References
Gough, H. J., Crystalline structure in relation to failure of metals-especially by fatigue, 8th Edgar Marburg Lecture, Proc. Amer. Soc. Test. Mat. 33, II (1933), 3–114.
Burgers, W. G., Plasticity of crystals, in: Elasticity, plasticity and structure of matter, Houwink, R. ed., Cambridge University Press (1937).
Mermin, N. D., The topological theory of defects in ordered media, Reviews of Modern Physics 51 (1979), 591–648.
Kröner, E., Continuum theory of defects, Proc. Summer School on the Physics of Defects, Jul.–Aug. 1980, Les Houches (France), North-Holland Publishing Co., Amsterdam (1981).
Ericksen, J. L., Thermoelastic considerations for continuously dislocated crystals, Proc. Int. Symp. on Mechanics of Dislocations, Houghton, MI, 28–31 Aug. 1983 (to appear).
Davini, C., A continuum approach to crystals with defects, Istituto di Meccanica Teorica ed Applicata (Udine), report IMTA/014 (1983).
Bilby, B. A., Continuous distributions of dislocations, in: Progress in Solids Mechanics, Vol. I, I. E. Sneddon ed., North-Holland Publishing Co.
Kröner, E., Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen, Arch. Rational Mech. Anal. 4 (1960), 273–334.
Noll, W., Materially uniform simple bodies with inhomogeneities, Arch. Rational Mech. Anal. 27 (1967), 1–32.
Toupin, R. A., Dislocated and oriented media, I.U.T.A.M. Symposium on: Mechanics of Generalized Continua, E. Kröner ed., Springer-Verlag, Berlin Heidelberg New York (1968).
Love, A. E. H., A treatise on the mathematical theory of elasticity, 4th edition Dover Publications, New York (1944).
Born, M., Dynamik der Kristallgitter, Teubner, Leipzig (1905).
Gough, H. J., & W. A. Wood, Strength in metals in the light of Modern Physics, J. Roy. Aeronaut. Soc. 40 (1936), 586–621.
Toupin, R. A., & R. S. Rivlin, Dimensional changes in crystals caused by dislocations, J. Math. Phys. 1 (1960), 8–15.
Kröner, E., Differential geometry of defects in condensed systems of particles with only translational mobility, Int. J. Engng. Sci. 19 (1981), 1507–1515.
Taylor, G. I., The mechanism of plastic deformation of crystals, Parts I and II, Proc. Roy. Soc. A 145 (1934), 362–387, 388–404.
Gibbs, J. W., On the equilibrium of heterogeneous substances, Trans. Conn. Acad. III, 108–248, (1876) and 343–524, (1878).
Truesdell, C., & R. Toupin, The classical field theories, Handbuch der Physik Band III/1, Springer-Verlag, Berlin Heidelberg New York (1960).
Goodman, M. A., & S. C. Cowin, A continuum theory for granular materials Arch. Rational Mech. Anal. 44 (1971–1972), 249–266.
Kröner, E., Zum Materialgesetz eines elastischen Mediums mit Momentenspannungen, Z. Naturforsch. 20 (1965), 336–350.
Capriz, G., Bodies with microstructure (I), Riv. Mat. Univ. Parma 4 (1979), 673–691.
Author information
Authors and Affiliations
Additional information
Communicated by W. O. Williams
Rights and permissions
About this article
Cite this article
Davini, C. A proposal for a continuum theory of defective crystals. Arch. Rational Mech. Anal. 96, 295–317 (1986). https://doi.org/10.1007/BF00251800
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00251800