Geodesic
Numerical Modelling of Contact Elastic-Plastic Flows
N. M. Bessonov1 ; S. F. Golovashchenko2 ; V. A. Volpert3
1 Institute of the Problems of Mechanical Engineering, 199178 St.Petersburg, Russia
2 Manufacturing Systems Department, Ford Research Laboratory, 481214 Dearborn, USA
3 Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France
Mathematical modelling of natural phenomena, Tome 4 (2009) no. 1, pp. 44-87

Voir la notice de l'article provenant de la source EDP Sciences

Wilkins' method has been successfully used since early 60s for numerical simulation of high velocity contact elastic-plastic flows. The present work proposes some effective modifications of this method including more sophisticated material model including the Baushinger effect; modification of the algorithm based on correction of the initial configuration of a solid; a contact algorithm based on the idea of a mild contact.
DOI : 10.1051/mmnp/20094103

N. M. Bessonov 1 ; S. F. Golovashchenko 2 ; V. A. Volpert 3

1 Institute of the Problems of Mechanical Engineering, 199178 St.Petersburg, Russia
2 Manufacturing Systems Department, Ford Research Laboratory, 481214 Dearborn, USA
3 Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France 
@article{10_1051_mmnp_20094103,
     author = {N. M. Bessonov and S. F. Golovashchenko and V. A. Volpert},
     title = {Numerical {Modelling} of {Contact} {Elastic-Plastic} {Flows}},
     journal = {Mathematical modelling of natural phenomena},
     pages = {44--87},
     publisher = {mathdoc},
     volume = {4},
     number = {1},
     year = {2009},
     doi = {10.1051/mmnp/20094103},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20094103/}
}
TY  - JOUR
AU  - N. M. Bessonov
AU  - S. F. Golovashchenko
AU  - V. A. Volpert
TI  - Numerical Modelling of Contact Elastic-Plastic Flows
JO  - Mathematical modelling of natural phenomena
PY  - 2009
SP  - 44
EP  - 87
VL  - 4
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20094103/
DO  - 10.1051/mmnp/20094103
LA  - en
ID  - 10_1051_mmnp_20094103
ER  - 
%0 Journal Article
%A N. M. Bessonov
%A S. F. Golovashchenko
%A V. A. Volpert
%T Numerical Modelling of Contact Elastic-Plastic Flows
%J Mathematical modelling of natural phenomena
%D 2009
%P 44-87
%V 4
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20094103/
%R 10.1051/mmnp/20094103
%G en
%F 10_1051_mmnp_20094103
N. M. Bessonov; S. F. Golovashchenko; V. A. Volpert. Numerical Modelling of Contact Elastic-Plastic Flows. Mathematical modelling of natural phenomena, Tome 4 (2009) no. 1, pp. 44-87. doi: 10.1051/mmnp/20094103

[1] G. Alfano, F. De Angelis, L. Rosati Computer Methods in Applied Mechanics and Engineering 2001 5123 5147

[2] F. Auricchio International Journal of Plasticity 1997 697 721

[3] F. Auricchio International Journal of Plasticity 2001 971 990

[4] F. Auricchio, R.L. Taylor Computer Methods in Applied Mechanics and Engineering 1997 175 194

[5] I.A. Balagansky, Yu.A. Karanik, V.A. Agureikin, A.V. Vinogradov, A.I. Balagansky Theoretical and applied fracture mechanics 2001 165 173

[6] R.R. Balokhonov, P.V. Makarov, V.A. Romanova, I.Yu. Smolin Computational Materials Science 1999 355 361

[7] E. Baron, M.B. Rubin, D.Z. Yankelevsky International Journal of Solids and Structures 2003 4519 4548

[8] J.B. Bdzil, D. S. Stewart, T. L. Jackson Journal of Computational Physics 2001 870 902

[9] D.J. Benson, L. Stainier Computer Methods in Applied Mechanics and Engineering 2000 571 590

[10] G. C. Bessette, E. B. Becker, L. M. Taylor, D. L. Littlefield Computer Methods in Applied Mechanics and Engineering 2003 1649 1679

[11] N.M. Bessonov, D.J. Song Journal of Computational Physics 2001 22 38

[12] N. Bessonov, S. Golovashchenko. Numerical simulation of pulsed electromagnetic stamping processes. Proceedings of 1st International Conference on High Speed Forming, Dortmund, Germany, 2004, 83-91.

