Physics-informed neural network approach to randomly rough surface contact mechanics

In this study, we employed the Green’s function molecular dynamics (GFMD) to simulate the non-adhesive contact between an elastic half-space and a rough counter face in \((1+1)\) dimensions, obtaining the contact stress distribution under varying length scales and Hurst exponents. Subsequently, based on the dataset generated by GFMD and adopting the diffusion equation form from Persson’s theory, we obtained the stress distribution as well as the relative contact area using Physics-informed neural network (PINN). The results demonstrate that in full contact case, the diffusion equation coefficient aligns almost perfectly with Persson’s theoretical prediction. In cases of partial contact, assuming the diffusion coefficient follows a power-law function of the length scale, the stress distribution predicted by PINN exhibits an error of less than \(0.5\%\) compared to GFMD. Furthermore, we verified that PINN can predict contact stress distribution and relative contact area at larger scales based on small-scale data, with predictions closely matching GFMD results.