Analytical and Numerical Models for Tangential Stiffness of Rough Elastic Contacts

The paper considers elastic contact of rough surfaces and develops a simple analytical expression for the stiffness of the contact under tangential loading, which predicts that the contact stiffness is proportional to normal load and independent of Young??s Modulus. The predictions of this model are compared to a full numerical analysis of a rough elastic contact of finite size. The two approaches are found to be in good agreement at low loads, when the asperity spacing is large, but the numerical approach predicts much lower stiffnesses at medium and high loads. It is shown that the overall stiffness cannot exceed that of the equivalent smooth contact, and a simple means of modifying the analytical approach is proposed and validated.