|Researchers have developed many models to simulate the elasto-plastic contact of spheres. However, there does not appear to exist a closed-form analytical model for elasto-plastic three dimensional sinusoidal contact. This work uses a finite element model (FEM) to characterize elasto-plastic sinusoidal contact. Although at initial contact the sphere and sinusoidal cases are very similar and can both be described by the classic elastic Hertz contact case, once the contact is pressed past a certain range of deformation the two cases are very different. The FEM model is used to produce equations which can be employed to approximately relate the area of contact to the contact pressure for elasto-plastic sinusoidal contact. The equations are obtained by fitting to the FEM results and existing elastic solutions to sinusoidal contact. An empirical expression for the average pressure which causes complete contact between elasto-plastic sinusoidal contacts was also developed. It is shown that required pressure for complete contact is significantly less in the elasto-plastic regime than the elastic regime. In addition, this pressure is shown to be greater than the traditional hardness, of .
One of the major motivations for this work was to generate a model that could be used in sinusoidal and frequency based rough surface contact models. A multiscale model is a non-statistical model and non-fractal that is used to describe normal contact between rough surfaces featuring multiple scales. The Empirical equations developed in the sinusoidal contact model are used to characterize asperity contact in the multiscale contact model. Based on this, predictions are made for contact area as a function of applied load. It was interesting to note that the real area of contact versus the applied load exhibits a linear relationship for both elastic and elasto-plastic cases up until the surface is completely flattened out. As expected, the real area of contact undergoing elasto-plastic deformation predicted by the multiscale model was higher than when the surface is undergoing elastic deformation. For a given applied load it was also found that the lower frequency ranges, as opposed to higher frequency ranges, dictated the predicted level of real contact area.