensite variant versus the applied loads exhibits an unusual
...
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