• Ashby, M. F., , and S. D. Hallam, 1986: The failure of brittle solids containing small cracks under compressive stress states. Acta Metall., 34, 497510, doi:10.1016/0001-6160(86)90086-6.

    • Search Google Scholar
    • Export Citation
  • Bratchie, I., 1984: Rheology of an ice floe field. Ann. Glaciol., 5, 2328.

  • Coon, M. D., , G. A. Maykut, , R. S. Pritchard, , D. A. Rothrock, , and A. S. Thorndike, 1974: Modelling the pack ice as an elastic-plastic material. AIDJEX Bulletin, No. 24, University of Washington, Seattle, WA, 1–105.

  • Coon, M. D., , G. S. Knoke, , D. C. Echert, , and R. S. Pritchard, 1998: The architecture of anisotropic elastic-plastic sea ice mechanics constitutive law. J. Geophys. Res., 103 (C10), 21 91521 925.

    • Search Google Scholar
    • Export Citation
  • Coon, M. D., , R. Kwok, , G. Levy, , M. Pruis, , H. Schreyer, , and D. Sulsky, 2007: Arctic Ice Dynamics Joint Experiment (AIDJEX) assumptions revisited and found inadequate. J. Geophys. Res., 112, C11S90, doi:10.1029/2005JC003393.

    • Search Google Scholar
    • Export Citation
  • Cowin, S. C., 1974: The theory of polar fluids. Adv. Appl. Mech., 14, 279347, doi:10.1016/S0065-2156(08)70034-6.

  • Dempsey, J. P., , R. M. Adamson, , and S. V. Mulmule, 1999: Scale effects on the in-situ tensile strength and fracture of ice. Part II: First-year sea ice at Resolute, N.W.T. Int. J. Fract., 95 (1–4), 347366, doi:10.1023/A:1018650303385.

    • Search Google Scholar
    • Export Citation
  • Erlingsson, B., 1988: Two-dimensional deformation patterns in sea ice. J. Glaciol., 34, 301308.

  • Feltham, D. L., 2008: Sea ice rheology. Annu. Rev. Fluid Mech., 40, 91112, doi:10.1146/annurev.fluid.40.111406.102151.

  • Girard, L., , S. Bouillon, , J. Weiss, , D. Amitrano, , T. Fichefet, , and V. Legat, 2011: A new modelling framework for sea-ice mechanics based on elasto-brittle rheology. Ann. Glaciol., 52, 123132.

    • Search Google Scholar
    • Export Citation
  • Hibler, W. D., III, 1979: A dynamic thermodynamic sea ice model. J. Phys. Oceanogr., 9, 815846.

  • Hibler, W. D., III, 1980: Modeling a variable thickness sea ice cover. Mon. Wea. Rev., 108, 19431973.

  • Hibler, W. D., III, 2001: Modeling the formation and evolution of oriented fractures in sea ice. Ann. Glaciol., 33, 157164, doi:10.3189/172756401781818680.

    • Search Google Scholar
    • Export Citation
  • Hibler, W. D., III, , and E. M. Schulson, 2000: On modeling the anisotropic failure and flow of flawed sea ice. J. Geophys. Res., 105 (C7), 17 10517 120.

    • Search Google Scholar
    • Export Citation
  • Hopkins, M. A., 1996: On the mesoscale interaction of lead ice and floes. J. Geophys. Res., 101 (C8), 18 31518 326.

  • Hopkins, M. A., 1998: Four stages of pressure ridging. J. Geophys. Res., 103 (C10), 21 88321 891.

  • Hopkins, M. A., , and A. S. Thorndike, 2006: Floe formation in Arctic sea ice. J. Geophys. Res., 111, C11S23, doi:10.1029/2005JC003352.

  • Hopkins, M. A., , S. Frankenstein, , and A. S. Thorndike, 2004: Formation of an aggregate scale in Arctic sea ice. J. Geophys. Res., 109, C01032, doi:10.1029/2003JC001855.

    • Search Google Scholar
    • Export Citation
  • Jaeger, J. C., , and N. G. W. Cook, 1979: Elasticity and strength of rock. Fundamentals of Rock Mechanics, J. C. Jaeger and N. G. W. Cook, Eds., Chapman and Hall, 95–100.

  • Lewis, J. K., , and J. A. Richter-Menge, 1998: Motion-induced stresses in pack ice. J. Geophys. Res., 103 (C10), 21 83121 843.

  • Marko, J. R., , and R. E. Thomson, 1977: Rectilinear leads and internal motions in the pack ice in the western Arctic Ocean. J. Geophys. Res., 82, 77877802.

