Macroscopic response of strongly anisotropic porous viscoplastic single crystals and applications to ice

A recently developed iterated homogenization procedure (Agoras and Ponte Castañeda, 2013) is generalized for porous viscoplastic single crystals and applied to characterize the effective behavior of low-symmetry high-anisotropy porous HCP single crystals (e.g., ice), focusing on the complex coupled effects of the porosity, void shape and crystal anisotropy. Consistent estimates for the average strain rate in the voids are also obtained and their implications for the evolution of the microstructure are explored. The intrinsic effect of the strong crystal anisotropy of porous ice is deduced from comparisons with corresponding results for porous isotropic materials, and found to be significant. In particular, as a consequence of the strong crystal anisotropy of ice, the porosity growth is found to be quite fast at low stress triaxiality, while the void distortion rates can be more significant at high stress triaxialities. Finally, the coupling between the “morphological” anisotropy induced by the void shape and the underlying crystalline anisotropy is investigated and found to have significant effects on the void growth and the void distortion, leading to significantly different behaviors for porous ice in comparison to porous isotropic materials.