Micromechanical analysis of deformation of snow using X-ray tomography

Snow exhibits an elastic response followed by a softening behavior under compression at a strain rate of 10− 4 s− 1 and higher. The strain softening behavior is postulated due to initiation and growth of damage in the ice matrix. A deformation controlled compression experiment at a strain rate of 2 × 10− 4 s− 1 was conducted on a round grained snow sample. To investigate the link between behavior of snow and ice, X-ray tomographic imaging of the sample was performed and the size of representative volume element (RVE) with respect to ice volume fraction V ϕ i RVE was estimated. From the set of scanned images 112 sub-volumes of sizes equal to and larger than V ϕ i RVE were selected. The ice matrix formed by these images was meshed with finite elements (FE) to simulate the stress–strain curve of snow under deformation controlled compression. An elasto-plastic constitutive law for ice with provision for degradation of elastic modulus due to damage was used to simulate the stress–strain response including strain softening as observed in the experiment. The statistical representativeness of the RVE with respect to ultimate strength (S) and elastic modulus (E) of snow was further analyzed in terms of the precision of the numerical estimates of the effective properties. It was found that the standard deviation in the ultimate strength & elastic modulus is reduced by 50% for sub-volume of size 8 V ϕ i RVE as compared to the sub-volume of size V ϕ i RVE . The sensitivity of overall stress–strain response to the finite size effects is also analyzed and the average coefficient of variation of the simulated stress–response with respect to the experimental response reduces from 44% for 5.745 mm3 to 18% for 45.96 mm3.