Skip to main content Accessibility help
  • Print publication year: 2009
  • Online publication date: February 2010

7 - Modeling the ductile behavior of isotropic and anisotropic polycrystalline ice



During the gravity-driven flow of glaciers and ice sheets, isotropic ice at the surface progressively becomes anisotropic with the development of textures. Strain-induced textures, combined with the strong anisotropy of the ice crystal, make the polycrystal anisotropic. A polycrystal of ice with most of its c-axes oriented in the same direction deforms at least ten times faster than an isotropic polycrystal, when it is sheared parallel to the basal planes. Depending on the flow conditions, this anisotropy varies from place to place. To construct ice-sheet flow models for the dating of deep ice cores, this evolving viscoplastic anisotropy must be taken into account. Computation with isotropic and anisotropic flow models predicts at depth an age of ice that can differ by several thousand years. From Mangeney et al. (1997), anisotropic ice could be more than 10% younger above the bumps of the bedrock and could be older by more than 100% within hollows. An adequate constitutive relationship must be also incorporated within large-scale flow models to simulate the variation of polar ice sheets with climate.

Various models have been proposed to simulate the evolution of the anisotropy and the behavior of such ices. The increasing numerical capability of computers and the advances in theories that link materials' microstructures and properties have enabled the development of new concepts and algorithms that constitute the so-called multiscale approach for the modeling of material behavior. In this chapter, we restrict our analysis to physically based micro-macro models using a self-consistent approach.

