Linking snow microstructure to its macroscopic elastic stiffness tensor: A numerical homogenization method and its application to 3-D images from X-ray tomography

Abstract

The full 3-D macroscopic mechanical behavior of snow is investigated by solving kinematically uniform boundary condition problems derived from homogenization theories over 3-D images obtained by X-ray tomography. Snow is modeled as a porous cohesive material, and its mechanical stiffness tensor is computed within the framework of the elastic behavior of ice. The size of the optimal representative elementary volume, expressed in terms of correlation lengths, is determined through a convergence analysis of the computed effective properties. A wide range of snow densities is explored, and power laws with high regression coefficients are proposed to link the Young's and shear moduli of snow to its density. The degree of anisotropy of these properties is quantified, and Poisson's ratios are also provided. Finally, the influence of the main types of metamorphism (isothermal, temperature gradient, and wet snow metamorphism) on the elastic properties of snow and on their anisotropy is reported. Key Points A robust methodology is proposed to investigate the mechanical behavior of snow from 3-D images The full effective elastic stiffness tensor of snow was computed for 31 tomographic images The influence of density and microstructure (metamorphism, anisotropy, etc.) of snow are highlighted