The generalized Cattaneo partial slip plane contact problem. I - Theory

The Cattaneo problem is considered for a general plane contact between elastically similar materials, i.e. a monotonically increasing tangential load, starting from zero, with normal loading held fixed. Instead of the classical argument on the displacement field in the stick zone of Cattaneo solution, we attack the problem implicitly from the governing integral equations in the stick zones. After discussing and solving the full-stick case, we move to the more realistic (for finite friction) case of partial slip. We show that, upon isolating the effect of full sliding, the equalities and inequalities governing the corrective solution for the corrective shearing tractions in the stick zone are exactly the same as those governing the solution of the normal contact problem with a lower load, but the same rotation as the actual one. This analogy permits us to deduce several general properties, and gives a general procedures for solving partial slip Cattaneo problems as frictionless normal indentation ones. Therefore, the general solutions for single, multiple and periodic contacts is given. A comprehensive set of explicit results is given in the part II of the paper. (C) 1998 Elsevier Science Ltd. All rights reserved.