On geometrically nonlinear contact problems with friction

Abstract The analysis of quasi-static contact problems applying an ‘updated’ respectively a ‘total Lagrangian’ formulation is extended in a way that frictional effects according to Coulomb's law are being incorporated into the incremental procedure which is closely related to the unit load method. Further novel aspects are to be found in the iterative computation of the tangential components of the stress distribution in the contact area due to various boundary conditions. The second part of the paper deals with the application of the nonlinear programming technique to problems with unilateral constraints. Using standard finite element techniques an ‘augmented Lagrangian’ is defined for a predeformed compressed rod. Neglecting frictional effects, the contact zones and the nodal contact forces between the deformed rod and lateral rigid objects are described by the Kuhn-Tucker conditions.