Related content

Powered by UNSILO
Alley, R. B. (1992). Flow-law hypotheses for ice-sheet modeling. J. Glaciol., 38, 245–256.
Ashby, M. F. and Duval, P. (1985). The creep of polycrystalline ice. Cold Reg. Sci. Technol., 11, 285–300.
Azuma, N. A. (1994). A flow law for anisotropic ice and its application to ice sheets. Earth Planet. Sci. Lett., 128, 601–614.
Azuma, N. A. (1995). A flow law for anisotropic polycrystalline ice under uniaxial compressive deformation. Cold Reg. Sci. Technol., 23, 137–147.
Azuma, N. and Higashi, A. (1985). Formation processes of ice fabric pattern in ice sheets. Ann. Glaciol., 6, 130–134.
Boehler, J. P. (1987). Representations for isotropic and anisotropic non-polynomial tensor functions. In Applications of Tensor Functions in Solid Mechanics, ed. Boehler, J. P.. Berlin: Springer-Verlag, pp. 31–53.
Budd, W. F. and Jacka, T. H. (1989). A review of ice rheology for ice sheet modelling. Cold Reg. Sci. Technol., 16, 107–144.
Castelnau, O., Duval, P., Lebensohn, R. A. and Canova, G. R. (1996a). Viscoplastic modelling of texture development in polycrystalline ice with a self-consistent approach: comparison with bound estimates. J. Geophys. Res., 101 (B6), 13,851–13,868.
Castelnau, O., Thorsteinsson, Th., Kipfstuhl, J., Duval, P. and Canova, G. R. (1996b). Modelling fabric development along the GRIP ice core, central Greenland. Ann. Glaciol., 23, 194–201.
Castelnau, O., Canova, G. R., Lebensohn, R. A. and Duval, P. (1997). Modelling viscoplastic behavior of anisotropic polycrystalline ice with a self-consistent approach. Acta Mater., 45, 4823–4834.
Castelnau, O., Duval, P., Montagnat, M. and Brenner, R. (2008). Elastoviscoplastic micromechanical modelling of the transient creep of ice. J. Geophys. Res., 113, B11203.
Chapelle, S., Castelnau, O., Lipenkov, V. and Duval, P. (1998). Dynamic recrystallization and texture development in ice as revealed by the study of deep ice cores in Antarctica and Greenland. J. Geophys. Res., 103 (B3), 5091–5105.
Durand, G. and 10 others (2006). Effect of impurities on grain growth in cold ice sheets. J. Geophys. Res., 111, FO1015, 1–18.
Duval, P. (1976). Lois de fluage transitoire ou permanent de la glace polycristalline pour divers états de contrainte. Ann. Geophys., 32, 335–350.
Duval, P. and Gac, H. (1982). Mechanical behavior of Antarctic ice. Ann. Glaciol., 3, 92–95.
Faria, S. H. (2006). Creep and recrystallization of large polycrystalline masses. I. General continuum theory. Proc. R. Soc. A, 462, 1493–1514.
Gagliardini, O. and Meyssonnier, J. (1999). Analytical derivations for the behaviour and fabric evolution of a linear orthotropic ice polycrystal. J. Geophys. Res., 104 (B8), 17,797–17,809.
Gagliardini, O., Gillet-Chauvet, F. and Montagnat, M. (in press). A review of anisotropic polar ice models: from crystal to ice-sheet flow models. In Physics of Ice Core Records 11, ed. Hondoh, T.. Sapporo: Hokkaido University Press.
Gillet-Chaulet, F. (2006). Modélisation de l'écoulement de la glace polaire anisotrope et premières applications au forage de Dôme C. Thèse de l'Université Joseph Fourier, Grenoble, France.
Gillet-Chaulet, F., Gagliardini, O., Meyssonnier, J., Montagnat, M. and Castelnau, O. (2005). A user-friendly anisotropic flow law for ice-sheet modelling. J. Glaciol., 51, 1–14.
Gillet-Chaulet, F., Gagliardini, O., Meyssonnier, J., Zwinger, T. and Ruokolainen, J. (2006). Flow-induced anisotropy in polar ice and related ice-sheet flow modeling. J. Non-Newtonian Fluid Mech., 134, 33–43.
Gödert, G. and Hutter, K. (1998). Induced anisotropy in large ice shields: theory and its homogenization. Continuum Mech. Thermodyn., 10, 293–318.
Gundestrup, N. S. and Hansen, B. L. (1984). Bore-hole survey at Dye 3, South Greenland. J. Glaciol., 30, 282–288.
Hansen, D. P. and Wilen, L. A. (2002). Performance and applications of an automated c-axis fabric analyser. J. Glaciol., 48, 159–170.
Hutchinson, J. W. (1976). Bounds and self-consistent estimates for creep of polycrystalline materials. Proc. R. Soc. Lond. A, 348, 101–127.
Hutchinson, J. W. (1977). Creep and plasticity of hexagonal polycrystals as related to single crystal slip. Metall. Trans. 8A (9), 1465–1469.
Hutter, K. (1983). Theoretical Glaciology. Dordrecht: Reidel Publishing Company.
Kamb, W. B. (1961). The glide direction in ice. J. Glaciol., 3, 1097–1106.
Lebensohn, R. A. (2001). N-site modeling of a 3D viscoplastic polycrystal using Fast Fourier Transform. Acta Mater., 49, 2723–2737.
Lebensohn, R. A. and Tomé, C. N. (1993). A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: application to zirconium alloys. Acta Metall., 41, 2611–2624.
Lebensohn, R. A., Liu, Yi and Castaneda, P. Ponte (2004a). On the accuracy of the self-consistent approximation for polycrystals: comparison with full-field numerical simulations. Acta Mater., 52, 5347–5361.
Lebensohn, R. A., Liu, Yi and Castaneda, P. Ponte (2004b). Macroscopic properties and field fluctuations in model power-law polycrystals: full-field solutions versus self-consistent estimates. Proc. R. Soc. Lond. A, 460, 1381–1405.
