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History of Computational Classical Elasto-Plasticity

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Advances in Computational Plasticity

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 46))

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Abstract

This contribution was presented by the author at COMPLAS XII in 2013 as a plenary lecture but not published so far. The historical presentation of physical und mathematical modeling together with the computational foundation of related FEMs seems to be of current importance, also regarding the algorithms and applications of elasto-plastic deformations based on \(C^1\)-continuous kinematics for engineering applications, including a posteriori error analysis and adaptivity.

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References

  1. E.A. de Souza Neto, D. Peric, D.R.J. Owen, Computational Methods in Plasticity (Wiley, 2008)

    Google Scholar 

  2. J. Lemaitre, J.-L. Chaboche, Mechanics of Solid Materials (Cambridge University Press, 1985 (French), 1990 (English))

    Google Scholar 

  3. J.C. Simo, T.J.R. Hughes, Computational Inelasticity, Revised 2nd ed. 2006 (Springer Science & Business Media, 1998)

    Google Scholar 

  4. W. Han, B.D. Reddy, Plasticity (Springer, 2013)

    Google Scholar 

  5. O.T. Bruhns, On the history of plasticity—Heinrich Hencky, a pioneer of the early years, in the history of theoretical, material and computational mechanics—mathematics meets mechanics and engineering, ed. by E. Stein (Springer 2014), pp. 133–152

    Google Scholar 

  6. H.E. Tresca, Mémoire sûr l’écoulement soumis à des corps solids. Mémoire Présentée par Divers Savants, Academy des Science, Paris 59, 754–758 (1864)

    Google Scholar 

  7. J. Barré de Saint Venant, Mémoire sûr l’établissement des equations différentielles des mouvements intérieurs opérés dans les corps solids ductiles différentielles. J. Math. Pures et Appl. 16, 308–316 (1871)

    Google Scholar 

  8. M. Levy, Extrait de mémoire sûr les equations generales des mouvements interieurs des corps solids ductiles au dela des limites ou l’estacite pourrait les ramener a leur premier etat. J. Math. Pures Appl. 16, 369–372 (1871)

    Google Scholar 

  9. J. Bauschinger, Jahresreport, Mitt Mech. Lab, München (1886)

    Google Scholar 

  10. T.M. Huber, Wlaściwa praca odksztalcenia jako miara wytȩźenia materialu. Czasopismo Techniczne 22, 34–40, 49–50, 61–62, 80–81

    Google Scholar 

  11. R.E. von Mises, Mechanik der festen Körper im plastisch deformablen Zustand (Göttingen, Mathematisch-Physikalische Klasse, Nachrichten der Gesellschaft der Wissenschaften, 1913), pp. 582–592

    Google Scholar 

  12. H. Hencky, Über einige statisch bestimmte Fälle des Gleichgewichts in plastischen Körpern. ZAMM 3, 241–251 (1913)

    Google Scholar 

  13. H. Hencky, Die Bewegungsgleichungen beim nichtstationären Fließen plastischer Massen. ZAMM 5, 144–175 (1925)

    MATH  Google Scholar 

  14. J.-L. Chaboche, G. Roùchellier, On the plastic and viscoplastic constitutive equations, part I: rules developed with internal variable concept. J. Press. Vess. Tech. 105, 153–164 (1983)

    Article  Google Scholar 

  15. R. Clausius, Über eine veränderte Form des 2. Hauptsatzes der mechanischen Wärmetheorie. Ann. Physik 93, 461–506 (1854); Abhandl. 1, 126–154

    Google Scholar 

  16. P. Duhem, Traité d’énergétique, vol. 2 (Gautier-Villars, Paris, 1911)

    Google Scholar 

  17. L. Prandtl, Spannungsverteilung in plastischen Kärpern. Proc. First Int. Congr. Appl. Mech., Delft, pp. 43–54 (1924)

    Google Scholar 

  18. E. Reuss, Berücksichtigung der elastischen Formänderung in der Plastizitätstheorie. Z. angew. Math. Mech. 10(3), 266–274 (1930)

    Article  MATH  Google Scholar 

  19. J.C. Simo, R.L. Taylor, Consistent tangent operators for rate independent plasticity. Comp. Meths. Appl. Mech. Engg. 48, 101–118 (1985)

    Google Scholar 

  20. J.C. Simo, A framework for finite strain elasto-plasticity based on maximum plastic dissipation and multiplicative decomposition: part I. Continuum formulation. Comput. Methods Appl. Mech. Eng. 66, 199–219 (1988)

    Google Scholar 

  21. D. Weichert, A. Ponter, A historical view on shakedown theory, in the history of theoretical, material and computational mechanics—mathematics meets mechanics and engineering, ed. by E. Stein. Lecture Notes in Applied Matehmatics and Mechanics 1 (Springer, 2014), pp. 169–194

    Google Scholar 

  22. J.A. König, G. Maier, Shakedown analysis of elastoplastic structures, a review of recent developments. Nucl. Eng. Des. 66, 81–85 (1981)

    Google Scholar 

  23. G. Maier, A generalization to nonlinear hardening of the first shakedown theorem for discrete elastic-plastic structures (Serie Ottava, Rendic. Acc. Naz. dei Lincei, 1988), pp. 161–174

    Google Scholar 

  24. D. Weichert, On the influence of geometrical nonlinearities on the shakedown of elastic-plastic structures. Int. J. Plast. 2, 135–148 (1986)

    Google Scholar 

  25. E. Stein, G. Zhang, J.A. König, Shakedown with nonlinear strain hardening including structural computations using finite element method. Int. J. Plast. 8, 1–31 (1992)

    Google Scholar 

  26. F.-J. Barthold, M. Schmidt, E. Stein, Error indicators and mesh refinements for finite element computations of elastoplastic deformations. Int. J. Comput. Mech. 22, 225–238 (1998)

    Google Scholar 

  27. E. Stein, M. Schmidt, Adaptive FEM for elasto-plastic deformations, in Error-controlled Adaptive Finite Elements in Solid Mechanics, ed. by E. Stein (Wiley, 2003), pp. 53–108

    Google Scholar 

  28. D. Peric, J. Yu, D.R.J. Owen, Error estimates and adaptivity in elastoplastic solids. Int. J. Num. Meth. Eng. 37, 1351–1379 (1994)

    Google Scholar 

  29. M. Ortiz, J.C. Simo, An analysis of a new class of integration algorithms for elastoplastic constitutive relations. Int. J. Num. Meth. Eng. 23, 353–366 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  30. E. Stein, S. Ohnimus, M. Rüter, Hierarchical model- and discretization-error estimation in elastoplastic structures, in: H. Aref and J.W. Philips (eds.): Mechanics of a new Millenium, Proceedings \(20^{th}\) Internat. Congress on Theretical and Applied Mechanics (IUTAM), Chicago, USA, Kluwer Acedemic Publishers, 40, 2001, 373–388

    Google Scholar 

  31. L. Gallimard, P. Ladevèze, J.P. Pelle, Error estimation and time-space parameters optimization for FEM non-linear computation. Comput. Struct. 64, 145–156 (1997)

    Google Scholar 

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Correspondence to Erwin Stein .

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Stein, E. (2018). History of Computational Classical Elasto-Plasticity. In: Oñate, E., Peric, D., de Souza Neto, E., Chiumenti, M. (eds) Advances in Computational Plasticity. Computational Methods in Applied Sciences, vol 46. Springer, Cham. https://doi.org/10.1007/978-3-319-60885-3_17

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  • DOI: https://doi.org/10.1007/978-3-319-60885-3_17

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  • Print ISBN: 978-3-319-60884-6

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