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A new mathematical theory of simple materials

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References

  1. Bernstein, B., Hypo-elasticity and elasticity. Arch. Rational Mech. Anal. 6, 89–104 (1960).

    Google Scholar 

  2. Bernstein, B., Remarks on materials of the rate type and the principle of determinism. Trans. Soc. Rheol. 5, 35–40 (1961).

    Google Scholar 

  3. Bourbaki, N., Topologie Générale, Chapitres 1 et 2, quatrième édition. Paris: Hermann 1965.

    Google Scholar 

  4. Coleman, B. D., Kinematical concepts with applications in the mechanics and thermodynamics of incompressible viscoelastic fluids. Arch. Rational Mech. Anal. 9, 273–300 (1962).

    Google Scholar 

  5. Coleman, B. D., & V. J. Mizel, On the general theory of fading memory. Arch. Rational Mech. Anal. 29, 18–31 (1968).

    Google Scholar 

  6. Coleman, B. D., H. Markovitz, & W. Noll, Viscometric Flows of Non-Newtonian Fluids. New York: Springer 1966.

    Google Scholar 

  7. Coleman, B. D., & W. Noll, On the thermostatics of continuous media. Arch. Rational Mech. Anal. 4, 97–128 (1959).

    Google Scholar 

  8. Coleman, B. D., & W. Noll, Material symmetry and thermostatic inequalities in finite elastic deformations. Arch. Rational Mech. Anal. 15, 87–111 (1964).

    Google Scholar 

  9. Day, W. A., Thermodynamics based on a work axiom. Arch. Rational Mech. Anal. 31, 1–34 (1968).

    Google Scholar 

  10. Fairchild, W. W., & C. Ionescu-Tulcea, Topology. Philadelphia-London-Toronto: W. B. Saunders 1971.

    Google Scholar 

  11. Kelley, J. L., General Topology. Princeton: Van Nostrand 1955.

    Google Scholar 

  12. Noll, W., On the continuity of the solid and fluid states. J. Rational Mech. Anal. 4, 3–81 (1955).

    Google Scholar 

  13. Noll, W., A mathematical theory of the mechanical behavior of continuous media. Arch. Rational Mech. Anal. 2, 197–226 (1958).

    Google Scholar 

  14. Noll, W., The foundations of classical mechanics in the light of recent advances in continuum mechanics. Proc. of the Berkeley Symposium on the Axiomatic Method, p. 266–281, Amsterdam 1959.

  15. Noll, W., Motions with constant stretch history. Arch. Rational Mech. Anal. 11, 97–105 (1962).

    Google Scholar 

  16. Noll, W., Proof of the maximality of the orthogonal group in the unimodular group. Arch. Rational Mech. Anal. 18, 100–102 (1965).

    Google Scholar 

  17. Noll, W., Space-time structures in classical mechanics. Delaware Seminar in the Foundations of Physics, p. 28–34. Berlin-Heidelberg-New York: Springer 1967.

    Google Scholar 

  18. Noll, W., Materially uniform simple bodies with inhomogeneities. Arch. Rational Mech. Anal. 27, 1–32 (1967).

    Google Scholar 

  19. Noll, W., The representation of monotonous processes by exponentials. To appear.

  20. Owen, D. R., Thermodynamics of materials with elastic range. Arch. Rational Mech. Anal. 32, 91–112 (1968).

    Google Scholar 

  21. Owen, D. R., A mechanical theory of materials with elastic range. Arch. Rational Mech. Anal. 37, 85–110 (1970).

    Google Scholar 

  22. Truesdell, C., Hypo-elasticity. J. Rational Mech. Anal. 4, 83–133 (1955).

    Google Scholar 

  23. Truesdell, C., & W. Noll, The Non-linear Field Theories of Mechanics. Encyclopedia of Physics, Vol. III/3. Berlin-Heidelberg-New York: Sringer 1965.

    Google Scholar 

  24. Sternberg, S., Lectures on Differential Geometry. Englewood Cliffs: Prentice Hall 1964.

    Google Scholar 

  25. Wang, C. C., A general theory of subfluids. Arch. Rational Mech. Anal. 20, 1–40 (1965).

    Google Scholar 

  26. Wang, C. C., On the geometric structures of simple bodies, a mathematical foundation for the theory of continuous distributions of dislocations. Arch. Rational Mech. Anal. 27, 33–94 (1967).

    Google Scholar 

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Dedicated to Clifford Truesdell, friend and mentor of the author

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Noll, W. A new mathematical theory of simple materials. Arch. Rational Mech. Anal. 48, 1–50 (1972). https://doi.org/10.1007/BF00253367

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