We investigate the normal contact stiffness in a contact of a rough sphere with an elastic half-space using 3D boundary element\r\ncalculations. For small normal forces, it is found that the stiffness behaves according to the law of Pohrt/Popov for nominally flat\r\nself-affine surfaces, while for higher normal forces, there is a transition to Hertzian behavior. A new analytical model is derived\r\ndescribing the contact behavior at any force.
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