DOI QR코드

DOI QR Code

The stick-slip decomposition method for modeling large-deformation Coulomb frictional contact

  • Amaireh, Layla. K. (Applied Science University) ;
  • Haikal, Ghadir (Lyles School of Civil Engineering, Purdue University)
  • 투고 : 2018.05.24
  • 심사 : 2018.06.23
  • 발행 : 2018.10.25

초록

This paper discusses the issues associated with modeling frictional contact between solid bodies undergoing large deformations. The most common model for friction on contact interfaces in solid mechanics is the Coulomb friction model, in which two distinct responses are possible: stick and slip. Handling the transition between these two phases computationally has been a source of algorithmic instability, lack of convergence and non-unique solutions, particularly in the presence of large deformations. Most computational models for frictional contact have used penalty or updated Lagrangian approaches to enforce frictional contact conditions. These two approaches, however, present some computational challenges due to conditioning issues in penalty-type implementations and the iterative nature of the updated Lagrangian formulation, which, particularly in large simulations, may lead to relatively slow convergence. Alternatively, a plasticity-inspired implementation of frictional contact has been shown to handle the stick-slip conditions in a local, algorithmically efficient manner that substantially reduces computational cost and successfully avoids the issues of instability and lack of convergence often reported with other methods (Laursen and Simo 1993). The formulation of this approach, however, has been limited to the small deformations realm, a fact that severely limited its application to contact problems where large deformations are expected. In this paper, we present an algorithmically consistent formulation of this method that preserves its key advantages, while extending its application to the realm of large-deformation contact problems. We show that the method produces results similar to the augmented Lagrangian formulation at a reduced computational cost.

