A new approach to the analysis of problems of surface contact is postulated, which takes into account the discrete nature of the process, but allows the simplicity of continuum methods, where possible; this is termed the discrete-continuum approach. The method is shown by developing the solution of the problem of the nominal interfacial pressure distribution and real area of contact density for rotating nominally flat but rough circular surfaces. The method allows the mathematical statement of the transitions which occur with surface wear, and thereby constitutes a mathematical description of some aspects of run-in. The method and solution to the present problem give insight into the nature of the pattern of contacts, and are therefore expected to find application in surface-contact temperature theory and in electrical-contact resistance theory.

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