On the Tangential Displacement of a Surface Point Due to a Cuboid of Uniform Plastic Strain in a Half-Space

The elastic solution of a tangentially loaded contact is known as Cerruti’s solution. Since the contact surfaces could be easily discretized in small rectangles of uniform shear stress the elastic problem is usually numerically solved by summation of well known integral solution. For soft metallic materials, metals at high temperature, rough surfaces, or dry contacts with high friction coefficient, the yield stress within the material could be easily exceeded even at low normal load. This paper presents the effect of a cuboid of uniform plastic strain in a half-space on the tangential displacement of a surface point. The analytical solutions are first presented. All analytical expressions are then validated by comparison with the finite element method. It is found that the influence coefficients for tangential displacements are of the same order of magnitude as the ones describing the normal displacement (Jacq et al., 2002, “Development of a Three-Dimensional Semi-Analytical Elastic-Plastic Contact Code,” ASME J. Tribol., 124(4), pp. 653–667). This result is of great importance for frictional contact problem when coupling the normal and tangential behaviors in the elastic-plastic regime, such as stick-slip problems, and also for metals and alloys with low or moderate yield stress.