키워드

참고문헌

  1. Alart, P. and Curnier, A. (1991), "A mixed formulation for frictional contact problems prone to Newton like solution methods", Comput. Meth. Appl. Mech. Eng., 92, 353-375. https://doi.org/10.1016/0045-7825(91)90022-X
  2. Baillet, L. and Sassi, T. (2005), "Mixed finite element formulation in large deformation frictional contact problem", Revue Eur. des E lem. Fin., 14(2-3), 287-304.
  3. Bonet, J. and Wood. R.D. (2008), Nonlinear Continuum Mechanics for Finite Element Analysis, 2nd Edition, Cambridge.
  4. Burman, E., Hansbo, P. and Larson, M.G. (2017), Augmented Lagrangian and Galerkin Least Squares Methods for Membrane Contact, arXiv: 1711.04494.
  5. Bussetta, P., Marceau, D. and Ponthot, J.P. (2012), "The adapted augmented Lagrangian method: A new method for the resolution of the mechanical frictional contact problem", Comput. Mech., 49(2), 259-275. https://doi.org/10.1007/s00466-011-0644-z
  6. Chouly, F., Mlika, R. and Renard, Y. (2018), "An unbiased Nitsche's approximation of the frictional contact between two elastic structures", Numer. Mathemat., 139(3), 593-631. https://doi.org/10.1007/s00211-018-0950-x
  7. De Saxce, G. and Feng, Z.Q. (1998), "The bipotential method: A constructive approach to design the complete contact law with friction and improved numerical algorithms", Math. Comput. Modell., 28(4-8), 225-245. https://doi.org/10.1016/S0895-7177(98)00119-8
  8. Fischer, K.A. and Wriggers, P. (2006), "Mortar based frictional contact formulation for higher order interpolations using the moving friction cone", Comput. Meth. Appl. Mech. Eng., 195, 5020-5036. https://doi.org/10.1016/j.cma.2005.09.025
  9. Galvez, J., Cardona, A., Cavalieri, F. and Bruls, O. (2017), "An augmented Lagrangian frictional contact formulation for nonsmooth multibody systems", Proceedings of the ENOC 2017, Budapest, Hungary.
  10. Gholami, F., Nasri, M., Kovecses, J. and Teichmann, M. (2016), "A linear complementarity formulation for contact problems with regularized friction", Mech. Mach. Theory, 105, 568-582. https://doi.org/10.1016/j.mechmachtheory.2016.07.016
  11. Gu, Q., Barbato, M. and Conte, J.P. (2009), "Handling of constraints in finite-element response sensitivity analysis", ASCE J. Eng. Mech., 135(12), 1427-1438. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000053
  12. Hild, P. and Renard, Y. (2010), "A stabilized lagrange multiplier method for the finite element approximation of contact problems in elastostatics", Numer. Math., 115, 101-129.
  13. Ibrahimbegovic A. and Wilson, E.L. (1991), "Unified computational model for static and dynamic frictional contact analysis", Int. J. Numer. Meth. Eng., 34, 233-247.
  14. Ibrahimbegovic, A. (2009), Nonlinear Solid Mechanics: Theoretical Formulations and Finite Element Solution Methods, Springer.
  15. Laursen, T.A. and Simo, J.C. (1993a), "Algorithmic symmetrization of coulomb frictional problems using augmented Lagrangians", Comput. Meth. Appl. Mech. Eng., 108(1-2), 133-146. https://doi.org/10.1016/0045-7825(93)90157-S
  16. Laursen, T.A. and Simo J.C. (1993b), "A continuum-based finite element formulation for the implicit solution of multibody, large-deformation frictional contact problems", Int. J. Numer. Meth. Eng., 36(20), 3451-3485. https://doi.org/10.1002/nme.1620362005
  17. McDevitt, T.W. and Laursen, T.A. (2000), "A mortar-finite element formulation for frictional contact problems", Int. J. Numer. Meth. Eng., 48, 1525-1547. https://doi.org/10.1002/1097-0207(20000810)48:10<1525::AID-NME953>3.0.CO;2-Y
  18. Masud, A., Truster, T.J. and Bergman, L.A. (2012), "A unified formulation for interface coupling and frictional contact modeling with embedded error estimation," Int. J. Numer. Meth. Eng., 92(2), 141-177. https://doi.org/10.1002/nme.4326
  19. Mlika, R., Renard, Y. and Chouly, F. (2017), "An unbiased Nitsche's formulation of large deformation frictional contact and self-contact", Comput. Meth. Appl. Mech. Eng., 325, 265-288.
  20. Pietrzak, G. and Curnier, A. (1999), "Large-deformation frictional contact mechanics: Continuum formulation and augmented Lagrangian treatment", Comput. Meth. Appl. Mech. Eng., 177(3-4), 351-381. https://doi.org/10.1016/S0045-7825(98)00388-0
  21. Popp, A., Wohlmuth, B.I., Gee, M.W. and Wall, W.A. (2012), "Dual quadratic mortar finite element methods for 3D finite deformation contact", SIAM J. Sci. Comput., 34(4), B421-B446. https://doi.org/10.1137/110848190
  22. Puso, M.A. and Laursen, T.A. (2004), "A mortar segment-to-segment contact method for large deformation solid mechanics", Comput. Meth. Appl. Mech. Eng., 193, 601-629. https://doi.org/10.1016/j.cma.2003.10.010
  23. Sheng, D., Wriggers, P. and Sloan, S.W. (2006), "Improved numerical algorithms for frictional contact in pile penetration analysis", Comput. Geotech., 33(6-7), 341-354. https://doi.org/10.1016/j.compgeo.2006.06.001
  24. Sheng, D., Wriggers, P. and Sloan, S.W. (2007), "Application of frictional contact in geotechnical engineering", Int. J. Geomech., 7(3), 176-185. https://doi.org/10.1061/(ASCE)1532-3641(2007)7:3(176)
  25. Sheng. D., Yamamoto, H. and Wriggers, P. (2008), "Finite element analysis of enlarged end piles using frictional contact", Soils Foundat. Jap. Geotech. Soc., 48(1), 1-14. https://doi.org/10.3208/sandf.48.1
  26. Simo, J.C., Taylor, R.L. and Pister, K.S. (1985), "Variational and projection methods for the volume constraint in finite-deformation elasto-plasticity", Comput. Meth. Appl. Mech. Eng., 51, 177-208. https://doi.org/10.1016/0045-7825(85)90033-7
  27. Simo, J.C. and Laursen, T.A. (1992), "An augmented Lagrangian treatment of contact problems involving friction", Comput. Struct., 42(1), 97-116. https://doi.org/10.1016/0045-7949(92)90540-G
  28. Stefancu, A.I., Melenciuc, S.C. and Budescu, M. (2011), "Penalty based algorithms for frictional contact problems", Bullet. Polytech. Inst. Iasi-Constr. Architect., 61(3), 119.
  29. Terfaya, N., Berga, A. and Raous, M. (2015), "A bipotential method coupling contact, friction and adhesion", Int. Rev. Mech. Eng., 9(4).
  30. Vulovic, S., Zivkovic, M., Grujovic, N. and Slavkovic, R. (2007), "A comparative study of contact problems solution based on the penalty and lagrange multiplier approaches", J. Serb. Soc. Comput. Mech., 1(1), 174-183.
  31. Wriggers, P. (2006), Computational Contact Mechanics, 2nd Edition, Springer.
  32. Wriggers, P. and Zavarise, G. (1993), "On the application of augmented Lagrangian techniques for nonlinear constitutive laws in contact interfaces," Commun. Numer. Meth. Eng., 9(10), 815-824. https://doi.org/10.1002/cnm.1640091005