The Constitutive Law in Thermoplasticity an Introduction

  • Theodor Lehmann
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 281)


Within this course we are dealing mainly with non-isothermic inelastic deformations of such solid bodies which can be considered phenomenologically as classical continua. This means, we assume that the deformations of the considered bodies are completely derivable from the description of the motion of the material points in a well defined space of observation (space-fixed coordinate system). We shall see, however, that the description of the deformations can also be based merely on the consideration of the deformations of a comoving body-fixed coordinate system.


Irreversible Process Inelastic Deformation Phenomenological Theory Plane Strain Tension Microscale Level 
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  1. 1.
    Rutter, K., The foundations of thermodynamics, its basic postulates and implications, Acta Mech. 27, 1977Google Scholar
  2. 2.
    Muschik, W., Thermodynamische Theorien, Überblick und Vergleich, ZAMM 61, 1981Google Scholar
  3. 3.
    Müller, I., Thermodynamik,Bertelsmann Universitätsverlag, Düsseldorf, 1973 Google Scholar
  4. 4.
    Meixner, J. and Reik, H.G., Thermodynamik der irreversiblen Prozesse, Handbuch der Physik, Flügge, S., ed., Vol. III/2, 413, Springer-Verlag Berlin/Göttingen/Heidelberg, 1959Google Scholar
  5. 5.
    de Groot, S.R. and Mazur, P., Non-equilibrium thermodynamics, North-Holland Publ. Comp., Amsterdam, 1962Google Scholar
  6. 6.
    Gyarmati, I., Non-equilibrium thermodynamics, Springer-Verlag, Berlin/Heidelberg/New York 1970CrossRefGoogle Scholar
  7. 7.
    Kluitenberg, G.A., Thermodynamical theory of elasticity and plasticity, Physica 28, 217, 1962MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    Meixner, J., Processes in simple thermodynamic materials, Arch. Rat. Mech. Anal. 33, 33, 1969MathSciNetCrossRefGoogle Scholar
  9. 9.
    Coleman, B.D. and Gurtin, M.E., Thermodynamics with internal state variables, Journ. Chem. Phys. 47, 597, 1967ADSCrossRefGoogle Scholar
  10. 10.
    Day, W.A., The thermodynamics of simple materials with fading memory, Springer-Verlag Berlin/Heidelberg/New York 1972Google Scholar
  11. 11.
    Coleman, B.D. and Owen, D.R., A mathematical foundation of thermodynamics, Arch. Rat. Mech. Anal. 54, 1, 1974MathSciNetMATHGoogle Scholar
  12. 12.
    Coleman, B.D. and Owen, D.R., On thermodynamics and elastic-plastic materials, Arch. Rat. Mech. Anal. 59, 25, 1975MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Truesdell, A.C., Rational thermodynamics, McGraw-Hill, New York 1969Google Scholar
  14. 14.
    Noll, J.W., A new mathematical theory of simple materials, Arch. Rat. Mech. Anal. 48, 1, 1972MathSciNetMATHGoogle Scholar
  15. 15.
    Green, A.E. and Naghdi, P.M., On continuum thermodynamics, Arch. Rat. Mech. Anal. 48, 352, 1972MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Anthony, K.H., Die Reduktion von nichteuklidischen Objekten in eine euklidische Form und physikalische Deutung der Reduktion durch Eigenspannungszustände in Kristallen, Arch. Rat. Mech. Anal. 37, 161, 1970MathSciNetCrossRefMATHGoogle Scholar
  17. Anthony, K.H., Die Theorie der Disklinationen, Arch. Rat. Mech. Anal. 39, 43, 1970MathSciNetCrossRefMATHGoogle Scholar
  18. Anthony, K.H., Die Theorie der nichtmetrischen Spannungen in Kristallen, Arch. Rat. Mech. Anal. 40, 50, 1971MathSciNetCrossRefMATHGoogle Scholar
  19. 17.
