Etats limites plastiques en présence de l’écrouissage isotrope
DOI:
https://doi.org/10.13052/EJCM.18.525-545Keywords:
limit analysis, strain hardening, mathematical programming, inite element methodAbstract
Either in Structural Engineering or Metalworking processes by plastic deformation, the limit analysis is among the direct methods of the plastic collapse assessment. Basing on the kinematical approach in the sense of limit analysis and using finite elements method, the main objective of this work is to deal with large plastic deformations of von Mises’s materials taking into account isotropic hardening. In order to overcome difficulties caused by the non differentiability of plastic dissipation, we adopt a regularization method originally developed for compressible materials. In order to follow up the sequences of large deformations, we have used the sequential limit analysis procedure; it consists in the updating of material properties and geometrical configuration after each sequence.
Downloads
References
Avitzur B., Metal forming: Processes and Analysis, McGraw-Hill, New York, 1968.
Avitzur B., Handbook of Metal forming Processes, Wiley, New York, 1983.
Bousshine L., Chaaba A., de Saxcé G. et Guerlement G., « Etat limite des métaux rigides
parfaitement plastique par l’analyse limite et la méthode des éléments finis », Les cahiers
de la recherche, série A : Sciences et Techniques, vol. 4, Septembre, 2002, p. 145-160.
Bousshine L., Chaaba A. et de Saxcé G., “Plastic limit load of frictional contact supports
plane frames”, lnt. Jour. of Mech. Sci., November 2002, vol. 44, p.2189-2216.
Capsoni A. et Corradi L., “A finite element formulation of the rigid plastic limit analysis
problem”, Int. Jour. Num. Engng, vol. 40, p. 2063-2086.
Chaaba A., Bousshine L. et de Saxcé G., “Kinematic limit analysis modelling of rigid
perfectly plastic material by a regularisation approach and finite element method”,
International Journal for Numerical Methods in Engineering, 2003, 57, p. 1899-1922.
Chaaba A. Analyse limite des métaux et des matériaux granulaires par la théorie du
bipotentiel. Formulation éléments finis et applications, Thèse de Doctorat en Sciences
Appliquées, ENSEM de Casablanca, Janvier, 2001.
Chen W.F. Limit analysis and Soil Plasticity, Elsevier, New York, 1975.
Corradi L., Panzeri N. “A triangular finite element for sequential limit analysis of shells”,
Advances in Engineering software, 35, 2004, p. 633-643.
De Saxcé G. et Bousshine L., “Limit Analysis Theorems for Implicit Standard Materials:
Application to the unilateral Contact with Dry Friction and Non-associated flow Rules in
Soils and Rocks”, lnt. Jour. Mech. Sci., 1998, vol. 40, n° 4, p. 387-398.
Drucker D.C., Greenberg, H.J. et Prager W., “The safety factor of an elastic-plastic body in
plane strain”, J. Appl. Mech., 18, 1951, p. 371-378.
Drucker D.C., Prager W. et Greenberg, H.J., “Extended limit design theorems for constitutive
media”, Quart. Appl. Math., 9, 1952, p. 381-389.
Fassi-Fihri H., Bousshine L., Elharif A. et Chaaba A., « Analyse élastoplastique des métaux
en présence du contact unilatéral avec frottement sec de Coulomb », Les cahiers de la
recherche, série A : Sciences et Techniques, vol. 4, Septembre, 2004, p. 145-160.
Fassi Fihri H., Bousshine L., Chaaba A. et Elharif A., “Numerical simulation of orthogonal
metal cutting by incremental elastoplastic analysis and finite element method”, Journal of
Material Processing Technology, 141, 2003, p. 181-188.
Friaâ A., Le matériau de Norton-Hoff généralisé et ses applications en analyse limite, C.R.
Acad. Sci. Paris, t. 286, Série A, pp. 953-956, 1978.
Friaâ A., La loi de Norton–Hoff généralisée en plasticité et viscoplasticité, Thèse de Doctorat
d’État, Paris VI, 1979.
Gaudrat V.F. “A Newton type algorithm for plastic limit analysis”, Computer Methods in
Applied Mechanics and Engineering, vol. 88, n° 2, July 1991, p. 207-224.
Greenberg H.J. et Prager W., “Limit Design of beams and frames”, Proc. ASCE, vol. 77,
n° 59, 1951.
Guennouni A. T., Matériau de Norton-Hoff pour divers critères de plasticité de mécanique
des sols, Thèse de Doctorat, ENPC, Paris, 1982.
Guennouni A. T., Letallec P., « Calcul à la rupture: Régularisation de Norton-Hoff et
lagrangien augmenté », J. Mé. Théorique et Appliquée, vol. 2, n° 1, 1982.
Halphen B. et Salençon J., Elsatoplasticité, Presse de l’Ecole Nationale des Ponts et
Chaussées, 1987.
Hill R., “On the state of stress in a plastic-rigid body at the yield point”, Phil. Mag., vol. 7,
n° 42, 1951, p. 868-875.
Hill R., “On note on estimating yield-point loads in a plastic-rigid body”, Phil. Mag. vol. 7,
n° 43, 1952, p. 353-355.
Hill R., The mathematical Theory of Plasticity, Oxford Sciences publications, 1950.
