A MODEL OF PLOWING BY A PYRAMIDAL INDENTER - UPPER BOUND METHOD FOR STRESS-FREE SURFACES

The upper bound method is a convenient tool for modeling friction. In this method, a rigid/perfectly plastic material is assumed to move by rigid blocks around asperities, and velocities are allowed to have discontinuities along a few assigned planes which are the boundaries of the rigid blocks. The locations of these planes and frictional forces are found by the process of rate of work minimization. However, the method is strictly applicable only for problems where the configuration of the surface is known a priori. This restriction is often ignored in the literature. For the example of an asperity with a square-based pyramidal shape we examine the consequences and show that the error might be significant. We also develop an algorithm still employing this rigid block scheme, but where the shape of the pile-up in front of the asperity is determined on a rigorous basis. We give examples and comparisons with previous approximate solutions.