    Kröner, E., Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen, Arch. Rat. Mech. Anal. 4, 273, 1960CrossRefMATHGoogle Scholar
  20. 18.
    Lippmann, H., Eine Cosserat-Theorie des plastischen Fließens, Acta Mech. 8, 255, 1969CrossRefMATHGoogle Scholar
  21. 19.
    Kröner, E., Dislocation: A new concept in the continuum theory of plasticity, Journ Math. Phys. 42, 28, 1963Google Scholar
  22. 20.
    Teodosiu, E. and Sidoroff, F., A theory of finite elastoviscoplasticity of single crystals, Int. J. Eng. Sci. 14, 165, 1976CrossRefMATHGoogle Scholar
  23. 21.
    Eimer, Cz., Plasticity of polycrystal, Arch. Mech. 29, 687, 1977MATHGoogle Scholar
  24. 22.
    Weng, G.J. and Phillips, A., An investigation of yield surfaces based on dislocation mechanics, Int. J. Eng. Sci. 15, I) 45, 1977 II) 61, 1977Google Scholar
  25. 23.
    Weng, G.J. and Phillips, A., The stress fields of continuous distribution of dislocations and of their movement in a polycrystalline aggregate, Int. J. Sol. Struct. 14, 535, 1978CrossRefMATHGoogle Scholar
  26. 24.
    Werne, R.W. and Kelly, J.M., A dislocation theory of isotropic polycrystalline plasticity, Int. J. Eng. Sci. 16, 951, 1978CrossRefMATHGoogle Scholar
  27. 25.
    Nemat-Nasser, S., Decomposition of strain measures and their rates in finite deformation elastoplasticity, Int. J. Sol. Struct. 15, 155, 1979CrossRefMATHGoogle Scholar
  28. 26.
    Lee, E.H. and McMeeking, R.M., Concerning elastic and plastic components of deformation, Int. J. Sol. Struct. 16, 715, 1980MathSciNetCrossRefMATHGoogle Scholar
  29. 27.
    Lee, E.H., Some comments on elastic-plastic analysis, Int. J. Sol. Struct. 17, 859, 1981CrossRefMATHGoogle Scholar
  30. 28.
    Lehmann, Th., Some remarks on the decomposition of deformations and mechanical work, Int. J. Eng. Sci. 20, 281, 1982CrossRefMATHGoogle Scholar
  31. 29.
    Rice, J.R., The localization of plastic deformation, Proc. 14. IUTAM Cong. Delft, 207, 1976Google Scholar
  32. 30.
    Needleman, A., Non-normality and bifurcation in plane strain tension and compression, J. Mech. Phys. Solids 27, 231, 1979MathSciNetADSCrossRefMATHGoogle Scholar
  33. 31.
    Bruhns, O., and Raniecki, B., Bounds to bifurcation stresses in solids with non-associated plastic flow law at finite strain, J. Mech. Phys. Solids 29, 153, 1981Google Scholar
  34. 32.
    Zander, G., Zur Bestimmung von Verzweigungslasten dünnwandiger Kreiszylinder unter kombinierter Längs-und Torsionslast., Diss. Ruhr-Universität Bochum, Mitt. Inst. für Mechanik, Ruhr-Univ. Bochum, Nr. 27, 1981Google Scholar
  35. 33.
    Lehmann, Th., On the concept of stress-strain relation in plasticity, Acta Mech. 42, 263, 1982CrossRefMATHGoogle Scholar
  36. 34.
    Lehmann, Th., Some theoretical considerations and experimental results concerning elastic-plastic stress-strain relations, to be published in Ing.-Arch. Google Scholar
  37. 35.
    Biot, M.A., Variational-Lagrangian irreversible thermodynamics of nonlinear thermorheology, Quart. AppZ. Math. 34, 213, 1976MathSciNetMATHGoogle Scholar
  38. 36.
    Mroz, Z. and Raniecki, B., Uniqueness and variational principles in thermoplasticity, Int. J. Eng. Sci. 14, 211, 1976MathSciNetCrossRefMATHGoogle Scholar
  39. 37.
    Besseling, J., Finite element methods, in: Trends in solid mechanics. Besseling and v.d.Heijden, Eds., Delft Univ. Press, 53, 1979Google Scholar

Copyright information

© Springer-Verlag Wien 1984

Authors and Affiliations

  • Theodor Lehmann
    • 1
  1. 1.Ruhr-University BochumBochumGermany

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