A Numerical Three-Dimensional Model for the Contact of Rough Surfaces by Variational Principle

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Abstract
A new numerical method for the analysis of elastic and elastic-plastic contacts of two rough surfaces has been developed. The method is based on a variational principle in which the real area of contact and contact pressure distribution are those which minimize the total complementary potential energy. The present variational approach guarantees the uniqueness of the solution of the contact problem and significantly reduces the computation time as compared with the conventional matrix inversion method, and thus, makes it feasible to solve 3-D contact problem with large number of contact points. The model is extended to elastic-perfectly plastic contacts. The model is used to predict contact statistics for computer generated surfaces.