Horne MR, Merchant W., The stability of frames, London, Maxwell, 1965.
Huh H., Kim K.P. et Kim H.S., “Collapse simulation of tubular structures using a finite
element limit analysis approach and shell elements”, Int Jour. of Mech. Sci., 2001, 43
p. 2171-2187.
Huh H., Lee C.H. et Yang W.H., “A general algorithm for plastic flow simulation by finite
element analysis”, lnt. Jour. Solids and Structures, 1999, 36, p. 1193-1207.
Hwan C. L., Large plastic deformation by sequential limit analysis : A finite element
approach with application in metal forming, Ph.D. Thesis, University of Michigan, 1992.
Jiang G.L., Application de l’analyse limite à l’étude de la stabilité des massifs de sol, Thèse
de Doctorat de l4ENPC, Septembre, 1992, Paris.
Johnson W., Sowerby R. et Venter R.D., Plane-Strain Slip-Line Fields For Metal-
Deformation Processes, Pergamon Press, 1982.
Jospin N.D., Etats limites des coudes par la méthode des éléments finis et la programmation
mathématique, Thèse de Doctorat en Sciences Appliquées, Université de Liège. 1992.
Kim Y.J. et Yang D.H. “A formulation for rigid-plastic finite element method, considering
work-hardening effect”, Int. J. Mech. Sci., 27 1985, p. 487-495.
Kobayashi S., Oh S. I. et Altan T., Metal forming and the finite element method, Oxford
Univ. Press, 1989.
Koiter W.T., “General Theorems for elastic-plastic solids”, Progress in solid mechanics,
vol. I, Sneddon & Hill. ed., North Holland, 1960, p. 163-221.
Lee C. H. And Kobayashi S., “New solutions to rigid-plastic deformations problems using a
matrix method”, Transactions of the ASME, J. Eng. Ind., 95, 1973, p. 865-886.
Lemaître J. et Chaboche J.L., Mechanics of solid materials, Cambridge University Press,
Cambridge, 1990.
Leu S. Y., “Limit analysis of strain-hardening viscoplastic cylinders under internal pressure
by using the velocity control: Analytical and numerical investigation”, International
journal of Mechanical Sciences, 50, 2008, p. 1578-1585.
Leu S. Y., “Analytical and numerical investigation of strain-hardening vicscoplastic thickwalled
cylinders under internal pressure using sequential limit analysis”, Compu. Methods
Appl. Mech Engrg., 196, 2007, p. 2713-2722.
Lung M. et Marenholtz O., “A finite element procedure for analysis of metal forming
process”, Transactions of the CSME, 2, 1974, p. 31-36.
Mercier B., « Sur la théorie et l’analyse numérique de problèmes de plasticité », Thèse d’Etat,
Université, Paris VI, 1977.
Moreau J. J., « Proximité et dualité dans un espace Hilbertien », Bull. Soc. Math., France, 93,
, p. 273-299.
Mori K., Osakada K. et Oda T. “Simulation of plane strain rolling by the rigid-plastic finite
element method”, Int. J. Mech. Sci., 24, 1982, 519.
Murtagh RA., et Saunders M.A., Minos 5.1 user’s guide, Stanford University, 1987.
Nagtegaal J.C., et De Jong J.E., “Some computational aspects of elastic-plastic large strain
analysis”, Int. J. Num. Meth. Eng., 17, 1981, p. 15-41.
Ponter A.R.S., “Carter K.F. Limit state solutions, based upon linear solutions with a spatially
varying elastic modulus”, Meth. Appl. Mech. Eng., 140, 1997, p. 237-258.
Ponter R.S., Fuschi P. et Engelhart M., “Limit analysis for a general class of yield
conditions”, Eur J Mech A/Solids, 2000, 19, p. 401-21.
Prager W., “The general theory of limit design”, Proc., 8th Int. Congress Appl. Mech., vol. 2,
Istambul, 1952, p. 65-72.
Prandtl L., “On the penetration hardness of plastic materials and the hardness of indenters”,
Zeits. Ang. Math. Mech., vol., 1921, p. 15.
Rockafellar R.T., Convex Analysis, Princeton University Press, 1996.
Salençon J., Calcul à la Rupture et Analyse Limite, Presses de l’ENPC, 1983.
Save M. et Massonet Ch., « Calcul plastique des constructions », vol. II, Structures Spatiales,
Structures dependant de plusieurs parameters, 2e éd., CBLIA, Bruxelles, 1972.
Voldoire F., “Regularized limit analysis and applications to the load carrying capacities of
mechanical components”, ECCOMAS, 2000, 11-14 September 2000, Barcelona, Spain.
Voldoire F., Limit analysis by the Norton-Hoff-Friaâ regularising method, M. Heitzer,
M. Staat, LISA project report 2001, publication du John von Neumann Institute for
Computing, 2003.
Wagoner R.H., Chenot J.L., Metal Forming Analysis, Cambridge University Press, 2001.
Yang W. H., “Large deformation of structures by sequential limit analysis”, Int. Jour. Solids
and Struc., 1993.
Yoon J.H. et Yang D.H., “Rigid-plastic finite element analysis of three dimensional forging
by considering friction on continuous curved dies with initial guess generation”, Int. J.
Mech. Sci., 30, 1988, p. 887-898.
