An Incremental Model for Interfacial Stiffness Unifying Sublinear and Linear Scaling Regimes

Accurately predicting the interfacial gap and stiffness between rough solids is essential for understanding contact behavior in tribological, sealing, and thermal systems. This work proposes a novel model that accurately captures the evolution of mean interfacial gap and stiffness from initial finite contacts to accumulated statistical response. The obtained load-gap relationship is validated against boundary element simulations of elastic rough contact, showing excellent agreement across a wide range of normal loads. Unlike conventional models, the proposed approach captures finite-size effects at light loads, yielding a sublinear power-law scaling of stiffness with load, and transitions seamlessly to the linear regime at higher loads. The model provides a simple, parameter-free tool for quantitative analysis of rough surface contacts.