Static Friction Coefficient Depends on the External Pressure and Block Shape due to Precursor Slip

TL;DR

This study demonstrates through numerical simulation and theoretical analysis that the static friction coefficient depends on external pressure and block shape due to precursor slip phenomena, challenging Amontons' law.

Contribution

The paper reveals the influence of external pressure and object shape on static friction, supported by FEM simulations and a theoretical model explaining precursor slip effects.

Findings

Static friction coefficient decreases with increased pressure and block dimensions.

Precursor slip occurs before bulk sliding, affecting static friction.

Critical slip area determines the macroscopic static friction coefficient.

Abstract

Amontons' law states that the maximum static friction force on a solid object is proportional to the loading force and is independent of the apparent contact area. This law indicates that the static friction coefficient does not depend on the external pressure or object shape. Here, we numerically investigate the sliding motion of a 3D viscoelastic block on a rigid substrate using the finite element method (FEM). The macroscopic static friction coefficient decreases with an increase in the external pressure, length, or width of the object, which contradicts Amontons' law. Precursor slip occurs in the 2D interface between the block and substrate before bulk sliding. The decrease in the macroscopic static friction coefficient is scaled by the critical area of the precursor slip before bulk sliding. A theoretical analysis of the simplified models reveals that bulk sliding results from the instability of the quasi-static precursor slip caused by velocity-weakening local friction. We also show that the critical slip area determines the macroscopic static friction coefficient, which explains the results of the FEM simulation.