    • Search Google Scholar
    • Export Citation
  • Overland, J. E., , and C. H. Pease, 1988: Modeling ice dynamics of coastal seas. J. Geophys. Res., 93 (C12), 15 61915 637.

  • Perovich, D. K., and Coauthors, 1999: Year on ice gives climate insights. Eos, Trans. Amer. Geophys. Union, 80, 485486.

  • Pritchard, R. S., 1988: Mathematical characteristics of sea ice dynamics models. J. Geophys. Res., 93 (C12), 15 60915 618.

  • Richter-Menge, J. A., , and K. F. Jones, 1993: The tensile stress of first-year sea ice. J. Glaciol., 39, 609618.

  • Richter-Menge, J. A., , S. L. McNutt, , J. E. Overland, , and R. Kwok, 2002: Relating Arctic pack ice stress and deformation under winter conditions. J. Geophys. Res., 107, 8040, doi:10.1029/2000JC000477.

    • Search Google Scholar
    • Export Citation
  • Rothrock, D. A., 1975: The energetics of the plastic deformation of pack ice by ridging. J. Geophys. Res., 80, 45144519.

  • Schreyer, H. L., , D. L. Sulsky, , L. B. Munday, , M. D. Coon, , and R. Kwok, 2006: Elastic-decohesive constitutive model for sea ice. J. Geophys. Res., 111, C11S26, doi:10.1029/2005JC003334.

    • Search Google Scholar
    • Export Citation
  • Schulson, E. M., 2001: Brittle failure of ice. Eng. Fract. Mech., 68 (17–18), 18391887, doi:10.1016/S0013-7944(01)00037-6.

  • Schulson, E. M., , A. L. Fortt, , D. Iliescu, , and C. E. Renshaw, 2006: On the role of frictional sliding in the compressive fracture of ice and granite: Terminal vs. post-terminal failure. Acta Mater., 54, 39233932, doi:10.1016/j.actamat.2006.04.024.

    • Search Google Scholar
    • Export Citation
  • Shen, H. H., , W. D. Hibler III, , and M. Leppäranta, 1987: The role of floe collision in sea ice rheology. J. Geophys. Res., 92 (C7), 70857096.

    • Search Google Scholar
    • Export Citation
  • Smith, R. B., 1983: A note on the constitutive law for sea ice. J. Glaciol., 29, 191195.

  • Stern, H. L., , and R. W. Lindsay, 2009: Spatial scaling of Arctic sea ice deformation. J. Geophys. Res., 114, C10017, doi:10.1029/2009JC005380.

    • Search Google Scholar
    • Export Citation
  • Sulsky, D., , and K. Paterson, 2011: Toward a new elastic–decohesive model of Arctic sea ice. Physica D, 240, 16741683, doi:10.1016/j.physd.2011.07.005.

    • Search Google Scholar
    • Export Citation
  • Taylor, P. D., , D. L. Feltham, , P. R. Sammonds, , and D. Hatton, 2006: Continuum sea ice rheology determined from subcontinuum mechanics. J. Geophys. Res., 111, C11015, doi:10.1029/2005JC002996.

    • Search Google Scholar
    • Export Citation
  • Thorndike, A. S., , D. A. Rothrock, , G. A. Maykut, , and R. Colony, 1975: The thickness distribution of sea ice. J. Geophys. Res., 80, 45014513.

    • Search Google Scholar
    • Export Citation
  • Tremblay, L. B., , and L. A. Mysak, 1997: Modeling sea ice as a granular material, including the dilatancy effect. J. Phys. Oceanogr., 27, 23422360.

    • Search Google Scholar
    • Export Citation
  • Walter, B. A., , J. E. Overland, , and P. Turet, 1995: A comparison of satellite-derived and aircraft-measured regional surface sensible heat fluxes over the Beaufort Sea. J. Geophys. Res., 100 (C3), 45854591.

    • Search Google Scholar
    • Export Citation
  • Weiss, J., , and E. M. Schulson, 2009: Coulombic faulting from the grain scale to the geophysical scale: lessons from ice. J. Phys. D Appl. Phys., 42, 214017, doi:10.1088/0022-3727/42/21/214017.

    • Search Google Scholar
    • Export Citation
  • Weiss, J., , E. M. Schulson, and H. L. Stern, 2007: Sea ice rheology from in-situ, satellite and laboratory observations: Fracture and friction. Earth Planet. Sci. Lett., 255 (1–2), 18, doi:10.016/j.epsl.2006.11.033.

    • Search Google Scholar
    • Export Citation
  • Wilchinsky, A. V., , and D. L. Feltham, 2004: A continuum anisotropic model of sea-ice dynamics. Proc. Roy. Soc. London, 460A, 21052140, doi:10.1098/rspa.2004.1282.

