The contact problem and stress state for indentation by a flat punch with rounded edges is studied. For the contact problem itself analytical solutions are obtained for both surface pressure and interior stress fields. Cases of normal indentation and frictional contact, the latter in both sliding or partial slip conditions, are all treated.<br/>The transition from the Hertzian configuration to the contact between a nominally flat pad and contacting flat surface is discussed, and it is found that the strength of the contact decays surprisingly slowly. Regarding the von Mises yield parameter, there is a range of configurations for which the strength is actually higher than the Hertzian one, and the strength decays only when the corner radii are very small. The present solution is therefore a realistic alternative to the classical rigid-flat punch idealization, and has particular application to fretting fatigue tests
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