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  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 (k) and interfacial normal force fluctuation during sliding (ΔF_N/Δx). 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.

广泛使用的阿蒙顿定律描述了两个表面之间的干摩擦与法向载荷成正比的常见观察结果，自从列奥纳多·达·芬奇时代发现以来，它一直被明确推导出来。在这里，阿蒙顿定律使用由负载参数化的摩擦能景观的简明微扰理论分析明确推断为摩擦系数。这揭示了阿蒙顿定律可能源于滑动过程中法向刚度 （k） 和界面法向力波动 （ΔF_N/Δx） 之间的竞争。通过原子力显微镜 （AFM） 实验和从块状到层状材料的摩擦系统的原子模拟，对预测的摩擦系数进行了定量验证。与传统的粗接触理论框架不同，本研究简明扼要地推断了阿蒙顿定律和摩擦系数，并追溯了它们的微观起源到固有的力学性能，从而能够对其进行合理设计。