This work examines the average pressure required to cause complete contact between sinusoidal shaped surfaces deforming elastically and plastically. Complete contact is defined as when there are no gaps remaining between the surfaces. The material of the surface is modeled as being elastic-perfectly plastic. This work confirms the results of a recent finite element analysis using a semi-analytical model. The results suggest that the pressure required to cause complete contact between surfaces can be much higher than the yield strength or hardness of the surface (in some cases 9 times the yield strength or more). This is because it appears that as the surfaces near complete contact, they begin to act again like an elastic contact. The critical amplitude of a sinusoidal surface below which it will deform entirely in the elastic regime from initial to complete contact is also derived.

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