Large deformation frictional contact formulation based on a velocity description (original) (raw)

Abstract

A special contact formulation which is compatible with the so-called 'Solid-Shell' is developed for applications involving large deformation and frictional contact. The contact conditions are considered in the covariant form from the surface geometry point of view, which is very similar to shell theory. The contact integral and the necessary kinematical values are considered on the tangent plane of the contact surface for which a special surface coordinate system is introduced. A focus is on the regularization of the frictional conditions, which leads to evolutions equations in the form of covariant derivatives. A geometrical interpretation of these equations as the parallel translation is used to overcome the problem of discontinuity of the characteristics on element boundaries. The main advantage of the developments is a more algorithmic and geometrical structure of the tangent matrix. Different integration techniques based on higher order integration formulae as well as based on the subdivision of the contact area into subdomains allow to construct elements with diminishing error for the contact patch test in the non-frictional case. The segment-to-segment and the segment-to-analytical surface approaches are developed for the frictional problems with large sliding. Within the numerical examples the focus is also on the effect where a 3D continuum approach as e.g. for the solid-shell elements appears to be beneficial in the context with frictional contact.

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References (13)

  1. P. Wriggers, Vu Van, E. Stein. Finite element formulation of large deformation impact- contact problem with friction. Comp. Struct., vol. 37, pp. 319-331, 1990.
  2. T. A. Laursen and J. C. Simo. A continuum-based finite element formulation for the im- plicit solution of multibody large deformation frictional contact problems. Int. J. Numer. Methods Engng., vol. 35, pp. 3451-3485, 1993.
  3. H. Parisch and Ch. Lübbing. A formulation of arbitrarily shaped surface elements for three- dimensional large deformation contact with friction. Int. J. Numer. Methods Engng., 40, pp. 3359-3383, 1997.
  4. G. Pietrzak and A. Curnier. Large deformation frictional contact mechanics: continuum formulation and augmented Lagrangian treatment. Comp. Meth. Appl. Mech. Engng., vol. 177, pp. 351-381, 1999.
  5. L. Krstulovic-Opara, P. Wriggers, J. Korelc. A C 1 -continuous formulation for 3D finite deformation frictional contact. Comput. Mech., vol. 29, pp. 27-42, 2002.
  6. M. A. Puso and T. A. Laursen. A 3D contact smoothing method using Gregory patches. Int. J. Numer. Methods Engng., vol. 54, pp. 1161-1194, 2002.
  7. R. Hauptmann and K. Schweizerhof. A systematic development of solid-shell element formulations for linear and nonlinear analyses employing only displacement degrees of freedom. Int. J. Numer. Methods Engng., vol. 42, 49-70, 1998.
  8. R. Hauptmann, S. Doll, M. Harnau, K. Schweizerhof. 'Solid-Shell' elements with linear and quadratic shape functions at large deformations with nearly incompressible materials. Comp. Struct., vol. 79, 1671-1685, 2001.
  9. A. Konyukhov and K. Schweizerhof. Contact formulation via a velocity description allowing efficiency improvements in frictionless contact analysis. Comput. Mech., vol. 33, 165-173, 2003.
  10. P. Wriggers. Computational Contact Mechanics. John Wiley & Sons, 2002.
  11. T. A. Laursen. Computational Contact and Impact Mechanics. Springer, 2002.
  12. P. J. Davis and P. Rabinowitz. Methods of numerical integration. Academic Press, 1984.
  13. M.A. Crisfield. Re-visiting the contact patch test. Int. J. Numer. Methods Engng., 48:435- 449, 2000.