On the geometric phenomenology of static friction

Abstract

In this note we introduce a hierarchy of phase spaces for static friction, which give a graphical way to systematically quantify the directional dependence in static friction via subregions of the phase spaces. We experimentally plot these subregions to obtain phenomenological descriptions for static friction in various examples where the macroscopic shape of the object affects the frictional response. The phase spaces have the universal property that for any experiment in which a given object is put on a substrate fashioned from a chosen material with a specified nature of contact, the frictional behaviour can be read off from a uniquely determined classifying map on the control space of the experiment which takes values in the appropriate phase space.

A geometric framework for dynamics with unilateral constraints and friction, illustrated by an example of self-organized locomotion

“…The physical parameters for the dumbbells are = 16 mm, r = 3 mm, t = 0.75 mm. The data in the figure are reproduced from [14]. (Online version in colour.…”

“…Note that the frictional response of a dumbbell is highly anisotropic as it rolls much more easily than it slides. We combine the kinematics given by the polyhedral geometry with our earlier construction of phase spaces for anisotropic friction [14] and an analogue for dumbbells of our earlier analysis of auto-toggling between rolling and sliding states of spheres in a rotating cylinder [15] to arrive at an understanding of the observed dynamics of the dumbbells. For concreteness, the general polyhedral framework is presented in tandem with the description of this experiment and its results.…”

Internal geometric friction in a Kitaev-chain heat engine

“…Since the early studies performed by Leonardo da Vinci, it is traditionally accepted that the friction force between two identical objects is independent of their geometry-i.e., shape and size. Modern tribology studies, however, revealed that the bulk of the sliding bodies, in addition to the interface, played also a role on the friction [17,18]. The effects of orientation, shape, and size on friction can be significant at any lengthscale, ranging from earthquake fractures to nanoparticles [19] or biological cells [20].…”

Tuning of friction noise by accessing the rolling-sliding option

“…The balls can access two motional states -(i) rolling and(ii) sliding [8][9][10]. They will be referred to as 'rollers' and 'sliders' respectively.…”

“…In contrast, we do not hold the balls in cages and the noise observed in running our experimental system is related to the collective dynamics of these balls. As a closing remark, we would like to point out that the conventional wisdom that the coefficient of friction is approximately constant for a pair of surfaces [9] can easily be circumvented by harnessing the complexity of the third body interaction forces.…”