Contact mechanics provides a basis for the study of many practical problems in the area of tribology. The foundation for the study of tribology is laid in contact mechanics. Contact mechanics was also instrumental in the formulation of geometrical continuum mechanics.
In the past, most elasticity analysts have focused on the deformation of solid bodies. As a consequence, the mechanical behavior of solids could be analyzed by applying the theories of linear elasticity and finite elasticity. In the early 1960s, it was noted that the interfaces of elastic solids could behave in a nonlinear manner. The theory of contact mechanics was thus developed to describe the nonlinear interface behavior of elastic solids. The theory of contact mechanics provided a framework for the nonlinear analysis of adhesion, friction, contact area, and deformation of solid bodies. The theory of contact mechanics was further developed to describe the nonlinear behavior of materials with memory and viscoelastic properties. In the 1980s, the nonlinear contact mechanics was further developed to consider the effect of plasticity on the mechanical behavior of solid bodies.
Contact mechanics is also related to frictional force. The force between a pair of rough surfaces in contact may be considered in two different ways: (1) as a sum of contributions due to single contacts, and (2) as a superposition of forces due to many contacts. The forces due to single contacts are evaluated by an effective contact area or by a contact stiffness. The summation of forces from many contacts is referred to as the contact torque.
Contact mechanics is now commonly used to study the effect of surface treatments, surface roughness, surface lubrication, and the surface adhesion of friction partners on the performance of mechanical systems.
The study of contact mechanics has led to some fundamental concepts in the theory of elasticity as well as to the formulation of geometrical continuum mechanics. The methods used for contact mechanics include the finite element method (based on the theory of finite elasticity), the boundary element method, and the boundary integral method, which were initially introduced by Struik in his book The equilibrium of plane elastic bodies (1960). The method based on the theory of finite elasticity is often used to solve contact problems that involve large deformations, while the two other methods are used for problems involving small or intermediate deformations.
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