Abstract
The theory of continuous distributions of inhomogeneities is extended to the context of elastic media with internal structure. Homogeneity conditions are derived in terms of three material connections naturally arising from the uniform constitutive laws.
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References
K.H. Antony, Die Theorie der Disklinationen.Arch. Rational Mech. Anal. 39 (1970) 43–88.
B.A. Bilby, Continuous distributions of Dislocations,Progress in Solid Mechanics, Volume 1. North-Holland, Amsterdam (1960) pp. 329–398.
E. Cosserat and F. Cosserat,Théorie des corps Déformables, Hermann, Paris (1909).
M.de León, M. Epstein, On the integrability of second orderG-structures with applications to continuous theories of dislocations,Reports on Mathematical Physics 33 (1993) 419–436.
M.de León, M. Epstein, Material bodies of higher grade,C. R. Acad. Sc. Paris 319 Sér. I (1994) 615–620.
M.de León, M. Epstein, The geometry of uniformity in second-grade elasticity,Acta Mechanica 114 (1996) 217–224.
M. Elzanowski, M. Epstein and J. Sniatycki,G-structures and material homogeneity,J. Elasticity 23 (1990) 167–180.
A.C. Eringen and Ch.B. Kafadar, Polar field theories. In A. Cemal Eringen (ed.),Continuum Physics, Vol. IV, Part I. Academic Press, New York (1976) pp. 1–73.
K. Kondo,Geometry of Elastic Deformation and Incompatibility, Memoirs of the Unifying Study of the Basic Problems in Engineering Sciences by Means of Geometry, Tokyo Gakujutsu Benken Fukyu-Kai,1C (1955).
E. Kröner, Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen,Arch. Rational Mech. Anal. 4 (1960) 273–334.
K.C. Le and H. Stumpf, Constitutive Equations for Elastoplastic Bodies at Finite Strain: Thermodynamic Implementation,Acta Mechanica 100 (1993) 155–170.
K.C. Le and H. Stumpf, Finite Elastoplasticity with Microstructure, Mitteilung Nr. 92,Institut für Mechanik, Ruhr-Universität Bochum (1994).
G. Maugin,Material Inhomogeneities in Elasticity, London, Chapman & Hall (1993).
W. Noll, Materially Uniform Simple Bodies with Inhomogeneities,Arch. Rational Mech. Anal. 27 (1967) 1–32.
J.F. Pommaret,Lie Pseudogroups and Mechanics, Mathematics and Its Applications, Gordon and Breach, New York (1988).
C. Truesdell and R.A. Toupin,Principles of Classical Mechanics and Field Theory, Handbuch der Physik, Vol. III/1, Berlin-New York, Springer (1960).
C. Truesdell and W. Noll,The Non-Linear Field Theories of Mechanics, Handbuch der Physik, Vol. III/3, Berlin-New York, Springer (1965).
C.C. Wang, On the geometric structures 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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Epstein, M., De León, M. Homogeneity conditions for generalized cosserat media. J Elasticity 43, 189–201 (1996). https://doi.org/10.1007/BF00042500
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DOI: https://doi.org/10.1007/BF00042500