The asperities of rough surfaces have long been considered to be points higher than their immediate neighbors. Based on this concept, theories were developed for quantitatively understanding the elastic and plastic nature of contact between rough surfaces. Recently it has been recognized that the above model for asperities is inadequate. Consequently, all the models that have been constructed based on that model are inadequate too. In this paper, based on a newly developed multiple-point asperity model, the elastic and plastic contact problem between nominally flat surfaces is reformulated. This leads to finding the deformed area, and load produced by the contact. The model is developed for the general form of isotropic rough surfaces with arbitrary height distribution and autocorrelation function (ACF). The microcontact areas generated by each asperity contact are considered to be circles. The Gaussian distribution of heights and exponential ACF are considered as a benchmark to compare the results of the new model with the existing models. Using results from numerical models developed by other groups, the new model is validated.

For several decades, asperities of nominally flat rough surfaces were considered to be points higher than their immediate neighbors. Recently, it has been recognized that this model is incorrect. To address the issue, a new multiple-point asperity model, called the n-point asperity model, is introduced in this paper. In the new model, asperities are composed of n neighboring sampled points with n-2 middle points being above a certain level. When the separation between two surfaces decreases, new asperities with higher number of sample points, n, will come into existence. Based on the above model, the height and curvature of n-point asperities are defined and their distributions are found. The model is developed for Gaussian surfaces and for the general case of an autocorrelation function (ACF). As a case study, the exponential ACF is applied to the new model, which is shown to produce remarkably good agreement with measurements from real and simulated surfaces.

Stiction, a term commonly used in micro electro-mechanical systems (MEMS) to refer to adhesion, is a major failure mode in MEMS. Undesirable stiction, which results from contact between surfaces, can severely compromise the reliability of MEMS. In this paper, a model is developed to predict the dry stiction between uncharged micro parts in MEMS. In dry stiction the interacting surfaces are assumed to be either hydrophobic or placed in a dry environment. In this condition the van der Waals (vdW) and asperity deformation forces are dominant. Here a model is developed for the vdW force between rough micro surfaces, and the new model is combined with a newly developed multiple asperity point model for the elastic/plastic deformation of rough surfaces in contact to solve the equilibrium condition of the forces. This in turn will yield the equilibrium distance between micro surfaces, using which the apparent work of adhesion can be found. The theory result is compared with the available experimental data from the literature. The developed model can be easily used for design purposes. If the topographic data and material constants are known, the desirable adhesion parameters can be quickly found from the model.

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