Hertzian contact in two and three dimensions

Abstract

The basic solution to the problem of mechanical contact between elastically deforming solids was proposed by Hertz over a century ago and has been used by tribologists and others ever since in a steadily increasing number of applications. While the theoretical development is not conceptually difficult and treatments exist to suit all tastes, it is nonetheless interesting to trace the relationships among the solutions in different dimensions. Such an approach is used herein to shed light on the curious and sometimes perplexing behavior of line contacts. A number of the more frequently used contact expressions together as a convenient reference and for comparative purposes.