On the adhesion of sinusoidal surfaces

In this work, we study the adhesive loading and unloading of a one-dimensional sinusoidal surface and use design of experiments to provide for response surface maps for the work of adhesion and the interaction length, which depend only on Johnson's alpha parameter and the Maugis parameter mu. As showcased by some example, these can be used to replace the fine scale roughness by a cohesive zone model. Besides that, we provide ranges of alpha and mu in which the most common analytical solutions present accurate results. Finally, we characterize the presence of instabilities in the loading and unloading profiles.