A new efficient numerical method for contact mechanics of rough surfaces

In this work, a numerical method has been developed to investigate the adhesionless contact mechanics between rough surfaces. To solve the elastic problem a boundary elements approach is used with self-equilibrated square elements. The domain of integration is discretized developing an “intelligent” adaptive mesh and obtaining a considerable memory saving. The numerical convergence of the method has been verified by comparing the results with the Hertzian solution and by checking the stress probability distribution at the contact interface. The methodology has been then utilized to analyse the contact between an elastic flat substrate and a periodic numerically generated self-affine fractal rigid surface. The fractal surface has been generated by employing spectral methods. The results of our investigation supports the findings of some analytical theories (Persson, 2001) and numerical findings (Yang et al., 2006; Hyun et al., 2004; Carbone and Bottiglione, 2008; Campana and Muser, 2007) in terms of linearity between contact area and load and stress probability distributions.