Skip to main content
Log in

Micro-structure in linear elasticity

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Ericksen, J. L., & C. Truesdell, Exact theory of stress and strain in rods and shells. Arch. Rational Mech. Anal. 1, 295–323 (1958).

    Google Scholar 

  2. Cosserat, E. Cosserat F., Théorie des Corps Déformables. Paris: A. Hermann & Fils 1909. For the linear, two-dimensional theory, with applications, see H. Schaefer, Versuch einer Elastizitätstheorie des Zweidimensionalen ebenen Cosserat-Kontinuums. Miszellaneen der Angewandten Mechanik, pp. 277–292. Berlin: Akademie-Verlag 1962.

    Google Scholar 

  3. Jeffreys, H., & Jeffreys B. S., Methods of Mathematical Physics, Second Edition. Cambridge: University Press 1950.

    Google Scholar 

  4. Love, A. E. H., A Treatise on the Mathematical Theory of Elasticity, Fourth Edition. Cambridge: University Press 1927.

    Google Scholar 

  5. Grioli, G., Elasticità asimmetrica. Ann. di Mat. pura ed appl., Ser. IV 50, 389–417 (1960).

    Google Scholar 

  6. Aero, E. L., & E. V. Kuvshinskii, Fundamental equations of the theory of elastic media with rotationally interacting particles. Fizika Tverdogo Tela 2, 1399–1409 (1960); Translation: Soviet Physics Solid State 2, 1272–1281 (1961).

    Google Scholar 

  7. Rajagopal, E. S., The existence of interfacial couples in infinitesimal elasticity. Ann. der Physik 6, 192–201 (1960).

    Google Scholar 

  8. Toupin, R. A., Elastic materials with couple-stresses. Arch. Rational Mech. Anal. 11, 385–414 (1962).

    Google Scholar 

  9. Mindlin, R. D., & H. F. Tiersten, Effects of couple-stresses in linear elasticity. Arch. Rational Mech. Anal. 11, 415–448 (1962).

    Google Scholar 

  10. Mindlin, R. D., Influence of couple-stresses on stress-concentrations. Experimental Mechanics 3, 1–7 (1963).

    Google Scholar 

  11. Mindlin, R. D., & M. A. Medick, Extensional vibrations of elastic plates. J. Appl. Mech. 26, 561–569 (1959).

    Google Scholar 

  12. Gazis, D. C., & R. F. Wallis, Extensional waves in cubic crystal plates. Proc. 4th U.S.Nat. Cong. Appl. Mech., 161–168 (1962).

  13. Mindlin, R. D., High frequency vibrations of plated, crystal plates. Progress in Applied Mechanics, pp. 73–84. New York: Macmillan Co. 1963.

    Google Scholar 

  14. Gazis, D. C., & R. F. Wallis, Surface vibrational modes in crystal lattices with complex interatomic interactions. J. Math. Phys. 3, 190–199 (1962).

    Google Scholar 

  15. Brockhouse, B. N., & P. K. Iyengar, Normal modes of germanium by neutron spectroscopy. Phys. Rev. 111, 747–754 (1958).

    Google Scholar 

  16. Mindlin, R. D., Thickness-shear and flexural vibrations of crystal plates. J. Appl. Phys. 22, 316–323 (1951).

    Google Scholar 

  17. Mindlin, R. D., High frequency vibrations of crystal plates. Q. Appl. Math. 19, 51–61 (1961).

    Google Scholar 

  18. Kane, T. R., & R. D. Mindlin, High frequency extensional vibrations of plates. J. Appl. Mech. 23, 277–283 (1956).

    Google Scholar 

  19. Mindlin, R. D., Influence of rotatory inertia and shear on flexural vibrations of isotropic, elastic plates. J. Appl. Mech. 18, 31–38 (1951).

    Google Scholar 

  20. Jaramillo, T. J., A generalization of the energy function of elasticity theory. Dissertation, Department of Mathematics, University of Chicago, 1929.

  21. Mindlin, R. D., Force at a point in the interior of a semi-infinite solid. Proc. First Midwestern Conf. on Solid Mech., Urbana, Illinois, 56–59 (1953).

  22. Papkovitch, P. F., The representation of the general integral of the fundamental equations of elasticity theory in terms of harmonic functions. Izv. Akad. Nauk SSSR, Phys.-Math. Ser. 10, 1425 (1932).

    Google Scholar 

  23. Mindlin, R. D., Note on the Galerkin and Papkovitch stress functions. Bull. Amer. Math. Soc. 42, 373–376 (1936).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by R. A. Toupin

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mindlin, R.D. Micro-structure in linear elasticity. Arch. Rational Mech. Anal. 16, 51–78 (1964). https://doi.org/10.1007/BF00248490

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00248490

Keywords

Navigation