journal article·2020-09Open access

Combined sticking: a new approach for finite-amplitude Coulomb frictional contact

P. Areias, F. Queirós de Melo, J. Carrilho Lopes

Abstract

Engineering-level accuracy of discretization methods for frictional contact originates from precise representation of discontinuous frictional and normal interaction laws and precise discrete contact techniques. In terms of discontinuous behavior in the quasi-static case, two themes are of concern: the normal interaction (i.e. impact) and the jumps in tangential directions arising from high frictional values. In terms of normal behavior, we use a smoothed complementarity relation. For the tangential behavior, we propose a simple and effective algorithm, which is based a stick predictor followed by corrections to the tangential velocity. This allows problems with impact and stick-slip behavior to be solved with an implicit code based on Newton–Raphson iterations. Three worked examples are shown with comparisons with published results. An extension to node-to-face form in 3D is also presented.
Source: openaire · Quality: candidate unverified · Source record ↗

Research context

OpenAlex topics: Mechanical stress and fatigue analysis · Contact Mechanics and Variational Inequalities · Adhesion, Friction, and Surface Interactions

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (31)

Show source-provided references
1. Alart, P., Curnier, A.: A mixed formulation for frictional contact problems prone to Newton like methods. Comput. Methods Appl. Mech. 92, 353–375 (1992)10.1016/0045-7825(91)90022-X ↗
2. Amontons, G.: Sur les frottements des machines. Académie Royale des Sciences, Paris, France, Troiséme (1732) edition, pp. 104–109 (1699)
3. Anitescu, C., Atroshchenko, E., Alajlan, N., Rabczuk, T.: Artificial neural network methods for the solution of second order boundary value problems. CMC: Comput. Mater. Continua 59(1), 345–359 (2019)10.32604/cmc.2019.06641 ↗
4. Areias, P.: Simplas. http://www.simplassoftware.com . Portuguese Software Association (ASSOFT) registry number 2281/D/17
5. Areias, P.: Finite element technology, damage modeling, contact constraints and fracture analysis. Doutoramento, FEUP - Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias s/n 4200-465 Porto, Portugal (2003). www.fe.up.pt
6. Areias, P.: 3D contact source code. https://github.com/PedroAreias/Contact3DElement/tree/master (2018)
7. Areias, P., César de Sá, J.M.A., Conceição António, C.A.: Algorithms for the analysis of 3D finite strain contact problems. Int. J. Numer. Methods Eng. 61, 1107–1151 (2004)10.1002/nme.1104 ↗
8. Areias, P., Pinto da Costa, A., Rabczuk, T., Queirós de Melo, F.J.M., Dias-da Costa, D., Bezzeghoud, M.: An alternative formulation for quasi-static frictional and cohesive contact problems. Comput. Mech. 53, 807–824 (2014)10.1007/s00466-013-0932-x ↗
9. Areias, P., Rabczuk, T., Queirós de Melo, F.J.M., César de Sá, J.: Coulomb frictional contact by explicit projection in the cone for finite displacement quasi-static problems. Comput. Mech. 55(1), 57–72 (2015)10.1007/s00466-014-1082-5 ↗
10. Chen, C., Mangasarian, O.L.: Smoothing methods for convex inequalities and linear complementarity problems. Math. Program. 71(1), 51–69 (1995)10.1007/BF01592244 ↗
11. Chen, C., Mangasarian, O.L.: A class of smoothing functions for nonlinear and mixed complementarity problems. Comput. Optim. Appl. 5, 97–138 (1996)10.1007/BF00249052 ↗
