Open Access
Issue
Mechanics & Industry
Volume 17, Number 5, 2016
Article Number 511
Number of page(s) 11
DOI https://doi.org/10.1051/meca/2016001
Published online 07 July 2016
  1. A. Considère, Mémoire sur l’emploi du fer et de l’acier dans les constructions, Annales des Ponts et Chaussées 9 (1885) 574–775 [Google Scholar]
  2. R. Hill, On discontinuous plastic states, with special reference to localized necking in thin sheets, J. Mech. Phys. Solids 1 (1952) 19–30 [CrossRef] [Google Scholar]
  3. Z. Marciniak, K. Kuczynski, Limit strains in the processes of stretch-forming sheet metal, Int. J. Mech. Sci. 9 (1967) 609–620 [CrossRef] [Google Scholar]
  4. Z. Marciniak, K. Kuczynski, T. Pokora, Influence of the plastic properties of a material on the forming limit diagram for sheet metal in tension, Int. J. Mech. Sci. 15 (1973) 789–805 [CrossRef] [Google Scholar]
  5. S. Stören, J.-R. Rice, Localized necking in thin sheets, J. Mech. Phys. Solids 23 (1975) 421–441 [CrossRef] [Google Scholar]
  6. J.-W. Hutchinson, K.-W. Neale, Sheet Necking 2: Time-independent behavior, in: Proceedings of a Symposium on Mechanics of Sheet Metal Forming, General Motors Research Laboratories, Warren, Michigan, 17-18 october 1977, edited by D.-P. Koistinen, N.-M. Wang, Plenum Press, New York, 1978, pp. 127–150 [Google Scholar]
  7. D. Dudzinski, A. Molinari, Instabilité de la déformation viscoplastique en chargement biaxial, Compte Rendu à l’Académie des Sciences de Paris 307 (1988) 1315–1321 [Google Scholar]
  8. D. Dudzinski, A. Molinari, Perturbation analysis of thermoviscoplastic instabilities in biaxial loading, Int. J. Solids Struct. 27 (1991) 601–628 [CrossRef] [Google Scholar]
  9. G. Chatzigeorgiou, N. Charalambakis, Instability analysis of non-homogeneous materials under biaxial loading, Int. J. Plasticity 21 (2005) 1970–1999 [CrossRef] [Google Scholar]
  10. J.-W. Hutchinson, H. Obrecht, Tensile instabilities in strain-rate dependent materials, in Proceedings of the Fourth International Conference on Fracture ICF4, edited by D.-M.-R. Taplin, Pergamon Press, Université de Waterloo, Canada, 19-24 june 1977, Vol. 1, pp. 101–116 [Google Scholar]
  11. J.-W. Hutchinson, K.-W. Neale, Influence of strain-rate sensitivity on necking under uniaxial tension, Acta Metallurgica 25 (1977) 839–846 [CrossRef] [Google Scholar]
  12. J.-W. Hutchinson, K.-W. Neale, A. Needleman, Sheet Necking 1: Validity of plane stress assumptions of the long-wavelength approximation, in Proceedings of a Symposium on Mechanics of Sheet Metal Forming, General Motors Research Laboratories, Warren, Michigan, 17-18 october 1977, edited by D.-P. Koistinen, N.-M. Wang, Plenum Press, New York, 1978, pp. 111–126 [Google Scholar]
  13. C. Fressengeas, A. Molinari, Instability and bifurcation in the plane tension test, Archives of Mechanics 44 (1992) 93–104 [Google Scholar]
  14. C. Fressengeas, A. Molinari, Fragmentation of rapidly stretching sheets, Eur. J. Mech. A/Solids 13 (1994) 251–268 [Google Scholar]
  15. D. Jouve, Étude analytique de l’instabilité plastique de striction pour une plaque sollicitée en traction biaxiale, Thèse, École Polytechnique, 2010 [Google Scholar]
  16. D. Jouve, Étude analytique d’instabilités plastiques pour une plaque métallique sollicitée biaxialement, en traction ou en compression : modes symétriques et antisymétriques par rapport au plan médian, Rapport CEA-R 6306, 2012 [Google Scholar]
  17. D. Jouve, Analytic study of the onset of plastic necking instabilities during biaxial tension tests on metallic plates, Eur. J. Mech. A/Solids 50 (2015) 59–69 [CrossRef] [Google Scholar]
