A fabric tensor based small strain constitutive law for the elastoplastic behavior of snow

Abstract

The mechanical behavior of snow depends on its density and microstructure. The anisotropy in the microstructure is expressed in terms of fabric tensor that leads to an anisotropic stress-strain relation. Lately, fabric-based relations have successfully estimated the elastic properties of snow. Motivated by this, we propose a fabric-based macroscopic elasto-plastic constitutive law for snow, which can be used to study avalanche initiation. Mean Intercept Length tensor used as a measure of material fabric is determined by X-ray tomography. Fabric tensor and density-dependent yield surface with a provision for isotropic hardening/softening are used in this process. Beyond the initial yield, the yield function grows till the strength of the snow is reached and then softens. Since snow exhibits tension and compression behavior asymmetry, a piece-wise quadratic yield function is used. Stress-strain curves needed for determining the equation of the hardening/softening law and other parameters of the proposed macroscopic constitutive law are obtained through micro-Finite Element (μ-FE) simulations. The macroscopic constitutive law has been implemented as a user subroutine in a FE code and can predict the snow's multiaxial behavior.