16. And Now What?

The most valuable aspect of the method of dimensionality reduction is the fact that it is a practical tool for many engineering applications. In several applications, such as the contact mechanics of axially-symmetric bodies, it provides exact results. In the case of the contact of randomly rough surfaces, the method provides asymptotically exact results (for very small and very large forces) and offers in the transitional domain a very good approximation, the accuracy of which exceeds that of the typically available values for material and surface parameters. In this chapter, we would like to discuss several ideas that are also only valid to the extent of “engineering accuracy,” but expand the possibilities of the method of dimensionality or can further simplify its application. At no point in this chapter will a claim to a final and ultimate truth be made. Our goal is much more to make the simulation possible to within a good approximation for instances in which simulations have not yet been possible.