Lebensohn, R. A., Tomé, C. N. and Castaneda, P. Ponte (2007). Self-consistent modeling of the mechanical behavior of viscoplastic polycrystals incorporating intragranular field fluctuations. Phil. Mag., 87, 4287–4322.
Lebensohn, R. A., Montagnat, M., Mansuy, al. (2009). Modeling viscoplastic behavior and heterogeneous intracrystalline deformation of columnar ice polycrystals, Acta Mater. (in press).
Lipenkov, V., Barkov, N. I., Duval, P. and Pimienta, P. (1989). Crystalline structure of the 2083 m ice core at Vostok Station, Antarctica. J. Glaciol., 35, 392–398.
Lipenkov, V., Salamatin, A. and Duval, P. (1997). Bubbly-ice densification in ice sheets: applications. J. Glaciol., 43, 397–407.
Liu, Yi and Castaneda, P. Ponte (2004). Second-order theory for the effective behavior and field fluctuations in viscoplastic polycrystals. J. Mech. Phys. Solids, 52, 467–495.
Lliboutry, L. (1993). Anisotropic, transversely isotropic nonlinear viscosity of rock ice and rheological parameters inferred from homogenization. Int. J. Plast., 9, 619–632.
Mangeney, A., Califano, F. and Hutter, K. (1997). A numerical study of anisotropic, low Reynolds number, free surface flow of ice-sheet modeling. J. Geophys. Res., 102 (B10), 22,749–22,764.
Manley, M. E. and Schulson, E. M. (1997). Kinks bands and cracks in S1 ice under across-column compression. Phil. Mag., 75, 83–90.
Mansuy, Ph. (2001). Contribution à l'étude du comportement viscoplastique d'un multicristal de glace: hétérogénéité de la déformation et localisation, expériences et modèles. Thèse de l'Université Joseph Fourier, Grenoble, France.
Masson, R. and Zaoui, A. (1999). Self-consistent estimates for the rate-dependent elasto-plastic behaviour of polycrystalline materials. J. Mech. Phys. Sol., 47, 1543–1568.
Meyssonnier, J., Duval, P., Gagliardini, O. and Philip, A. (2001). Constitutive modeling and flow simulation of anisotropic polar ice. In Continuum Mechanics and Applications in Geophysics and the Environment. Berlin: Springer-Verlag.
Molinari, A., Canova, G. R. and Ahzy, S. (1987). A self-consistent approach of the large deformation polycrystal viscoplasticity. Acta Metall., 35, 2983–2994.
Montagnat, M., Duval, P., Bastie, P., Hamelin, B. and Lipenkov, V. Ya. (2003). Lattice distortion in ice crystals from the Vostok core (Antarctica) revealed by hard X-ray diffraction: implication in the deformation of ice at low stresses. Earth Planet. Sci. Lett., 214, 369–378.
Montagnat, M., Weiss, J., Duval, al. (2006). The heterogeneous nature of slip in ice single crystals deformed under torsion. Phil. Mag., 86, 4259–4270.
Morland, L. and Staroszczyk, R. (1998). Viscous response of polar ice with evolving fabric. Continuum Mech. Thermodyn., 10, 135–152.
Nishikawa, O. and Takeshita, T. (1999). Dynamic analysis and two types of kink bands in quartz veins deformed under subgreenschist conditions. Tectonophysics, 301, 21–34.
Pimienta, P., Duval, P. and Lipenkov, V. Ya. (1987). Mechanical behavior of anisotropic polar ice. In The Physical Basis of Ice Sheet Modeling, eds. Waddington, E. D. and Walder, J. S.. Vancouver: IAHS Publication 170, pp. 57–66.
Placidi, L., Hutter, K. and Faria, S. H. (2006). A critical review of the mechanics of polycrystalline polar ice. GAMM-Mitteilungen, 29, 80–117.
Rigsby, G. P. (1951). Crystal fabric studies on Emmons Glacier, Mount Rainier, Washington. J. Geol., 59, 590–598.
Russell-Head, D. S. and Budd, W. F. (1979). Ice-flow properties derived from bore-hole shear measurement combined with ice-core studies. J. Glaciol., 24, 117–130.
Russell-Head, D. S. and Wilson, C. J. L. (2001). Automated fabric analyzer system for quartz and ice. Geol. Soc. Austral. Abstr., 64, 159.
Sachs, G. (1928). Zur Ableitung einer Fliessbedingung. Z. Ver. Dtsch. Ing., 72, 734–736.
Shoji, H. and Langway, C. C.. (1988). Flow-law parameters of the Dye 3, Greenland, deep ice core. Ann. Glaciol., 10, 146–150.
Staroszczyk, R. and Morland, L. W. (2000). Plane ice-sheet flow with evolving orthotropic fabric. Ann. Glaciol., 30, 93–101.
Svendsen, B. and Hutter, K. (1996). A continuum approach for modeling induced anisotropy in glaciers and ice sheets. Ann. Glaciol., 23, 262–269.
Taylor, G. I. (1938). Plastic strain in metals. J. Inst. Met., 62, 307–324.
Thorsteinsson, Th. (2001). An analytical approach to deformation of anisotropic ice-crystal aggregates. J. Glaciol., 47, 507–516.
Thorsteinsson, Th. (2002). Fabric development with nearest-neighbor interaction and dynamic recrystallization. J. Geophys. Res., 107 (B1), 1–13.
Thorsteinsson, Th., Kipfstuhl, J. and Miller, H. (1997). Textures and fabrics in the GRIP ice core. J. Geophys. Res., 102 (C12), 26,583–26,599.
Thorsteinsson, Th., Waddington, E. D., Taylor, K. C., Alley, R. B. and Blankenship, D. D. (1999). Strain-rate enhancement at Dye 3, Greenland. J. Glaciol., 45, 338–345.
Veen, C. J. and Whillans, I. M. (1994). Development of fabric in ice. Cold Reg. Sci. Technol., 22, 171–195.
Wilson, C. J. L., Burg, J. P. and Mitchell, J. C. (1986). The origin of kinks in polycrystalline ice. Tectonophysics, 127, 27–48.
Zhou, A. G., Basu, S. and Barsoum, M. W. (2008). Kinking nonlinear elasticity, damping and microyielding of hexagonal close-packed metals. Acta Mater., 56, 60–67.