Sharp contact problems are examined theoretically and numerically. The analysis is focused on elastic-plastic materials and, in particular, the behavior of global contact quantities, such as mean contact pressure and the size of the contact area, in the transition region where elastic and plastic effects are of equal magnitude. It is shown that under these circumstances, the global contact quantities can be correlated accurately using a single parameter, comprising both geometrical and mechanical properties, if the uniaxial stress-strain curve of the material is represented by the stress level(s) at appropriate value(s) of the accumulated plastic strain. From a practical point of view, the presented results are directly applicable to material characterization or measurements of residual mechanical fields by sharp indentation tests, but also for situations such as contact in gears or in electronic devices. The numerical analysis is performed by using the finite-element method.
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