Solving Frictional Contact Problems within the Bipotential Framework

Abstract:

The main objective of this paper is to present a theoretical and numerical analysis of frictional contact problems for large deformation elasto-plastic based on the finite element method (FEM) and the mathematical programming. The study is done on an elasto-plastic material obeying to the von Mises criterion. The Coulomb’s friction contact is used to implement the frictional boundary conditions and is formulated by the bipotential concept leading us to minimize only one variational principle of minimum in displacement. In order to follow up the sequences of large deformations, we have used the sequential analysis procedure; it consists in the updating of material properties and geometrical configuration after each sequence.

• Periodical: Key Engineering Materials (Volume 498)
• Pages: 55-66
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.498.55
• Online since: January 2012
• Authors: El Hassan Boudaia, Lahbib Bousshine, Ali Chaaba
• Keywords: Bipotential, Frictional Contact, Large Deformation, Mathematical Programming, Sequential Analysis

References

[1] N. Kikuchi and J.T. Oden, Contact problems in elasticity: A study of variational inequalities and finite elements, SIAM Philadelphia (1988).

DOI: 10.1137/1.9781611970845

[2] Z.H. Zhong, Finite element procedures in contact-impact problems, Oxford University Press (1993).

[3] P. Wriggers, Computational contact mechanics, Wiley New York (2002).

[4] T.A. Laursen, Computational contact and impact mechanics: fundamentals of modeling interfacial phenomena in nonlinear finite element analysis, Springer Berlin (2002).

[5] G. De Saxce and Z.Q. Feng: Math. Comput. Model., 28 (1998), p.225.

[6] T.A. Laursen and B.N. Maker: Inter. J. for Num. Meth. in Eng., 38 (1995), p.3571.

[7] T.A. Laursen and J.C. Simo: Inter. J. for Num. Meth. in Eng., 36 (1993), p.3451.

[8] T.A. Laursen and J.C. Simo: Computer Meth. in App. Mech. and Eng., 108 (1993), p.133.

[9] P. Wriggers: Comp. Meth. in Eng., 2, 4 (1995), p.1.

[10] A. Curnier: Inter. J. for Solids Structures, 20 (1984), p.637.

[11] D. Tabor: J. of Lubrication Tech., 103 (1981), p.169.

[12] A.A. Bandeira, P. Wriggers and P.M. Pimenta: 7th US Nat. Cong. on Comp. Mech., Albuquerque, New Mexico, USA (2003).

[13] A.A. Bandeira, P. Wriggers and P.M. Pimenta: European Conf. on Comp. Mech.: ECCM, Krakow, Poland (2001).

[14] J.C. Simo and T.A. Laursen: Computers & Struct., 42 (1992), p.97.

[15] M. Jean and G. Touzot, Journal of theoretical and applied mechanics, Special issue, supplement n°1 vol 7, (1988).

[16] E. Boudaia, L. Bousshine, A. Chaaba and G. De Saxsé: Inter. J. of App. Mech., Vol. 1, No. 4 (2009), p.1.

[17] G. De Saxce, and Z.Q. Feng: Mech. Struct. Mach., 19, 3 (1991), p.301.

[18] E. Boudaia, L. Bousshine, A. Chaaba, H.F. Fihri and G. De Saxsé: Mécanique & Industries, 10 (2009), p.487.

DOI: 10.1051/meca/2010008

[19] G. Dhatt and G. Touzot, Une présentation de la méthode des éléments finis, Maloine S.A. (1984).

[20] R.A. Murtagh and M.A. Saunders, Minos 5. 1 user's guide, Stanford University (1987).