Numerical Analysis and Simulations of Quasistatic Frictionless Contact Problems

Contact phenomena among deformable bodies abound in industry and everyday life, and play an important role in structural and mechanical systems. The complicated surface structure, physics and chemistry involved in contact processes make it necessary to model them with highly complex and nonlinear initial-boundary value problems. Indeed, the now famous Signorini problem was formulated as an idealized model of unilateral frictionless contact between an elastic body and a rigid foundation. The mathematical analysis of this problem was first provided by Fichera (1964). Duvaut and Lions, in their monograph (Duvaut and Lions, 1976), systematically modelled and analyzed many important contact problems within the framework of the theory of variational inequalities. Numerical approximations of variational inequalities arising from contact problems were described in detail in (Hlaváček et al., 1988), and in (Kikuchi and Oden, 1988). The mathematical, mechanical and numerical state of