On the validity of the method of reduction of dimensionality: area of contact, average interfacial separation and contact stiffness

Abstract

It has recently been suggested that many contact mechanics problems between solids can be accurately studied by mapping the problem on an effective one dimensional (1D) elastic foundation model. Using this 1D mapping we calculate the contact area and the average interfacial separation between elastic solids with nominally flat but randomly rough surfaces. We show, by comparison to exact numerical results, that the 1D mapping method fails even qualitatively. We also calculate the normal interfacial stiffness $K$ and compare it with the result of an analytical study. We attribute the failure of the elastic foundation model to the neglect of the long-range elastic coupling between the asperity contact regions.

5 pages, 4 figures, 29 references

References in corpus (6)

• Contact mechanics: relation between interfacial separation and load
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• Capillary adhesion between elastic solids with randomly rough surfaces
• Elastic contact between self-affine surfaces: Comparison of numerical stress and contact correlation functions with analytic predictions
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Cited by in corpus (2)

• Field-theoretical approach to estimate mean gap and gap distribution in randomly rough surface contact mechanics
• On the contact area and mean gap of rough, elastic contacts: Dimensional analysis, numerical corrections and reference data