A microstructure-based parameterization of the effective, anisotropic elasticity tensor of snow, firn, and bubbly ice
Abstract. Quantifying the link between microstructure and effective elastic properties of snow, firn, and bubbly ice is essential for many applications in cryospheric sciences. The microstructure of snow and ice can be characterized by different types of fabrics (crystallographic, geometrical) that gives rise to macroscopically anisotropic elastic behavior. While the impact of the crystallographic fabric has been extensively studied in deep firn, the present work investigates the influence of the geometrical fabric over the entire range of possible volume fractions. To this end we have computed the effective elasticity tensor of snow, firn, and ice by finite element simulations based on 395 X-ray tomography images comprising samples from the laboratory, Alps, Greenland, and Antarctica. We employed a variant of the Eshelby tensor that has been previously utilized for the parametrization of thermal and dielectric properties of snow and utilized Hashin-Shtrikman bounds to capture the nonlinear interplay between density and geometrical anisotropy. From that we derive a closed-form parametrization for all components of the (transverse isotropic) elastic tensor for all volume fractions using 2 fit parameters per tensor component. Finally we used the Thomsen parameter to compare the geometrical anisotropy to the crystallographic anisotropy in bubbly ice. While the geometrical anisotropy is clearly dominating up to ice volume fractions of Ø ≈ 0.7, a thorough understanding of elasticity in bubbly ice may require a coupled elastic theory that includes geometrical and crystallographic anisotropy.
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