I have developed a theory of contact mechanics between randomly rough surfaces. The solids are assumed to deform elastically when the stress $\sigma$ is below the yield stress ${\sigma }_Y$, and plastically when $\sigma$ reaches ${\sigma }_Y$. I study the dependence of the (apparent) area of contact on the magnification. I show that in most cases the area of real contact $A$ is proportional to the load. If the rough surface is self-affine fractal (Hurst exponent $H$) the whole way up to the lateral size $L$ of the nominal contact area, then (assuming no plastic deformation) $A\sim L^H$.

• Received 29 January 2001

DOI:https://doi.org/10.1103/PhysRevLett.87.116101