On the elastic energy and stress correlation in the contact between elastic solids with randomly rough surfaces

TL;DR

This paper investigates the stress distribution and elastic energy in the contact interface of elastic solids with self-affine fractal rough surfaces, revealing a power-law correlation related to surface roughness.

Contribution

It establishes a theoretical relationship between stress correlation functions and elastic energy for self-affine fractal surfaces in contact mechanics.

Findings

Stress correlation function scales as q^{-(1+H)} for self-affine surfaces.

Elastic energy at the interface is related to the stress distribution.

Provides a theoretical framework linking surface roughness to stress correlations.

Abstract

When two elastic solids with randomly rough surfaces are brought in contact, a very inhomogeneous stress distribution sigma(x) will occur at the interface. Here I study the elastic energy and the correlation function <sigma(q)sigma(-q)>, where sigma(q) is the Fourier transform of sigma(x) and where <...> stands for ensemble average. I relate <sigma(q})sigma(-q)> to the elastic energy stored at the interface, and I show that for self affine fractal surfaces, quite generally <sigma(q)sigma(-q)> \sim q^{-(1+H)}, where H is the Hurst exponent of the self-affine fractal surface.