Nonhertzian contact: Geometric and computational issues

This talk will focus on some of the consequences that arise due to improvements that were made in such areas as surface characterization, materials development, power requirements and other technological advances, but primarily advances in computer hardware and software. These have led analysis from the arena of a closed-form solution of a single smooth contact (Hertz theory) to the semi-analytical analysis of rough contact, in which there may occur a large number of contacts due to the presence of many asperities. This paper will limit itself to the following aspects involved with contact that is not Hertzian: geometrical issues, friction, and finally, purely numerical issues that may relate to inelastic behavior. To illustrate how the development of high-speed computers enabled the solution of relatively complex problems, two specific examples are given. The first is the case of rough contact, which is solved by a combination of fast Fourier transform and some computer-enhanced methods. The second example is indentation of an inelastic body and calculation of residual stresses. Future research in contact mechanics will involve calculations at even smaller length scales that depend upon the ever-increasing computational speed and development of sensors to investigate materials at these scales.