Abstract

For a wide range of systems in structural mechanics, it is crucial to take into account contact and friction between rigid or elastic bodies. Among numerous applications, let us mention foundations in civil engineering, metal forming processes, crash tests of cars, and design of car tires (see, e.g., Wriggers 2002). Contact and friction conditions are usually formulated with a set of inequalities and nonlinear equations on the boundary of each body, with corresponding unknowns that are displacements, velocities, and surface stresses. Basically, contact conditions allow to enforce nonpenetration on the whole candidate contact surface, and the actual contact surface is not known in advance. A friction law may be taken into account additionally, and various models exist that correspond to different surface properties, the most popular one being Coulomb friction (see, e.g., Kikuchi and Oden 1988 and the references therein).

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