Contact mechanics

Contact problems are central to Solid Mechanics, because contact is the pri ncipal method of applying loads to a deformable body and the resulting stre ss concentration is often the most critical point in the body. Contact is c haracterized by unilateral inequalities, describing the physical impossibil ity of tensile contact tractions (except under special circumstances) and o f material interpenetration. Additional inequalities and/or non-linearities are introduced when friction laws are taken into account. These complex bo undary conditions can lead to problems with existence and uniqueness of qua si-static solution and to lack of convergence of numerical algorithms, In f rictional problems, there can also be lack of stability, leading to stick-s lip motion and frictional vibrations. If the material is non-linear, the solution of contact problems is greatly complicated, but recent work has shown that indentation of a power-law mate rial by a power law punch is self-similar, even in the presence of friction , so that the complete history of loading in such cases can be described by the (usually numerical) solution of a single problem. Real contacting surfaces are rough, leading to the concentration of contact in a cluster of microscopic actual contact areas. This affects the conduct ion of heat and electricity across the interface as well as the mechanical contact process. Adequate description of such systems requires a random pro cess or statistical treatment and recent results suggest that surfaces poss ess fractal properties that can be used to obtain a more efficient mathemat ical characterization. Contact problems are very sensitive to minor profile changes in the contact ing bodies and hence are also affected by thermoelastic distortion. Importa nt applications include cases where non-uniform temperatures are associated with frictional heating or the conduction of heat across a non-uniform int erface. The resulting coupled thermomechanical problem can be unstable, lea ding to a rich range of physical phenomena. Other recent developments are also briefly surveyed, including examples of anisotropic materials, elastodynamic problems and fretting fatigue. (C) 199 9 Published by Elsevier Science Ltd. All rights reserved.