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A uniform stress, multi-grain model for migration recrystallization in polar ice

Staroszczyk R.

Acta Geophysica

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2011

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Vol. 59, no. 5

833-857

EN

A multi-grain model for a migration recrystallization process in polar ice is presented. The model is based on the Sachs-Reuss approximation of the stress homogeneity in a polycrystalline aggregate. An individual crystal of ice is treated as a transversely isotropic and incompressible medium which deforms by viscous creep. The highly anisotropic viscous behaviour of the ice crystal is described by a constitutive law expressing microscopic strain-rate in terms of the deviatoric stress and three fluidity parameters that define different viscous resistances of the crystal in different glide directions. It is assumed that the recrystallization occurs in those crystals in the aggregate which are most slowly deforming, and new crystals are nucleated at orientations which favour the crystal deformation by basal glide. The model predictions are illustrated by results of numerical simulations of simple flows, showing the evolution of the microscopic structure of ice and the variation of macroscopic viscosities with increasing deformations.

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A multi-grain model for migration recrystallization in polar ice

Staroszczyk H.

Archives of Mechanics

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2009

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Vol. 61, nr 3-4

259-282

EN

In the paper a multi-grain model for a migration recrystallization phenomenon in polar ice is presented. A single crystal of ice is treated as a transversely isotropic and incompressible medium which deforms by viscous creep. The anisotropic viscous behaviour of the ice crystal is described by a constitutive law that includes three microscopic viscosity parameters, and the macroscopic behaviour of the polycrystal is derived by adopting the Taylor-Voigt approximation of the velocity gradient homogeneity in the material. It is assumed that recrystallize, that is gradually disappear, these crystals which are most stressed, and at their expense new crystals are nucleated with the orientations that enhance the deformation of the polycrystal. The model predictions are illustrated by results of numerical simulations of simple ?ows, showing the evolution of the oriented structure of ice and the variation of macroscopic viscosities with increasing strains.

3

Axi-symmetric ice sheet flow with evolving anisotropic fabric

Staroszczyk R.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2006

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Vol. 54, nr 4

419-428

EN

An axially symmetric, gravity driven, steady flow of a grounded polar ice sheet with a prescribed temperature field is considered. The ice is treated as an incompressible, non-linearly viscous, anisotropic fluid, the internal structure (fabric) of which evolves as ice descends from the free surface to depth in an ice sheet. The evolution of the ice fabric is described by an orthotropic constitutive law which relates the deviatoric stress to the strain-rate, strain, and three structure tensors based on the current (rotating) principal stretch axes. The solution of the problem is constructed as a leading-order approximation derived from asymptotic expansions in a small parameter that reflects the small ratio of stress and velocity gradients in the lateral direction of the ice sheet to those in the thickness direction. Numerical simulations of the flow problem have been carried out for various sets of rheological parameters defining the limit strength of the anisotropic fabric in ice. The results of calculations illustrate the influence of the ice anisotropy, basal melt conditions and temperature field in ice on the glacier thickness and lateral span, and on the depth profiles of the flow velocity.