An analysis of three-dimensional elasto-plastic sinusoidal contact

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 case are very similar and can both be described by the classic elastic Hertz contact case, once the contact is pressed past a critical range of deformation the two cases are very different. The model produces equations which can be used to approximately relate the area of contact to the contact pressure for elasto-plastic sinusoidal contact. The equations are fit 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 is also provided.