On a Continuous Transfer of History Variables for Frictional Contact Problems Based on Interpretations of Covariant Derivatives as a Parallel Translation

Summary

Regularization methods based on the penalization of the tangent displacements are among the most exploited techniques in combination with finite element methods to model frictional interactions. Usually the global tangent displacements are described via convective coordinates which are e.g. used in a finite element discretization of the contact surface. These displacements serve to compute the tangent tractions in the case of sticking via a regularization procedure as well as in the case of sliding via a return-mapping scheme. The convective coordinates of the contact point as well as the corresponding tangent tractions are considered as history variables and have to be stored for each load step. In this contribution, we discuss the particular issue of continuous transfer for history variables in the case of large deformation problems adapted for the covariant contact description developed in Konyukhov and Schweizerhof [4]. Some specific examples are chosen to illustrate the effect of incorrect transfer for both non-frictional and frictional problems and, therefore, the necessity of the proposed techniques.