Anomalous Enhancement of Yield Strength due to Static Friction

TL;DR

This paper investigates how static friction can anomalously increase the yield strength of a simple three-particle structure, providing a predictive analytical expression for the collapse threshold based on friction and elasticity.

Contribution

It introduces a minimal model analyzing the impact of static friction on yield strength and derives a quantitative formula for the collapse threshold using singular perturbation analysis.

Findings

Derived an analytical expression for yield force as a function of static friction and elasticity.

Showed static friction can significantly enhance the structural yield strength.

Validated the predictive model through theoretical analysis.

Abstract

Friction is fundamental to mechanical stability across scales, from geological faults and architectural structures to granular materials and animal feet. We study the mechanical stability of a minimal friction-stabilized structure composed of three cylindrical particles arranged in a triangular stack on a floor under gravity. We analyze the yield force, defined as the threshold compressive force applied quasi-statically from above at which the structure collapses due to sliding at the floor contact. Using singular perturbation analysis, we derive an expression which quantitatively predicts the yield force as a function of the static friction coefficient and a small dimensionless parameter $\epsilon$ characterizing elastic deformation.