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On a class of conservation laws in linearized and finite elastostatics

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References

  1. J. D. Eshelby, The Continuum Theory of Lattice Defects. Solid State Physics, edited by F. Seitz & D. Turnbull, Volume 3, Academic Press, New York, 1956.

    Google Scholar 

  2. J. R. Rice, A path-independent integral and the approximate analysis of strain concentrations by notches and cracks. Journal of Applied Mechanics 35 (1968), 2, 379.

    Google Scholar 

  3. J. L. Sanders, On the Griffith-Irwin fracture theory. Journal of Applied Mechanics 27 (1960), 2, 352.

    Google Scholar 

  4. G. P. Cherepanov, Crack propagation in continuous media. Journal of Applied Mathematics and Mechanics, English Translation 31 (1967), 3, 504.

    Google Scholar 

  5. J. W. Hutchinson, Singular behavior at the end of a tensile crack in a hardening material. Journal of the Mechanics and Physics of Solids 16 (1968), 13.

    Google Scholar 

  6. J. W. Hutchinson, Plastic stress and strain fields at a crack tip. Journal of the Mechanics and Physics of Solids 16 (1968), 337.

    Google Scholar 

  7. E. Noether, Invariante Variationsprobleme. Göttinger Nachrichten, Mathematisch-physikalische Klasse 2 (1918), 235.

    Google Scholar 

  8. E. Bessel-Hagen, Über die Erhaltungssätze der Elektrodynamik. Mathematische Annalen 84 (1921), 259.

    Google Scholar 

  9. M. D. Kruskal & N. J. Zabusky, Exact invariants for a class of nonlinear wave equations. Journal of Mathematical Physics 7 (1966), 7, 1256.

    Google Scholar 

  10. R. G. Casten, Methods for deriving conservation laws. Doctoral Dissertation, California Institute of Technology, (1970).

  11. O. D. Kellogg, Foundations of Potential Theory. Frederick Ungar, New York, 1929.

    Google Scholar 

  12. I. M. Gelfand & S. V. Fomin, Calculus of Variations, English translation by R. A. Silverman, Prentice-Hall, Englewood Cliffs, New Jersey, 1963.

    Google Scholar 

  13. C. Truesdell & W. Noll, The Non-Linear Field Theories of Mechanics. Handbuch der Physik, vol. III/3. Springer-Verlag, Berlin-Heidelberg-New York, 1965.

    Google Scholar 

  14. C. Truesdell & R. Toupin, The Classical Field Theories. Handbuch der Physik, vol. III/1. Springer-Verlag, Berlin-Göttingen-Heidelberg, 1960.

    Google Scholar 

  15. R. S. Rivlin, Some Topics in Finite Elasticity. Proceedings, First Symposium on Naval Structural Mechanics, Pergamon, New York, 1960.

    Google Scholar 

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Authors and Affiliations

  1. California Institute of Technology, Pasadena

    J. K. Knowles & Eli Sternberg

Authors
  1. J. K. Knowles
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  2. Eli Sternberg
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Additional information

The results communicated in this paper were obtained in the course of an investigation supported under Contract N 00014-67-A-0094-0020 of the California Institute of Technology with the Office of Naval Research in Washington, D. C.

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Knowles, J.K., Sternberg, E. On a class of conservation laws in linearized and finite elastostatics. Arch. Rational Mech. Anal. 44, 187–211 (1972). https://doi.org/10.1007/BF00250778

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  • DOI: https://doi.org/10.1007/BF00250778

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