An Educational Elasticity Problem With Friction, Part 3: General Load Paths

Abstract

This concluding paper treats general load paths when the two components of the concentrated force are allowed to change independently with time. It is shown that there are two kinds of dependence on the load path. For certain directions of the forward tangent, the dependence is strict in that the deformations depend on the full details of the path. For other directions, however, the dependence is loose, and the deformations do not depend on the exact nature of the path as long as the forward tangent falls within given bounds. The problem also shows that, given an initial state, the load space can be subdivided into different regions each corresponding to a certain mode of deformations.