Abstract
Linear elasticity is defined by a set of linear relations between stresses σ ij and strains ε ij (assumed to be very small). Using the dummy index rule:
This is a preview of subscription content, log in via an institution to check access.
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
I. N. Sneddon and D. S. Berry: The classical theory of elasticity. In Encyclopedia of Physics (S. Flügge, ed.), Springer Verlag, Berlin (1958) pp. 1–126.
L. Lliboutry and P. Duval: Various isotropic and anisotropic ices found in glaciers and polar ice caps and their corresponding rheologies, Annales Geophysicae, 3 (1985) pp. 207–224.
J. R. Willis: Variational and related methods for the overall properties of composites, Advances in Appl. Mech., 21 (1981) pp. 1–78.
M. F. Ashby and P. Duval: The creep of polycrystalline ice, Cold Reg. Sci. Tech., 11 (1985) pp. 285–300.
B. Michel: Ice mechanics, Presses de l’Université Laval, Quebec (1978).
N. K. Sinha: Short term rheology of polycrystalline ice, J. Glaciol., 21 (1978) p. 457–473.
N. K. Sinha: Grain boundary sliding in polycrystalline materials, Phil. Mag. A, 40 (1979) pp. 825–842.
R. Hill: Continuum micromechanics of elastoplastic polycrystals, J. Mech. Phys. Solids, 13 (1965) pp. 89–101.
U. F. Kocks: The relation between polycrystal deformation and single-crystal deformation, Met. Trans., 1 (1970) pp. 1121–1143.
J. W. Hutchinson: Bounds and self-consistent estimates for creep of polycrystalline materials, Proc. Roy. Soc. London A, 348 (1976) pp. 101–127.
J. W. Hutchinson: Creep and plasticity of hexagonal polycrystals as related to single crystal slip, Met. Trans. A, 8 (1977) pp. 1465–1469.
A. R. S. Ponter and F. A. Leckie: Constitutive relationships for the time-dependent deformation of metals, J. Eng. materials techn., (1976) pp. 47–51.
W. D. Means and M. W. Jessel: Accommodation migration of grain boundaries, Tectonophysics, 127 (1986) pp. 67–86.
G. P. Rigsby: Crystal orientation in glacier and in experimentally deformed ice, J. Glaciol., 3 (1960) pp. 589–606.
A. V. Hershey: The elasticity of an isotropic aggregate of anisotropic cubic crystals, J. Appl. Mech., 21 (1954) pp. 236–240.
B. Budiansky: On the elastic moduli of some heterogeneous materials, J. Mech. Phys. Solids, 13 (1965) pp. 223–227.
J. D. Eshelby: The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. Roy. Soc. London A, 241 (1957) pp. 376–396.
A. F. Johnson: Creep characterization of transversely-isotropic metallic materials, J. Mech. Phys. Solids, 25 (1977) pp. 117–126.
L. Lliboutry and I. Andermann: Extension de la loi de Norton-Hoffà un matériau orthotrope de révolution, Comptes-rendus Ac. Sci., 294 II (1982) pp. 1309–1312.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1987 Martinus Nijhoff Publishers, Dordrecht
About this chapter
Cite this chapter
Lliboutry, L.A. (1987). Homogenization, and the transversely isotropic power-law viscous body. In: Very Slow Flows of Solids. Mechanics of Fluids and Transport Processes, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3563-1_16
Download citation
DOI: https://doi.org/10.1007/978-94-009-3563-1_16
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8094-1
Online ISBN: 978-94-009-3563-1
eBook Packages: Springer Book Archive