Abstract
There is a large literature1 in continuum mechanics on the mathematical representation of the mechanical response of material particles. In the physical world, of course, material particles present themselves in various bodies. It is the purpose of this research to construct a mathematical theory for such bodies.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Truesdell, C., & W. Noll, The Non-linear Field Theories of Mechanics. Handbuch der Physik, Vol. III/3. Berlin-Heidelberg-New York: Springer 1965.
Noll, W., Arch. Rational Mech. Anal. 2, 197–226 (1958/59).
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.
Nye, J. F., Acta Met. 1, 153–162 (1953).
Bilby, B. a., R. Bullough, & E. Smith, Proc. Roy. Soc. Lond. a231, 263–273 (1955).
Bilby, B. A., Progress in Solid Mechanics 1, 329–398 (1960). Ed. I. N. Sneddon & R. Hill.
Kröner, E., & A. Seeger, Arch. Rational Mech. Anal. 3, 97–119 (1959).
Chern, S. S., Differentiable Manifolds. Lecture Notes, Dept. Math., Univ. Chicago (1959).
Sternberg, S., Lectures on Differential Geometry. Prentice-Hall 1964.
Nomizu, K., Lie Groups and Differential Geometry. Math. Soc. Japan (1956).
Kobayashi, S., & K. Nomizu, Foundations of Differential Geometry. John Wiley & Sons Interscience Publishers 1963.
Lang, S., Introduction to Differentiable Manifolds. John Wiley & Sons Interscience Publishers 1962.
Auslander, L., & R. Mackenzie, Introduction to Differentiable Manifolds. McGraw-Hill 1963.
Nono, T., Paper to appear in J. Math. Anal. Appl.
Lie, S., & F. Engel, Theorie der Transformationsgruppen. Vol. 3. Leipzig: Teubner 1893.
Noll, W., Proc. Sym. Applied Math. Vol. XVII, 93–101 (1965).
Gurtin, M. E., & W. C. Williams, Arch. Rational Mech. Anal. 23, 163–172 (1966).
Halmos, P. R., Measure Theory. Van Nostrand 1950.
Coleman, B. D., Arch. Rational Mech. Anal. 20, 41–58 (1965).
Wang, C.-C., Arch. Rational Mech. Anal. 20, 1–40 (1965).
Chevalley, C., Theory of Lie Groups. Princeton University Press 1946.
Cohn, P. M., Lie Groups. Cambridge University Press 1957.
Coleman, B. D., & W. Noll, Arch. Rational Mech. Anal. 6, 355–370 (1960).
Wang, C.-C., Arch. Rational Mech. Anal. 18, 343–366 (1965).
Wang, C.-C., Arch. Rational Mech. Anal. 18, 117–126 (1965).
Coleman, B. D., & V. J. Mizel, Arch. Rational Mech. Anal. 23, 87–123 (1966).
Mizel, V. J., & C.-C. Wang, Arch. Rational Mech. Anal. 23, 124–134 (1966).
Steenrod, N., The Topology of Fibre Bundles. Princeton University Press 1951.
Frank, F. C., Phil. Mag. 42, 809–819 (1951).
Schouten, J. A., Ricci-Calculus. Berlin-Göttingen-Heidelberg: Springer 1954.
Ambrose, W., & I. M. Singer, Trans. Amer. Math. Soc. 75, 428–443 (1953).
Coleman, B. D., & W. Noll, Arch. Rational Mech. Anal. 15, 87–111 (1964).
Green, A. E., & J. E. Adkins, Large Elastic Deformations and Non-linear Continuum Mechanics. Oxford: Clarendon Press 1960.
Kröner, E., Arch. Rational Mech. Anal. 3, 273–334 (1959/60).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1968 Springer-Verlag Berlin · Heidelberg
About this chapter
Cite this chapter
Wang, CC. (1968). On the Geometric Structures of Simple Bodies, a Mathematical Foundation for the Theory of Continuous Distributions of Dislocations. In: Continuum Theory of Inhomogeneities in Simple Bodies. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-85992-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-85992-2_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-85994-6
Online ISBN: 978-3-642-85992-2
eBook Packages: Springer Book Archive