On the accuracy of the Hertz model to describe the normal contact of soft elastic spheres

The finite element method is used to investigate the validity of the Hertz model for normal contact under conditions that violate some of the assumptions on which the Hertz model was derived. The conditions investigated are: frictional contact, non-flat contact surface and large strains. The investigations were performed for the case of two elastic spheres in contact as well as that of a sphere in contact with a flat plate. The existence of friction for normal contact does not appear to lead to any erroneous predictions of the force-deflection relationship by the Hertz model. The Hertz model also does not appear to predict significant errors when the contact surface is not flat. However, large strains were found to cause important prediction errors by the Hertz model. Calibration curves for the corrections on the Hertz model are proposed.