Changing boundary conditions: contact problems

After detailed discussions of the three main sources of nonlinearity in a boundary value problem in mechanics, pertaining to kinematics, equilibrium and constitutive equations, we turn in this chapter to the studies of the last potential source of nonlinearity that concerns the changing boundary conditions. The problems of this kind are yet referred to as contact problems. The boundary conditions for contact problem are neither those of Dirichlet with imposed value of displacement, nor of Neumann with imposed traction, but rather the boundary conditions where we cannot impose the exact values other than the limitation (or constraint) that the displacements and/or traction should obey. One example of this kind is the unilateral contact, corresponding to a deformable body placed next to a rigid obstacle that cannot be penetrated and thus prevents the free deformation of the body under an arbitrary loading. We can also have a bilateral contact with two or more deformable solid bodies that enter in contact, or yet a self-contact where a body can undergo very large displacements and deformations which bring different parts of the body in contact with each other. All such contact problems are of great practical interest, and are discussed in this chapter.