Abstract
A material body with smoothly distributed microstructure can be seen geometrically as a fibre bundle. Within this very general framework, we show that a theory of continuous distributions of dislocations can be formulated and specialized to particular applications, both old and new.
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References
B.A. Bilby, Continuous distributions of dislocations. In: Progress in Solid Mechanics, Vol. 1. North-Holland, Amsterdam (1960) pp. 329–398.
G. Capriz, Continua with Microstructure. Springer (1989).
E. Cosserat and F. Cosserat, Théorie des Corps Déformables, Paris, Hermann (1909).
M. Epstein, Eshelby-like tensors in thermoelasticity. In: W. Muschik and G.A. Maugin (eds), Nonlinear Thermomechanical Processes in Continua, Vol. 61. TUB-Dokumentation, Berlin (1992) pp. 147–159.
M. Epstein, On the anelastic evolution of second-grade materials. Extracta Mathematicae 14 (1999) 157–161.
M. Epstein, Towards a complete second-order evolution law. Math. Mech. Solids 4 (1999) 251–266.
M. Epstein and M. de Leön, Homogeneity conditions for generalized Cosserat media. J. Elasticity 43 (1996) 189–201.
M. Epstein and M. de Leön, Geometrical theory of uniform Cosserat media. J. Geom. Physics 26 (1998) 127–170.
M. Epstein and G.A. Maugin, Sur le tenseur de moment matériel d’Eshelby en élasticité non linéaire. C. R. Acad. Sci. Paris 310/II (1990) 675–768.
M. Epstein and G.A. Maugin, The energy-momentum tensor and material uniformity in finite elasticity. Acta Mechanica 83 (1990) 127–133.
J.D. Eshelby, The force on an elastic singularity. Philos. Trans. Roy. Soc. London A 244 (1951) 87–112.
M.E. Gurtin, Configurational Forces as Basic Concepts of Continuum Physics. Springer, Berlin (2000).
K. Kondo, Geometry of elastic deformation and incompatibility. In: Memoirs of the Unifying Study of the Basic Problems in Engineering Science by Means of Geometry. Tokyo Gakujutsu Benken Fukyu-Kai (1955).
E. Kroener, Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen. Arch. Rational Mech. Anal. 4 (1960) 273–334.
M. de Leön, A geometrical description of media with microstructure: Uniformity and homogeneity. In: Gepmetry, Continua and Microstructure, Collection Travaux en Cours 60. Herrmann, Paris (1999) pp. 11–20.
M. de Leön and M. Epstein, Geometric characterization of the homogeneity of continua with microstructure. Extracta Mathematicae 11 (1996) 1116–1126.
G.A. Maugin, Material Inhomogeneities in Elasticity. Chapman and Hall, London (1993).
W. Noll, Materially uniform simple bodies with inhomogeneities. Arch. Rational Mech. Anal. 27 (1967) 1–32.
C.C. Wang, On the geometric structure of simple bodies: A mathematical foundation for the theory of continuous distributions of dislocations. Arch. Rational Mech. Anal. 27 (1967) 33–94.
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Dedicated to the memory of Clifford Ambrose Truesdell III.
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© 2004 Kluwer Academic Publishers
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Epstein, M., Bucataru, I. (2004). Continuous Distributions of Dislocations in Bodies with Microstructure. In: Man, CS., Fosdick, R.L. (eds) The Rational Spirit in Modern Continuum Mechanics. Springer, Dordrecht. https://doi.org/10.1007/1-4020-2308-1_20
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DOI: https://doi.org/10.1007/1-4020-2308-1_20
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