Mechanical origin of Amonton’s law in nanoscale friction

The widely used Amonton’s law, describing the common observation that dry friction between two surfaces is proportional to normal load, has yet been explicitly derived since its discovery from Leonardo da Vinci era. Here, Amonton’s law is explicitly extrapolated as friction coefficient &nbsp;using a concise perturbation theory analysis of frictional energy landscape parametrized by load. This unveils Amonton’s law may arise from the competition between normal stiffness (<em>k</em>) and interfacial normal force fluctuation during sliding (Δ<em>F</em>_N/Δ<em>x</em>). The predicted friction coefficient is quantitatively validated through both atomic force microscopy (AFM) experiments and atomistic simulations of frictional systems ranging from bulk to layered materials. Different from the traditional framework of recondite rough contact theory, this study concisely extrapolates Amonton’s law as well as friction coefficient and traces their microscopic origins to the inherent mechanical properties, thereby enabling their rational design.