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On a Thermodynamic Constitutive Theory and Its Application to Various Nonlinear Materials

  • R. A. Schapery
Part of the IUTAM Symposia book series (IUTAM)

Summary

The author’s thermodynamic constitutive theory for nonlinear viscoelastic behavior is extended to account for rate-independent plastic flow and for nonlinear creep with strong stress-dependence. It is then shown that the resulting stress-strain equations are consistent with mechanical behavior reported for several different materials under small and large strains; although principal concern here is with metals and polymeric solids, preliminary indications are that a variety of other materials, such as soils and biological tissue, can be characterized using the same basic equations. In this theory, history effects, with uniaxial or multiaxial loading, are taken into account by means of single integrals which are very similar to the Boltzmann type in linear viscoelastic theory.

Keywords

Entropy Production Relaxation Modulus Relaxation Test Linear Viscoelasticity Thermodynamic Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Fung, Y. C.: Fundamentals of Solid Mechanics. Englewood Cliffs, N. J.: Prentice-Hall. 1965.Google Scholar
  2. [2]
    Hult, J. A. H.: Creep in Engineering Structures. Waltham, Mass.: Blaisdell. 1966.Google Scholar
  3. [3]
    Green, A. E., and R. S. Rivlin: The Mechanics of Non-linear Materials with Memory — Part I. Arch. Rati Mech. Anal. 1, 1–21 (1957).MathSciNetMATHGoogle Scholar
  4. [4]
    Coleman, B. D., and W. Noll: Foundations of Linear Viscoelasticity. Rev. Mod. Phys. 88, 239 - 249 (1961).MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    Onat, E. T.: Description of Mechanical Behavior of Inelastic Solids. Proc. 5th U. S. National Congress of Applied Mechanics, ASME, p. 421–434 (1966).Google Scholar
  6. [6]
    Fung, Y. C.: Biomechanics — Its Scope, History, a,nd Some Problems of Continuum Mechanics in Physiology. Appl. Mech. Rev. 21, 1–20 (1968).Google Scholar
  7. [7]
    Schapery, R. A.: Application of Thermodynamics to Thermomechanical, Fracture, and Birefringent Phenomena in Viscoelastic Media. J. Appl. Phys. 35, 1451–1465 (1964).MathSciNetADSCrossRefGoogle Scholar
  8. [8]
    Schapery, R. A.: A Theory of Non-linear Thermoviscoelasticity Based on Irreversible Thermodynamics. Proc. 5th U. S. National Congress of Applied Mechanics, ASME, p. 511–530 (1966).Google Scholar
  9. [9]
    Biot, M. A.: Theory of Stress-Strain Relations in Anisotropic Viscoelasticity and Relaxation Phenomena. J. Appl. Phys. 25, 1385–1391 (1954).ADSMATHCrossRefGoogle Scholar
  10. [10]
    Morland, L. W., and E. H. Lee: Stress Analysis for Linear Viscoelastic Materials with Temperature Variation. Trans. Soc. Rheology 4, 233–263 (1960).MathSciNetADSCrossRefGoogle Scholar
  11. [11]
    Schapery, R. A.: Stress Analysis of Viscoelastic Composite Materials. J. Composite Materials 1, 228–267 (1967).Google Scholar
  12. [12]
    Sokolnikoff, I. S.: Mathematical Theory of Elasticity. New York: McGraw- Hill. 1956.MATHGoogle Scholar
  13. [13]
    Bueche, F.: Physical Properties of Polymers. New York: Interscience. 1962.Google Scholar
  14. [14]
    DeGroot, S. R., and P. Mazur: Non-Equilibrium Thermodynamics, p. 206. Amsterdam: North-Holland Publ. Co. 1962.Google Scholar
  15. [15]
    Titchener, A. L., and M. B. Beyer: Progress in Metal Physics 7, Ed. by B. Chalmers and R. King. New York: Pergamon. 1958.Google Scholar
  16. [16]
    Green, A. E., and W. Zerna: Theoretical Elasticity, 2nd Ed. London: Oxford. 1968.MATHGoogle Scholar
  17. [17]
    Eringen, A. C.: Nonlinear Theory of Continuous Media. New York: McGraw- Hill. 1962.Google Scholar
  18. [18]
    Ferry, J. D.: Viscoelastic Properties of Polymers. New York: Wiley. 1961.Google Scholar
  19. [19]
    Biot, M. A.: Linear Thermodynamics and the Mechanics of Solids. Proc. 3rd U. S. National Congress of Applied Mechanics, ASME. p. 1 –18 (1958).Google Scholar
  20. [20]
    Huseby, T. W. and S. Matsuoka: Mechanical Properties of Solid and Liquid Polymers. Mater. Sci. Eng. 1, 321–341 (1967).CrossRefGoogle Scholar
  21. [21]
