Gauging Persson Theory on Adhesion

In this work, we propose three amendments to Persson’s contact mechanics theory, the most important one being a modification of the way in which the stress distribution broadens with increasing resolution of random roughness features. The three adjustable coefficients of our treatment are gauged on existing reference data and tested against results of the contact mechanics challenge and a new set of data for adhesive slabs of finite width. Although the coefficients turn out to be of order unity, their problem-specific tuning is required to achieve highly accurate results, such as an essentially perfect dependence of contact area on load for non-adhesive, self-affine solids. Despite an overall convincing agreement between theory and full simulations, we find it to be intrinsically impossible to make the theory reflect the exact asymptotics of the stress distribution at small and large stresses. In addition, we find that the transition from small to large contact happens too abruptly with decreasing thickness of the elastic slab.