Anomalous Enhancement of Yield Strength due to Static Friction

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.