  18. R. Hill, The mathematical theory of plasticity, Oxford Classic Texts in the Physical Sciences, Clarendon Press, Oxford, 1950 [Google Scholar]
  19. P.-G. Hodge, The method of characteristics applied to problems of steady motion in plane plastic stress, Quart. Appl. Math. 8 (1951) 381–386 [MathSciNet] [Google Scholar]
  20. G.-R. Johnson, W.-H. Cook, A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures, in: Proceedings of the Seventh International Symposium on Ballistics, The Hague, The Netherlands, 19-21 april 1983, pp. 541–547 [Google Scholar]
  21. D.-J. Steinberg, S.-G. Cochran, M.-W. Guinan, A constitutive model for metals applicable at high strain rate, J. Appl. Phys. 51 (1980) 1498–1504 [NASA ADS] [CrossRef] [Google Scholar]
  22. V.-B. Shenoy, L.-B. Freund, Necking bifurcations during high strain rate extension, J. Mech. Phys. Solids 47 (1999) 2209–2233 [CrossRef] [Google Scholar]
  23. S. Mercier, A. Molinari, Predictions of bifurcation and instabilities during dynamic extension, Int. J. Solids Struct. 40 (2003) 1995–2016 [CrossRef] [Google Scholar]
  24. S. Mercier, N. Granier, A. Molinari, F. Llorca, F. Buy, Multiple necking during the dynamic expansion of hemispherical metallic shells, from experiments to modelling, J. Mech. Phys. Solids 58 (2010) 955–982 [CrossRef] [Google Scholar]
  25. D. Jouve, Analytic study of the onset of plastic instabilities during plane tension and compression tests on metallic plates, Eur. J. Mech. A/Solids 47 (2014) 70–81 [CrossRef] [MathSciNet] [Google Scholar]
  26. R. Hill, J.-W. Hutchinson, Bifurcation phenomena in the plane tension test, J. Mech. Phys. Solids 23 (1975) 239–264 [CrossRef] [Google Scholar]
  27. N.-J.-B. Young, Bifurcation phenomena in the plane compression test, J. Mech. Phys. Solids 24 (1976) 77–91 [CrossRef] [Google Scholar]
  28. S. El Maï, Étude du développement des instabilités dans un anneau en expansion dynamique, Thèse, Université de Lorraine, 2014 [Google Scholar]
  29. D. Jouve, Analytic study of plastic necking instabilities during plane tension tests, Eur. J. Mech. A/Solids 39 (2013) 180–196 [CrossRef] [MathSciNet] [Google Scholar]
  30. F.-H. Norton, The creep of steel at high temperatures, McGraw-Hill, 1929 [Google Scholar]
  31. A.-L. Gurson, Continuum theory of ductile rupture by void nucleation and growth: Part 1 Yield criteria and flow rules for porous ductile media, Trans. ASME, J. Eng. Mater. Technol. (1977) 2–15 [Google Scholar]
  32. J. Lemaitre, J.-L. Chaboche, Mécanique des matériaux solides, 2nd édition, Dunod, 1984 [Google Scholar]
  33. R. Hill, A theory of the yielding and plastic flow of anisotropic metals, in: Proceedings of the Royal Society of London, Series A - Mathematical and Physical Sciences, 1948, Vol. 193, 1033, pp. 281–297 [Google Scholar]
  34. J.-L. Dequiedt, Localization in elasto-plastic materials: influence of the plasticity yield surface in biaxial loading conditions, Int. J. Solids Struct. 47 (2010) 2937–2951 [CrossRef] [Google Scholar]
  35. L.-S. Tóth, D. Dudzinski, A. Molinari, Forming limit predictions with the perturbation method using stress potential functions of polycrystal viscoplasticity, Int. J. Mech. Sci. 38 (1996) 805–824 [CrossRef] [Google Scholar]
  36. N. Boudeau, J.-C. Gelin, S. Salhi, Computational prediction of the localized necking in sheet forming based on microstructural material aspects, Comput. Mater. Sci. 11 (1998) 45–64 [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.