ANISOTROPIC ELASTICITY OF POLYCRYSTALLINE ICE IH

A theory to determine the complete tensor of elastic moduli of general ly anisotropic polycrystalline ice and its temperature dependence from the elastic properties of single ice crystals is presented in this pa per. The model. expressed in closed-form, predicts the upper and lower bound limits of the elastic moduli for such polycrystals by generaliz ing the methods of Voigt (1910) and Reuss (1929), respectively, that w ere developed for isotropic aggregates. This involves obtaining the sp atial average of the elastic moduli and compliances of individual crys tals of ice by weighting them with the relative frequency of their ori entations in the anisotropic fabric. Single ice crystals possess an op en hexagonal structure and are transversely isotropic in their elastic properties. The theory is then applied to predict the elastic constan ts of transversely isotropic S1 and S2 ice, and orthotropic S3 ice. Th e predicted upper and lower bound limits are in excellent agreement wi th available experimental data.