Contact deformation of bodies
As a result of contact interaction of bodies there is deformation of their surfaces which is called as contact deformation. Contact deformation practically does not have an influence on physical and chemical processes occurring in contact. However the elastic compliance of surfaces defines contact pressure which makes essential impact on these processes.
If the sizes of area of contact of bodies are small in comparison with characteristic radiuses of curvature of adjoining surfaces then at calculation of elastic displacement of surfaces at the set distribution of contact pressure it is possible with sufficient accuracy to consider these surfaces as flat and to use decisions of problems of the theory of elasticity for the medium limited to a plane. Such assumption is possible at calculation of some tooth gearings and rolling-contact bearings.
In the Cartesian system of co-ordinates the displacement along an axis of a point of the homogeneous elastic medium limited to the plane, under the influence of the pressure applied to its free surface, is defined under the formula 
Here and are Young’s module and Poisson’s ratio accordingly, is domain in which pressure is distributed. If domain represents a strip, and pressure does not depend from, that is, then 
If the sizes of domain of contact of bodies are commensurable with characteristic radius of curvature of adjoining surfaces that, for example, takes place in sliding bearings then calculation of contact deformations consists in the decision of corresponding problems of the theory of elasticity.