    • Search Google Scholar
    • Export Citation
  • Wilchinsky, A. V., , and D. L. Feltham, 2006a: Anisotropic model for granulated sea ice dynamics. J. Mech. Phys. Solids, 54, 11471185, doi:10.1016/j.jmps.2005.12.006.

    • Search Google Scholar
    • Export Citation
  • Wilchinsky, A. V., , and D. L. Feltham, 2006b: Modelling the rheology of sea ice as a collection of diamond-shaped floes. J. Non-Newtonian Fluid Mech., 138, 2232, doi:10.1016/j.jnnfm.2006.05.001.

    • Search Google Scholar
    • Export Citation
  • Wilchinsky, A. V., , and D. L. Feltham, 2011: Modeling Coulombic failure of sea ice with leads. J. Geophys. Res., 116, C08040, doi:10.1029/2011JC007071.

    • Search Google Scholar
    • Export Citation
  • Wilchinsky, A. V., , D. L. Feltham, , and M. A. Hopkins, 2010: The effect of shear rupture on aggregate scale formation in sea ice. J. Geophys. Res., 115, C10002, doi:10.1029/2009JC006043.

    • Search Google Scholar
    • Export Citation
  • Wilchinsky, A. V., , D. L. Feltham, , and M. A. Hopkins, 2011: Modelling the reorientation of sea-ice faults as the wind changes direction. Ann. Glaciol., 52, 8390.

    • Search Google Scholar
    • Export Citation
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Rheology of Discrete Failure Regimes of Anisotropic Sea Ice

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  • 1 National Centre for Earth Observation: Centre for Polar Observation and Modelling, University College London, London, United Kingdom
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ABSTRACT

A rheological model of sea ice is presented that incorporates the orientational distribution of ice thickness in leads embedded in isotropic floe ice. Sea ice internal stress is determined by coulombic, ridging and tensile failure at orientations where corresponding failure criteria are satisfied at minimum stresses. Because sea ice traction increases in thinner leads and cohesion is finite, such failure line angles are determined by the orientational distribution of sea ice thickness relative to the imposed stresses. In contrast to the isotropic case, sea ice thickness anisotropy results in these failure lines becoming dependent on the stress magnitude. Although generally a given failure criteria type can be satisfied at many directions, only two at most are considered. The strain rate is determined by shearing along slip lines accompanied by dilatancy and closing or opening across orientations affected by ridging or tensile failure. The rheology is illustrated by a yield curve determined by combining coulombic and ridging failure for the case of two pairs of isotropically formed leads of different thicknesses rotated with regard to each other, which models two events of coulombic failure followed by dilatancy and refreezing. The yield curve consists of linear segments describing coulombic and ridging yield as failure switches from one lead to another as the stress grows. Because sliding along slip lines is accompanied by dilatancy, at typical Arctic sea ice deformation rates a one-day-long deformation event produces enough open water that these freshly formed slip lines are preferential places of ridging failure.

Corresponding author address: Alexander Wilchinsky, NCEO: CPOM, Department of Earth Sciences, University College London, London WC1E 6BT, United Kingdom. E-mail: aw@cpom.ucl.ac.uk

ABSTRACT

A rheological model of sea ice is presented that incorporates the orientational distribution of ice thickness in leads embedded in isotropic floe ice. Sea ice internal stress is determined by coulombic, ridging and tensile failure at orientations where corresponding failure criteria are satisfied at minimum stresses. Because sea ice traction increases in thinner leads and cohesion is finite, such failure line angles are determined by the orientational distribution of sea ice thickness relative to the imposed stresses. In contrast to the isotropic case, sea ice thickness anisotropy results in these failure lines becoming dependent on the stress magnitude. Although generally a given failure criteria type can be satisfied at many directions, only two at most are considered. The strain rate is determined by shearing along slip lines accompanied by dilatancy and closing or opening across orientations affected by ridging or tensile failure. The rheology is illustrated by a yield curve determined by combining coulombic and ridging failure for the case of two pairs of isotropically formed leads of different thicknesses rotated with regard to each other, which models two events of coulombic failure followed by dilatancy and refreezing. The yield curve consists of linear segments describing coulombic and ridging yield as failure switches from one lead to another as the stress grows. Because sliding along slip lines is accompanied by dilatancy, at typical Arctic sea ice deformation rates a one-day-long deformation event produces enough open water that these freshly formed slip lines are preferential places of ridging failure.

Corresponding author address: Alexander Wilchinsky, NCEO: CPOM, Department of Earth Sciences, University College London, London WC1E 6BT, United Kingdom. E-mail: aw@cpom.ucl.ac.uk
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