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Atomistic simulations are used to test the equations of continuum contactmechanics in nanometer scale contacts. Nominally spherical tips, made bybending crystals or cutting crystalline or amorphous solids, are pressed into aflat, elastic substrate. The normal displacement, contact radius, stressdistribution, friction and lateral stiffness are examined as a function of loadand adhesion. The atomic scale roughness present on any tip made of discreteatoms is shown to have profound effects on the results. Contact areas, localstresses, and the work of adhesion change by factors of two to four, and thefriction and lateral stiffness vary by orders of magnitude. The microscopicfactors responsible for these changes are discussed. The results are also usedto test methods for analyzing experimental data with continuum theory todetermine information, such as contact area, that can not be measured directlyin nanometer scale contacts. Even when the data appear to be fit by continuumtheory, extracted quantities can differ substantially from their true values

Contact of single asperities with varying adhesion: Comparing continuum mechanics to atomistic simulations