A microstructure-based parameterization of the effectivetransverse isotropic elasticity tensor of snow, firn, and porous ice

Abstract

<p>Effective elastic properties of snow, firn, and porous ice are key for<br>various applications and influenced by ice volume fraction and<br>different types of anisotropy. The geometrical anisotropy of the ice-matrix created by temperature gradient metamorphism in low-density<br>snow and firn and the crystallographic anisotropy commonly created<br>upon deformation in high-density, porous ice. Towards a quantitative-distinction of the impact of the different anisotropies on elasticity,<br>we derived a parametrization for the effective elasticity tensor over<br>the entire range of volume fractions as a function of density and<br>geometrical anisotropy. We employed FEM simulations on 395 X-ray<br>tomography microstructures of Lab, Alpine, Arctic, and Antarctic<br>samples. We employed an empirical two-parameter modification of the<br>anisotropic Hashin Shtrikman bounds to obtain a closed-form<br>parametrization accounting for density, anisotropy, and the correct<br>limiting behavior for bubbly ice. We compare our prediction to<br>previous parametrizations derived in limited density regimes and we<br>utilize the Thomson parameter to compare the geometrical-elastic<br>anisotropy to the crystallographic-elastic anisotropy of<br>monocrystalline ice. Our results suggest that a coupled treatment of<br>geometrical and crystallographic effects would be beneficial for a<br>careful interpretation of acoustic measurements in deep firn.</p>