    Halpin, J. C.: Composite Materials Workshop, p. 87. Ed. by S. W. Tsai, J. C. Halpin, and N. J. Pagano. Stamford, Conn.: Technomic. 1968.Google Scholar
  22. [22]
    Passaglia, E., and J. R. Knox: Engineering Design for Plastics, Chapt. 3. Ed. by Eric Baer. New York: Reinhold. 1964.Google Scholar
  23. [23]
    Thorkildsen, R. L.: Engineering Design for Plastics, Chapt. 5. Ed. by Eric Baer. New York: Reinhold. 1964.Google Scholar
  24. [24]
    Findley, W. N., and G. Khosla: Application of the Superposition Principle and Theories of Mechanical Equation of State, Strain, and Time Hardening to Creep of Plastics under Changing Loads. J. Appl. Phys. 26, 821–832 (1955).ADSCrossRefGoogle Scholar
  25. [25]
    Passaglia, E., and H. P. Koppehele: The Strain Dependence of Stress Relaxation in Cellulose Monofilaments. J. Polymer Sci. 88, 281–289 (1958).ADSGoogle Scholar
  26. [26]
    Schapery, R. A.: On the Characterization of Nonlinear Viscoelastic Materials. Polymer Eng. Sci. 9, 295–310 (1969).Google Scholar
  27. [27]
    Schapery, R. A.: Unpublished Research.Google Scholar
  28. [28]
    Williams, M. L.: Structural Analysis of Viscoelastic Materials. AIAA J. 2, 785–808 (1964).MATHCrossRefGoogle Scholar
  29. [29]
    I wan, W. D.: On a Class of Models for the Yielding Behavior of Continuous and Composite Systems. J. Appl. Mech. 84, 612–617 (1967).Google Scholar
  30. [30]
    Hill, R.: The Mathematical Theory of Plasticity. London: Oxford. 1950.Google Scholar
  31. [31]
    Staverman, A. J., and F. Schwarzl: Die Physik der Hochpolymeren IV, p. 139. Ed. by H. A. Stuart. Berlin-Göttingen-Heidelberg: Springer. 1956.Google Scholar
  32. [32]
    Halpin, J. C.: Nonlinear Rubberlike Viscoelasticity — A Molecular Approach. J. Appl. Phys. 86, 2975–2982 (1965).ADSCrossRefGoogle Scholar
  33. [33]
    Smith, T. L.: Deformation and Failure of Plastics and Elastomers. Polymer Eng. Sci. 5, 270 (1965).Google Scholar
  34. [34]
    Bergen, J. T., D. C. Messersmith, and R. S. Riylin: Stress Relaxation for Biaxial Deformation of Filled High Polymers. J. Appl. Polymer Sci. 8, 153–167 (1960).CrossRefGoogle Scholar
  35. [35]
    Valanis, K. C., and R. F. Land el: Large Multi-axial Deformation Behavior of a Filled Rubber. Trans. Soc. Rheology 11, 243–256 (1967).ADSCrossRefGoogle Scholar
  36. [36]
    Schapery, R. A.: Approximate Methods for Thermoviscoelastic Characterization and Analysis of Nonlinear Solid Rocket Grains. AIAA J., to be published (1970).Google Scholar
  37. [37]
    Dickie, R. A., and T. L. Smith: Deformation and Rupture of Elastomers in Equal Biaxial and Simple Tension. Air Force Materials Laboratory, Wright- Patterson Air Force Base, Ohio, Tech. Rept. AFML-TR-68–112 (May 1968).Google Scholar
  38. [38]
    Schapery, R. A.: An Engineering Theory of Nonlinear Viscoelasticity with Applications. Int. J. Solids and Structures 2, 407–425 (1966).CrossRefGoogle Scholar
  39. [39]
    Mason, P.: The Viscoelastic Behavior of Rubber in Extension. J. Appl. Polymer Sci. 1, 63 - 69 (1959).CrossRefGoogle Scholar
  40. [40]
    Bueche, F., and J. C. Halpin: Molecular Theory for the Tensile Strength of Gum Elastomers. J. Appl. Phys. 85, 36–41 (1964).ADSCrossRefGoogle Scholar
  41. [41]
    Kubat, J.: A Similarity in the Stress Relaxation Behavior of High Polymers and Metals. A Summary of Several Papers. Royal Institute of Technology, Stockholm (1965).Google Scholar
  42. [42]
    Kelly, J. M.: Generalizations of Some Elastic-Viscoplastic Stress-Strain Relations. Trans. Soc. Rheology 11, 55–76 (1967).ADSCrossRefGoogle Scholar
  43. [43]
    Mitchell, J. K., R. G. Campanella, and A. Singh: Soil Creep as a Rate Process. J. Soil Mech. Foundations Div. A. S. C. E. 94, 231–253 (1968).Google Scholar
  44. [44]
    Singh, A., and J. K. Mitchell: General Stress-Strain-Time Functions for Soils. J. Soil Mech. Foundations Div. A. S. C. E. 94, 21–46 (1968).Google Scholar
  45. [45]
    Schapery, R. A.: Further Development of a Thermodynamic Constitutive Theory: Stress Formulation. Purdue U. Rept. AA & ES 69–2 (1969).Google Scholar

Copyright information

© Springer-Verlag/Wien 1970

Authors and Affiliations

  • R. A. Schapery
    • 1
  1. 1.LafayetteUSA

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