Anomalous Enhancement of Yield Force in a Minimal Friction-Stabilized Structure

Friction plays a crucial role in the mechanical stability of many structures, ranging from sand piles to masonry domes. This study aims to quantitatively understand how friction contributes to structural stability through a minimal model.

We consider a system of three elastic cylinders stacked under gravity, each interacting through frictional contacts, and analyze the yield force, defined as the threshold compressive force at which sliding occurs at the floor contact during quasi-static compression.

Numerical calculations reveal that the yield force exhibits an anomalous enhancement near the critical friction coefficient μ_c ~ 0.268. This anomaly is examined using singular perturbation theory, leading to an analytical expression for the yield force as a function of the static friction coefficient and a small parameter characterizing elastic deformation.

The results provide a tractable example for quantitatively understanding how friction contributes to the stability of stacked structures.