A comparison of the mechanical behavior of microscopical contact models

An accurate modeling of the contact between solid bodies requires the knowledge of the constitutive laws of the interfaces. The structure of an interface law depends heavily on the detailed description of the topography. On the other hand, a major characteristic of any contact model concerns the set of assumptions needed to describe the mechanical interactions between surface elements at such small scales. In the field of contact mechanics devoted to nominally smooth surfaces, the literature provides several statistical models. Among them we cite the well known Greenwood and Williamson, and the Cooper, Mikic and Yovanovic one. All the models are based on a small amount of data. Such values are usually obtained with a statistical or a fractal characterization of the surfaces. When these models are applied to the same surface it is not obvious that they will give the same mechanical answer. This is more and more true when the models are tested considering a wide range of contact pressures. In the paper the prediction of the results, in terms of pressure-closure response as well as for all the relevant contact parameters are compared with results obtained by means of the direct simulations of the contact between representative elastic surfaces. The contacting surfaces selected for the numerical simulations are generated by means of a technique based on the self-affinity properties of real surfaces. The statistical properties of the generated surfaces can be evaluated and used as an input to the statistical models. The results of numerical simulations of contact between certain classes of surfaces are presented, with reference to data from literature. Some conclusions are drawn on the capabilities and the limits of each model.