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On the geometric structures of simple bodies, a mathematical foundation for the theory of continuous distributions of dislocations

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References

  1. Truesdell, C., & W. Noll, The Non-linear Field Theories of Mechanics. Handbuch der Physik, Vol. III/3. Berlin-Heidelberg-New York: Springer 1965.

    Google Scholar 

  2. Noll, W., Arch. Rational Mech. Anal. 2, 197–226 (1958/59).

    Google Scholar 

  3. Kondo, K., Memoirs of the Unifying Study of the Basic Problems in Engineering by Means of Geometry, Vol. I (1955), II (1958). Tokyo: Gakujutsu Bunken Fukyu-Kai.

    Google Scholar 

  4. Nye, J. F., Acta Met. 1, 153–162 (1953).

    Google Scholar 

  5. Bilby, B. A., R. Bullough, & E. Smith, Proc. Roy. Soc. Lond. A231, 263–273 (1955).

    Google Scholar 

  6. Bilby, B. A., Progress in Solid Mechanics 1, 329–398 (1960). Ed. I. N. Sneddon & R. Hill.

  7. Kröner, E., & A. Seeger, Arch. Rational Mech. Anal. 3, 97–119 (1959).

    Google Scholar 

  8. Chern, S. S., Differentiable Manifolds. Lecture Notes, Dept. Math., Univ. Chicago (1959).

  9. Sternberg, S., Lectures on Differential Geometry. Prentice-Hall 1964.

  10. Nomizu, K., Lie Groups and Differential Geometry. Math. Soc. Japan (1956).

  11. Kobayashi, S., & K. Nomizu, Foundations of Differential Geometry. John Wiley & Sons Interscience Publishers 1963.

  12. Lang, S., Introduction to Differentiable Manifolds. John Wiley & Sons Interscience Publishers 1962.

  13. Auslander, L., & R. Mackenzie, Introduction to Differentiable Manifolds. McGraw-Hill 1963.

  14. Nôno, T., Paper to appear in J. Math. Anal. Appl.

  15. Lie, S., & F. Engel, Theorie der Transformationsgruppen. Vol. 3. Leipzig: Teubner 1893.

    Google Scholar 

  16. Noll, W., Proc. Sym. Applied Math. Vol. XVII, 93–101 (1965).

    Google Scholar 

  17. Gurtin, M. E., & W. C. Williams, Arch. Rational Mech. Anal. 23, 163–172 (1966).

    Google Scholar 

  18. Halmos, P. R., Measure Theory. Van Nostrand 1950.

  19. Coleman, B. D., Arch. Rational Mech. Anal. 20, 41–58 (1965).

    Google Scholar 

  20. Wang, C.-C., Arch. Rational Mech. Anal. 20, 1–40 (1965).

    Google Scholar 

  21. Chevalley, C., Theory of Lie Groups. Princeton University Press 1946.

  22. Cohn, P. M., Lie Groups. Cambridge University Press 1957.

  23. Coleman, B. D., & W. Noll, Arch. Rational Mech. Anal. 6, 355–370 (1960).

    Google Scholar 

  24. Wang, C.-C., Arch. Rational Mech. Anal. 18, 343–366 (1965).

    Google Scholar 

  25. Wang, C.-C., Arch. Rational Mech. Anal. 18, 117–126 (1965).

    Google Scholar 

  26. Coleman, B. D., & V. J. Mizel, Arch. Rational Mech. Anal. 23, 87–123 (1966).

    Google Scholar 

  27. Mizel, V. J., & C.-C. Wang, Arch. Rational Mech. Anal. 23, 124–134 (1966).

    Google Scholar 

  28. Steenrod, N., The Topology of Fibre Bundles. Princeton University Press 1951.

  29. Frank, F. C., Phil. Mag. 42, 809–819 (1951).

    Google Scholar 

  30. Schouten, J. A., Ricci-Calculus. Berlin-Göttingen-Heidelberg: Springer 1954.

    Google Scholar 

  31. Ambrose, W., & I. M. Singer, Trans. Amer. Math. Soc. 75, 428–443 (1953).

    Google Scholar 

  32. Coleman, B. D., & W. Noll, Arch. Rational Mech. Anal. 15, 87–111 (1964).

    Google Scholar 

  33. Green, A. E., & J. E. Adkins, Large Elastic Deformations and Non-linear Continuum Mechanics. Oxford: Clarendon Press 1960.

    Google Scholar 

  34. Kröner, E., Arch. Rational Mech. Anal. 3, 273–334 (1959/60).

    Google Scholar 

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Authors and Affiliations

  1. The Johns Hopkins University, Baltimore, Maryland

    C. -C. Wang

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  1. C. -C. Wang
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Communicated by W. Noll & C. Truesdell

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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). https://doi.org/10.1007/BF00276434

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  • DOI: https://doi.org/10.1007/BF00276434

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