The modern techniques for engineering analysis are based on a deep understanding of the proportional relationship between stress and strain and the description in terms of isotropic elastic constants, in many cases, is enough. In anisotropic materials the knowledge of the elastic constants is important for the manufacturing process and for micro mechanical modelling behaviour of the material to develop the new composite materials.
Theoretical calculations of elastics constants and anisotropies are applied to tough ceramics ZrO 2 , HfO 2 and in rutile TiO 2 and SnO 2 . Their dependence of the residual hydrostatic stress in the crystal are given. The microscopic elastic anisotropy determined in this work, could be applied in the macro scale in the case the constituent grains have a preferred orientation in the crystal lattice or the grains shape is not spherical (faceted) and it is aligned to a common crystal axis. To cover the case where the grains are distributed at randomly, the Voigt-Reuss-Hill polycrystalline approach is applied to obtain the average values of Young, bulk, shear modules, Poisson coefficient and sound velocity in the transversal and longitudinal modes.
These theoretical results, could be useful in the interpretation of experimental results obtained with the method known as diffraction elastic constant (DEC).