Variational and Numerical Theory of Contact

Abstract

The principle of virtual work and its dual, the principle of complementary virtual work, are the basis of many calculations in continuum mechanics. This also holds for the contact problem, which is a special kind of boundary value problem. In the past, the principles of virtual work and complementary virtual work for contact problems were derived for special constitutive relations such as linear elasticity and viscoelasticity (Fichera,1964; Duvaut-Lions, 1972), and nonlinear elastostatics (Kalker, 1977b). In Sec. 4.1 of this chapter, however, we derive these principles without any reference to the constitutive relations of the bulk material, in the manner of Bufler (1984), who confined himself to the normal contact problem, and Kalker (1986a). Here we confine ourselves to small deformations, and we present a new derivation.