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Large displacement frictional contact: A continuum framework for finite element discretization. (English) Zbl 0824.73061
Summary: The papers develops a continuum formulation of large displacement frictional contact of deformable bodies, which is suitable for finite element discretization. It is based on the construction of a particular type of convected coordinate system: an approach which is largely influenced by existing computational procedures. Objective measures of nearness of contact and relative tangential slip, which form the basis for a derivation of a virtual work principle, are given. It is pointed out that the virtual work of contact is objective only after the strong form of action and reaction is assumed. This imposes a rather restrictive requirement which has to be satisfied by any possible constitutive law. However, the combination of the classical laws of Coulomb and Signorini is admissible since these laws imply that contact force measures are different from zero only in exact physical contact. By combining these laws with the virtual work principle a mixed variational inequality formulation of the problem is given. Finally, the linearization of this formulation is prepared for by developing linearizations of the strain- like measures of contact interaction.

74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics