Abstract
The differential geometric aspects of the limited nonlinear continuum theory of crystal dislocations are developed in terms of a non-Riemannian geometry with vanishing Riemann-Christoffel curvature. The emphasis is on a general notation and a covariant formulation of the theory. Comparisons are made between the work of Kröner and classical continuum mechanics. The drawback of distant parallelism in passing to the general theory with non-vanishing curvature is discussed.
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References
Kröner, E.: Arcn. Rat. Mech. Anal. 4, 273 (1960).
Bilby, B.A.: Progr. Solid Mechanics 1, 329 (1960).
Kondo, K.: RAAG (Japan) Memoirs, Vols. 1–4, 1955–1967.
Eringen, A. C.: Nonlinear Theory of Continuous Media. New York: McGraw-Hill 1962, Chap. 1.
Bilby, B.A.: Proc. Roy. Soc. A 292, 105 (1966).
Fong, J. T.: Unpublished note dated 7–31–67, National Bureau of Standards.
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© 1968 Springer-Verlag Berlin Heidelberg
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de Wit, R. (1968). Differential Geometry of a Nonlinear Continuum Theory of Dislocations. In: Kröner, E. (eds) Mechanics of Generalized Continua. IUTAM Symposia. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-30257-6_28
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DOI: https://doi.org/10.1007/978-3-662-30257-6_28
Publisher Name: Springer, Berlin, Heidelberg
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