A discrete approach to describe the elastic-plastic behaviour of snow

Abstract

Snow is composed of small ice particles and, therefore, behaves as a granular material with a variety of sizes and shapes. Understanding the mechanical behaviour of snow is important in areas such as natural hazards e.g. snow avalanches, or traction characteristics of tires with a snow covered road. Therefore, the objective of the current contribution is to present an advanced discrete approach to predict the elastic-plastic behaviour of snow. For this purpose, snow is described by a finite number of discrete ice grains similar to the Discrete-Element Method (DEM) with ice bonds as a link between individual grains and including a creep law for ice. Bonds may rupture under excessive load or may be formed during a contact between ice grains. Hence, the integral behaviour of snow is represented by the combined properties of impact and bonds depending on strain rate, density and temperature. The collision model is based on the linear hysteretic model developed by Walton and Braun [], which accounts for the effect of plasticity. For this behaviour the impact between grains is distinguished into a loading and detaching phase represented by a loading and unloading stiffness constant. Additionally, friction behaviour into the tangential direction at the point of impact and dissipation i.e. coefficient of restitution is taken into account. A bond between two ice grains is represented by a cylinder that is allowed to undergo tension, shear, torsion about its axis and bending. These translational and rotational displacements of a bonding cylinder lead to appropriate strains that yield corresponding stresses with a constitutive model including Youngs modulus E and the Poisson ratio ν. The stresses acting on a bond are converted to forces and moments that determine in conjunction with Newtons 2nd law the kinematics of the ice grains and the overall mechanical behaviour of the ensemble.