On the geometric phenomenology of static friction

TL;DR

This paper introduces a hierarchical phase space framework to systematically analyze the directional dependence of static friction, providing a graphical method to interpret frictional responses based on object shape and contact properties.

Contribution

It develops a novel hierarchical phase space model for static friction that captures directional dependence and links experimental observations to a universal classifying map.

Findings

Graphical phase space representation of static friction

Experimental plots of frictional subregions for various shapes

Universal classifying map for frictional behavior

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 behavior 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.