1. Model: Sliding Wedge

2. Introduction This is a NAFEMS benchmark model which treats the behavior of a contactor wedge forced to slide over a stiff target wedge surface. The model includes contact and friction forces at the interface. This is a large sliding problem and requires large deformation analysis.

3. The 2D plane strain application is used to model the wedge. Problem Definition N F K G Contact interface Contactor wedge

4. Problem Definition, Constraints, and Loads. A distributed total gravity load G=3058 N is applied on the contactor wedge. The left vertical edge is subjected to a positive load F=1500 N which forces the wedge to move in the positive x-direction. A spring with a spring constant K (a displacement dependent force) is also added to this boundary. This spring prevents the model from sliding away.

5. Problem Definition, Constraints, and Loads. Contact forces: –Displacement dependent expressions are used to model the normal contact force F n. –where gap is the distance in normal direction between the contactor wedge and the stiff target wedge surface. –t n is an estimate of the contact pressure at gap=0 –e n is the penalty stiffness

6. Friction forces –Displacement dependent expressions are also used to model the frictional force F t : where u t is the displacement in the tangential direction of the surface between the contactor wedge and the stiff target wedge surface.  is the friction coeffcient K t is a high spring stiffness resulting in a small (negligible) deformation during stick. Problem Definition, Constraints, and Loads. Stick condition Slip condition if

7. Elastic properties: E=206 GPa and =0.3 Problem Definition, Material

8. Results For each friction coefficient an overall analytical spring stiffness K is calculated so that the analytical x-displacement is restricted to 1.0 m. Excellent agreement with benchmark values is reached. Friction coefficient  Overall spring stiffness K Calculated x-displacement by COMSOL Multiphysics 01194 N/m1.0 m 0.1882 N/m1.0 m 0.2563.9 N/m1.0 m