[13] M. Brünig Computers & Structures 1998 117 128

[14] D. Chen, S.T.S. Al-Hassani, Z. Yin, Y. Yu International Journal of Solids and Structures 2001 8787 8803

[15] O.I. Cherepanov Theoretical and applied fracture mechanics 1999 189 202

[16] O.I. Cherepanov, I.Yu. Smolin, Yu.P. Stefanov, P.V. Makarov Computational Materials Science 1999 25 31

[17] P.W. Christensen Computer Methods in Applied Mechanics and Engineering 2002 1189 1219

[18] P.G. Ciarlet. Mathematical Elasticity, 1, Three Dimensional Elasticity. North-Holland, Amsterdam, 1993.

[19] G. Cocchetti, U. Perego Computer Methods in Applied Mechanics and Engineering 2003 4909 4927

[20] A. Düster, E. Rank International Journal for Numerical Methods in Engineering 2002 49 63

[21] N.A. Fellows, P.C. Barton International Journal of Impact Engineering 1999 793 811

[22] Z.Q. Feng, Z. Feng, M. Domaszewski International Journal of Non-Linear Mechanics 2002 1029 1036

[23] J. Fish, K. Shek International Journal for numerical methods in engineering 1999 839 851

[24] S. Golovashchenko N. Bessonov. Development of Sharp Flanging Technology for Aluminum Panels. Proceedings of the 6th International Conference on Numerical Simulation of 3D Sheet Forming Processes, NUMISHEET 2005, Detroit, MI, 687-690.

[25] S. Golovashchenko, N. Bessonov, R. Davies. Analysis of Blank-Die Contact Interaction in Pulsed Forming Processes. 3st International Conference on High Speed Forming, Germany, 2008.

[26] J. Guo, J.V. Cox Computers & Structures 2000 65 82

[27] Y.M. Gupta, J.L. Ding. Impact load spreading in layered materials and structures: concept and quantitative measure. International Journal of Impact Engineering, 27 (2002),, 277-291.

[28] E. Hoashi, T. Yokomine, A. Shimizu, T. Kunugi International Journal of Heat and Mass Transfer 2003 4083 4095

[29] B. P. Howell, G. J. Ball Journal of Computational Physics 2002 128 167

[30] L. Jing International Journal of Rock Mechanics and Mining Sciences 2003 283 353

[31] L. Jing, J. A. Hudson International Journal of Rock Mechanics and Mining Sciences 2002 409 427

[32] G.R. Johnson, S.R. Beissel International Journal of Impact Engineering 2001 911 925

[33] A.S. Khan, S. Huang, Continuum theory of plasticity. John Wiley Sons, New-York, 1995.

[34] S.P. Kiselev, V.P. Kiselev International Journal of Impact Engineering 2002 135 152

[35] A. Le Van, G. De Saxcae, P. Le Grognec Computers and Structures 2003 2099 2109

[36] M. Lee, Y.H. Yoo International Journal of Impact Engineering 2001 819 829

[37] Z.Y. Liu, S. Kubota, S. Itoh International Journal of Impact Engineering 2001 443 452

[38] V. A. Lubarda. Elastoplatcity theory, CRP Press, New York, 2000.

[39] L.X. Luccioni, J.M. Pestana, A. Rodriguez-Marek Computer Methods in Applied Mechanics and Engineering 2000 1827 1844

[40] M. Maenchen, S. Sack. The tensor code. In: B. Alder (Ed.), Methods in Computational Physics, Vol. 3, Academic Press, New-York, 1964, 181-210.

