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

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