On the Continuum as an Assemblage of Homogeneous Elements or States

  • D. C. Drucker
Conference paper
Part of the IUTAM Symposia book series (IUTAM)


Some of the implications are explored of considering a continuum or a “point” in a material as an assemblage of simple models. A discussion is given of the need for and the distinction between a thermodynamics based upon a highly specialized or restricted model and one which is applicable to a wide class of material behavior. A thermodynamic statement developed on the basis of a model of material cannot be a valid general principle if it is not applicable to the combined response of two or more such models. Combinations of viscous models and combinations of elastic — perfectly plastic models are discussed in these terms. The significance of reversibility, or the ability to restore the initial state through mechanical deformation and moderate temperature changes alone, is related to dislocation concepts. Materials which work-harden with strain cycling are contrasted with those which work-soften and those which have been stabilized and do neither. The distinction between frictional and plastic behavior is discussed in thermodynamic terms along with the related questions of the degree of path independence in a space of controllable state variables and the order of the infinity of independent state variables.


Yield Surface Cyclic Strain Isotropic Hardening Kinematic Hardening Homogeneous Element 
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  1. [1]
    Truesdell, C. A.: Thermodynamics of Deformation, In Non-EquilibriumThermodynamics, Variational Techniques, and Stability. Chicago, Ill.: Univ. of Chicago. 1966. p. 110 referring to B. D. COLEMANGoogle Scholar
  2. [2]
    Kestin, J.: On the Application of the Principles of Thermodynamics to Strained Solid Materials. In: IUTAM Symposia 1966, 177. Wien-New York: Springer. 1968.Google Scholar
  3. [3]
    Green, A. E., and P. M. Nagidi: A General Theory of an Elastic Plastic Continuum. Arch. Ratl Mech. Anal. 18, 251–281 (1965).MATHGoogle Scholar
  4. [4]
    Pipkin, A. C., and R. S. Rivlin: Mechanics of Rate Independent Materials. ZAMP 16, 313–327 (1965).MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    Ziegler, H.: An Attempt to Generalize Onsager’s Principle. ZAMP 9b, 748–763 (1958).ADSCrossRefGoogle Scholar
  6. [6]
    Meixner, J.: Consequences of an Inequality in Nonequilibrium Thermodynamics. J. Appl. Mech. 33 (1966).Google Scholar
  7. Meixner, J.: IUTAM Symposia 1966, 236.Google Scholar
  8. Meixner, J.: Wien-New York: Springer. 1968.Google Scholar
  9. [7]
    Drucker, D. C.: Stress-Strain-Time Relations and Irreversible Thermodynamics. Proc. 1962 IUTAM Symposium on Second Order Effects in Elasticity, Plasticity, and Fluid Dynamics. Eds. D. ABIR and M. REINER. pp. 331–350. New York-London: Pergamon Press. 1964.Google Scholar
  10. [8]
    Sedov, L. I.: Introduction to the Mechanics of a Continuous Medium. Reading, Mass.: Addison-Wesley. 1965. ( Translation of 1962 Edition. )Google Scholar
  11. [9]
    Bohnenblust, H. F., and P. Duwez: Some Properties of a Mechanical Model of Plasticity. J. Appl. Mech. 15, Trans. ASME 70, 222–225 (1948).MathSciNetGoogle Scholar
  12. [10]
    White, G. N. Jr.: Application of the Theory of Perfectly Plastic Solids to Tech. Analysis of Strain Hardening Solids. Brown Univ. ech. Report All/51 (Aug. 1950).Google Scholar
  13. [11]
    Prager, W.: Introduction to Plasticity. Reading, Mass.: Addison-Wesley. 1959. Models of Plastic Behavior. Also Proceedings 5th U. S. National Congress of Applied Mechanics. pp. 435–450. ASME 1966. Refers to work of ILYUSHI\, ISHLINSKY, IVLEV, KACHANOV, KADASHEVICH and NOVOZIIILOV, MANDEL, SHIELD, and ZIEGLER.Google Scholar
  14. [12]
    Koiter, W. T.: General Theorems for Elastic-Plastic Solids. Progress in Solid Mechanics 1. Amsterdam: North-Holland Publishing Co. 1960.Google Scholar
  15. [13]
    Naghdi, P. M.: Stress-Strain Relations in Plasticity and Thermoplasticity. Second Symposium on Naval Structural Mechanics „Plasticity”. Eds. E. H. LEE and P. S. SYMONDS, pp. 121–167. New York: Pergamon Press. 1960.Google Scholar
  16. [14]
    Sanders, J. L.: Plastic Stress-Strain Relations Based on Infinitely Many Plane Loading Surfaces. Proc. 2nd U. S. National Congress of Applied Mechanics. pp. 455–460. ASME. 1954.Google Scholar
  17. [15]
    Hodge, P. G., Jr.: Plastic Analysis of Structures. New York: McGraw-Hill. 1959.MATHGoogle Scholar
  18. [16]
    Budiansky, B., and T. T. Wu: Theoretical Prediction of Plastic Strains of Polycrystals. Proc. 4th U. S. National Congress of Applied Mechanics. v. 2, pp. 1175–1185. ASME. 1962.Google Scholar
  19. [17]
    Drucker, D. C.: Extension of the Stability Postulate with Emphasis on Temperature Changes. Second Symposium on Naval Structural Mechanics “Plasticity”. Eds. E. H. LEE and P. S. SYMONDS, pp. 170–184. New York: Pergamon Press. 1960.Google Scholar
  20. [18]
    Drucker, D. C.: On the Postulate of Stability of Material in the Mechanics of Continua. J. Mécanique 3, 235–249 (1964).MathSciNetGoogle Scholar
  21. [19]
    Palmer, A. C., G. Maier, and D. C. Drucker: Convexity of Yield Surfaces and Normality Relations for Unstable Materials or Structural Elements. J. Appl. Mech. 34, Trans. ASME 89, 464–470 (1967).CrossRefGoogle Scholar
  22. [20]
    Calladine, C. R., and D. C. Drucker: Nesting Surfaces of Constant Rate of Energy Dissipation in Creep. Q. Appl. Math. 20, 79–84 (1962).MATHGoogle Scholar
  23. [21]
    Drucker, D.C.: On Time Independent Plasticity and Metals under Combined Stress at Elevated Temperature. Recent Progress in Applied Mechanics. The Folke Odqvist Volume. Stockholm Almqvist and Wiksell/Gebers. 1966.Google Scholar
  24. [22]
    Drucker, D. C.: The Continuum Theory of Plasticity on the Macroscale and the Microscale. 1966 ASTM Marburg Lecture. J. Materials 1, 873–910 (1966).Google Scholar
  25. [23]
    Ilyushin, A. A.: On the Postulate of Plasticity. Prikl. Mat. Mekh. 25, 503–507 (1961).Google Scholar
  26. [24]
    Rubin, D., and D. C. Drucker: On Stability of Viscoplastic Systems with Thermo-mechanical Coupling. Reiner Anniversary Volume. New York: Perga-mon Press. 1967.Google Scholar
  27. [25]
    Maier, G., and D. C. Drucker: Elastic-Plastic Continua Containing Unstable Elements Obeying Normality and Convexity Relations. Schweizerische Bauzeitung 84 (23), 447–450 (1966).Google Scholar
  28. [26]
    Drucker, D. C., and W. Prager: Soil Mechanics and Plastic Analysis or Limit Design. Q. Appl. Math. 10, 157–165 (1952).MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag/Wien 1968

Authors and Affiliations

  • D. C. Drucker
    • 1
  1. 1.Brown UniversityProvidenceUSA

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