12. Coulomb, C.-A.: Théorie des machines simples, en ayant égard au frottement de leurs parties et à roideur des cordages. Imprimerie de Huzard-Courcier, Rue du Jardinet, No 12, Paris, France, Nouvelle Édition edition (1821)
13. De Saxcé, G., Feng, Z.-Q.: The bipotential method: a constructive approach to design the complete contact law with friction and improved numerical algorithms. Math. Comput. Model. 28(4–8), 225–245 (1998)10.1016/S0895-7177(98)00119-8 ↗
14. Kanno, Y., Martins, J.A.C., Pinto da Costa, A.: Three-dimensional quasi-static frictional contact by using second-order cone linear complementarity problem. Int. J. Numer. Methods Eng. 65, 62–83 (2006)10.1002/nme.1493 ↗
15. Khenous, H.B., Laborde, P., Renard, Y.: Mass redistribution method for finite element contact problems in elastodynamics. Eur. J. Mech. A/Solids 27, 918–932 (2008)10.1016/j.euromechsol.2008.01.001 ↗
16. Kikuchi, N., Oden, J.T.: Contact Problems in Elasticity. A Study of Variational Inequalities and Finite Element Methods. volume 8 of SIAM Studies in Applied and Numerical Mathematics. SIAM Studies in Applied Mathematics, Philadelphia (1988)10.1137/1.9781611970845 ↗
17. Korelc, J.: Multi-language and multi-environment generation of nonlinear finite element codes. Eng. Comput. 18(4), 312–327 (2002)10.1007/s003660200028 ↗
18. Laursen, T.A.: Computational Contact and Impact Mechanics. Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis. Springer, Berlin (2002)
19. Martins, J.A.C., Simões, F.M.F., Gastaldi, F., Monteiro Marques, M.D.P.: Dissipative graph solutions for a 2 degree-of-freedom quasistatic frictional contact problem. Int. J. Eng. Sci. 33(13), 1959–1986 (1995)10.1016/0020-7225(95)00039-Z ↗
20. Pennestri, E., Rossi, V., Salvini, P., Valentini, P.P.: Review and comparison of dry friction force models. Nonlinear Dyn. 83, 1785–1801 (2016)10.1007/s11071-015-2485-3 ↗
21. Puso, M.A., Laursen, T.A.: A mortar segment-to-segment contact method for large deformation solid mechanics. Comput. Methods Appl. Mech. 193, 601–629 (2004a)10.1016/j.cma.2003.10.010 ↗
22. Puso, M.A., Laursen, T.A.: A mortar segment-to-segment frictional contact method for large deformations. Comput. Methods Appl. Mech. 193, 4891–4913 (2004b)10.1016/j.cma.2004.06.001 ↗
23. Raous, M., Chabrand, P., Lebon, F.: Numerical methods for frictional contact problems and applications. J. Theor. Appl. Mech. 7(Suppl. 1), 111–128 (1988)
24. Refaat, M.H., Meguid, S.A.: On the modeling of frictional contact problems using variational inequalities. Finite Elem. Anal. Des. 19(1–2), 29–101 (1995)
25. Simo, J., Laursen, T.: An augmented Lagrangian treatment of contact problems involving friction. Comput. Struct. 42, 97–116 (1992)10.1016/0045-7949(92)90540-G ↗
26. Simo, J.C., Taylor, R.L., Pister, K.S.: Variational and projection methods for the volume constraint in finite deformation elasto-plasticity. Comput. Methods Appl. Mech. 51, 177–208 (1985)10.1016/0045-7825(85)90033-7 ↗
27. Stewart, D.E.: Finite-dimensional contact mechanics. Philos. Trans. R. Soc. A 359, 2467–2482 (2001)10.1098/rsta.2001.0904 ↗
28. Wolfram Research Inc. Mathematica. Champaign, IL (2007)
29. Wriggers, P.: Computational Contact Mechanics. Wiley, New York (2002)
30. Wriggers, P., Haraldsson, A.: A simple formulation for two-dimensional contact problems using a moving friction cone. Commun. Numer. Methods Eng. 19, 285–295 (2003)10.1002/cnm.590 ↗
31. Zavarise, G., De Lorenzis, L.: The node-to-segment algorithm for 2D frictionless contact: classical formulation and special cases. Comput. Methods Appl. Mech. 198, 3428–3451 (2009)10.1016/j.cma.2009.06.022 ↗