The Intrinsic Lagrangian Metric and Stress Variables

  • P. Rougee
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)

Abstract

Strain and stress, and their rates, are fundamental concepts. Their modeling largely depends on basic kinematic choices that need to be well defined and uncontested. As shown in [1], to which we refer also for its extensive bibliography, this is not the case in large deformation theory. Even in the simplest case without any microstructure that we consider in this paper, many insufficiencies, inadequacies and inconsistencies remain, which are not sufficiently recognized.

Keywords

Entropy Manifold Stein Diene 

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References

  1. [1]
    NAGHDI P.M., “A critical review of the state of finite plasticity”, Journal of Appl. Math. And Phys., Vol. 41, 315–394, 1990CrossRefMATHMathSciNetGoogle Scholar
  2. [2]
    GREEN A.E. and NAGHDI P.M., “A General Theory of an Elastic Plastic Continuum”, Arch. Rat. Mech. Analysis 18, 251–281, 1965CrossRefMATHMathSciNetGoogle Scholar
  3. [3]
    HILL R, “On constitutive inequalities for simple material. I and II”, J. Mech. Phys. Solids“, Vol. 16, 229–242 and 315–322, 1968Google Scholar
  4. [4]
    HILL R., “Aspects of invariance in solid mechanics”, Adv. Appl. Mech., Vol. 18, 1–75, 1978CrossRefMATHGoogle Scholar
  5. [5]
    PERIC Dj., OWEN D.R.J., “A model for finite strain elastoplasticity”, Proc. Sd Int. Conf. on Comput. Plasticity, Barcelonne, OWEN, HINTON, ONATE editors, Pineridge Press, Swansea U.K., 1989Google Scholar
  6. [6]
    LEE E.H., “Elastic-plastic deformation at finite strains”, J. Appl. Mech. 36, 1–6, 1969CrossRefMATHGoogle Scholar
  7. [7]
    LUBARDA V.A. and LEEE H., “A correct definition of elastic and plastic deformation and its comput. significance” J. Appl. Mech. 48, 35–40, 1981CrossRefMATHGoogle Scholar
  8. [8]
    DIENES J.K., “On the analysis of rotation and stress rate in deforming bodies” Acta Mech. 53, 217–232, 1979CrossRefMathSciNetGoogle Scholar
  9. [9]
    LEEE H, MALLET R.L. and WERTHEIMER T.B., “Stress analysis for anisotropie for anisotropie hardening in finite def. plast.”, J. Appl. Mech., 50, 554–560, 1983CrossRefGoogle Scholar
  10. [10]
    DOGUI A. and SIDOROFF F., “Large strain formulation of anisotropic elasto-plasticity for metal forming”. In “Computational methods for predicting materials processing defects”, M. Predeleanu Ed., Elsevier Science, Amsterdam, 1987Google Scholar
  11. [11]
    KLEIBER M. and RANIECKI B., “Elastic-Plastic Materials at Finite Strains”, in “Plasticity today” Ed A. Sawczuk, 1983Google Scholar
  12. [12]
    NOLL W., “A new Mathematical Theory of Simple Material”, Arch. Rat. Mech. Anal., Vol. 48, 1–50, 1972CrossRefMATHMathSciNetGoogle Scholar
  13. [13]
    ROUGEE P., “Formulation Lagrangienne Intrinsèque en Mécanique des Milieux Continus”, Journal de mécanique, Vol. 18, n°1, 7–32, 1980Google Scholar
  14. [14]
    SIMO J.C., “A framework for finite strain elastoplasticity based on max. plastic dissipation and on multiplicative decomposition. Part 1”, Comp. Meth. in Appl.Mech and Eng., 66, 199–219, 1988CrossRefMATHMathSciNetGoogle Scholar
  15. [15]
    ROUGEE P., 1990, “A new Lagrangian intrinsic approach of continuous media in large deformation”, Eur. J. Mech. A/ Solids, 10, n° 1, 15–39, 1991MathSciNetGoogle Scholar
  16. [16]
    PHAM MAU QUAN, “Introduction à la géométrie des variétés différentielles”, Dunod Ed. Paris, 1968Google Scholar
  17. [17]
    LEHMANN Th., “On the balance of energy and entropy at inelastic deformations of solid bodies”, Eur. J. Mech., A/Solids, 8, n° 3, 235–251, 1989MATHMathSciNetGoogle Scholar
  18. [18]
    ROUGEE P., “Kinematics of finite deformations”(to appear)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • P. Rougee
    • 1
  1. 1.Laboratoire de Mécanique et TechnologieCachanFrance

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