Contact mechanics

Summary

Contact mechanics studies the deformation and the stresses of solid bodies that touch each other. Its basic difficulty is that the region of contact is not known in advance. It depends on the loads and the deformation, so the boundary conditions are unilateral inequalities. Classical results include Hertz's theory of elastic spheres and the Boussinesq problem of a point load on a half-space. Mathematically the subject leads to the Signorini problem and to variational inequalities. It is the basis of the design of bearings, gears, wheels on rails and of the study of friction and adhesion.