A constitutive relation for the deformation of snow

In this paper a constitutive equation which describes the uniaxial deformation of snow is developed. The basic assumption underlying this work is that the stress-strain response can be derived by considering the structure of the material. The equation which describes the plastic portion of the deformation is developed by considering the relationship between three fundamental variables: the mean spacing between ice grains, the relative velocity between grains, and the fraction of the total number of grains which participate in the deformation process.The mean distance between ice grains is determined by a stereological investigation of the snow structure, and the velocity component is found by empirically characterizing the relaxation of the snow. To determine the mobility of the ice grains acoustic emission data are used. An equation describing the pattern of acoustic emissions for constant rates of deformation is derived and applied to a number of tests. Combining the above variables produces a compressive and tensile constitutive equation which reflects the behavior of the snow under both uniaxial deformations.