[41] R. Mahnken Computer Methods in Applied Mechanics and Engineering 2002 1611 1637

[42] P.V. Makarov, V.A. Romanova Theoretical and Applied Fracture Mechanics 2000 1 7

[43] P.V. Makaraov, S. Schmauder, O.I. Cherepanov, I.Yu. Smolin, V.A. Romanova, R.R. Balokhonov, D.Yu. Saraev, E. Soppa, P. Kizler, G. Fischer, S. Hu, M. Ludwig Theoretical and Applied Fracture Mechanics 2001 183 244

[44] J. P. Mariotti, J. M. Perlat International Journal of Impact Engineering 2003 717 741

[45] G. H. Miller, P. Colella Journal of Computational Physics 2001 131 176

[46] F.J. Montáns Computer Methods in Applied Mechanics and Engineering 2000 673 700

[47] S. K. Naboulsi, A. N. Palazotto International Journal of Plasticity 2003 435 468

[48] L. Noels, L. Stainier, J.-P. Ponthot International Journal of Solids and Structures 2004 663693

[49] P. Papadopoulos, J. Lu Computer Methods in Applied Mechanics and Engineering 2001 4889 4910

[50] A.N. Parshikov, S.A. Medin Journal of Computational Physics 2002 358 382

[51] V.L. Popov, A. Gervé, B. Kehrwald, I. Yu. Smolin Computational Materials Science 2000 285 291

[52] J.P. Ponthot International Journal of Plasticity 2002 91 126

[53] B.A. Roeder, C.T. Sun International Journal of Impact Engineering 2001 169 185

[54] V. Romanova, R. Balokhonov, P. Makarov, S. Schmauder, E. Soppa Computational Materials Science 2003 518528

[55] M. B. Rubin, S. R. Bodner International Journal of Solids and Structures 2002 5081 5099

[56] D. Sherman International Journal of Impact Engineering 2000 313 328

[57] C.H.M. Simha, S.J. Bless, A. Bedford International Journal of Impact Engineering 2002 65 86

[58] J. C. Simo, T. J. R. Hughes. Computational inelasticity. In: Interdisciplinary Applied Mathematics, Vol.7, 1998.

[59] I.Y. Smolin, P.V. Makarov, D.V. Shmick, I.V. Savlevich Computational Materials Science 2000 133 142

[60] S.C. Song, Z.P. Duan, D.W. Tan International Journal of Solids and Structures 2001 5215 5222

[61] J.B. Stevens, R.C. Batra International Journal of Plasticity 1998 841 854

[62] Y.P. Stefanov Theoretical and Applied Fracture Mechanics 2000 101 108

[63] H.H. Vaziri, J.S. Jalali, R. Islam International Journal of Solids and Structures 2001 3735 3757

[64] M. Wallin, A. Ristnmaa Computer Methods in Applied Mechanics and Engineering 2001 5583 5601

[65] M.L. Wilkins. Calculation of elastic-plastic flow. In: B. Alder (Ed.), Methods in Computational Physics, Vol. 3, Academic Press, New-York, 1964, 211-263.

[66] M.L. Wilkins. Calculation of elastic-plastic flow. In: B. Alder (Ed.), Numerical Methods in Hydrodynamics, translated from English, Mir, Moscow, 1967.

[67] M.L. Wilkins. Computer simulation of dynamic phenomena. Scientific Computation, Springer, 1998.

[68] M.L. Wilkins International Journal of Engineering Sciences 1978 793 807

[69] M.L. Wilkins Journal of Computational Physics 1980 291 303

[70] M.L. Wilkins. Modelling the behavior of materials. In: International Conference on Structural Impact and Crachworthiness, 1984, 243-277.

[71] M.L Wilkins, M.W. Guinan Journal of Applied Physics 1973 1200 1206

[72] M.L, Wilkins, M.W. Guinan. Plane stress calculations with a two dimensional elastic-plastic computer program. UCRL-77251. University of California, Lawrence Livermore Laboratory, (1976).

[73] K. Wünnemann, B.A. Ivanov Planetary and Space Science 2003 831 845

[74] F. Xiao Journal of Computational Physics 2004 629 654

[75] R. Zaera, S. Sánchez-Sáez, J.L. Pérez-Castellanos, C. Navarro Composites part A: Applied Science and Manufacturing 2000 823 833

Cité par Sources :