Frictional contact mechanics

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. This can be divided into compressive and adhesive forces in the direction perpendicular to the interface, and frictional forces in the tangential direction. Frictional contact mechanics is the study of the deformation of bodies in the presence of frictional effects, whereas frictionless contact mechanics assumes the absence of such effects.

Frictional contact mechanics is concerned with a large range of different scales.

This page is mainly concerned with the second scale: getting basic insight in the stresses and deformations in and near the contact patch, without paying too much attention to the detailed mechanisms by which they come about.

Several famous scientists,engineers and mathematician contributed to our understanding of friction. They include Leonardo da Vinci, Guillaume Amontons, John Theophilus Desaguliers, Leonhard Euler, and Charles-Augustin de Coulomb. Later, Nikolai Pavlovich Petrov, Osborne Reynolds and Richard Stribeck supplemented this understanding with theories of lubrication.

Deformation of solid materials was investigated in the 17th and 18th centuries by Robert Hooke, Joseph Louis Lagrange, and in the 19th and 20th centuries by d’Alembert and Timoshenko. With respect to contact mechanics the classical contribution by Heinrich Hertz stands out. Further the fundamental solutions by Boussinesq and Cerruti are of primary importance for the investigation of frictional contact problems in the (linearly) elastic regime.

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