A DIRECT APPROACH to the problem of the separation of elastic strain energy in the case of generally anisotropic materials is described in the present work. It is based on a simple analysis of the strain tensor into a spherical and a deviatoric one. A definition of dilatational and distortional elastic strain densities is introduced, based on the consideration of the geometrical response of a material. Through the generalized Hooke's law, analytic expressions are obtained for the generally anisotropic materials. The present results coincide with the only available in the literature data for anisotropic materials with cubic symmetry. In addition, an application for transversally isotropic materials is presented.

The mechanical characteristics of transversely isotropic rocks are significantly different under various levels of inclination, and it is difficult to describe exactly the mechanical behaviour of transversely isotropic rocks. Assuming that rock consists of a great deal of microelements, and the microelement strength controlled by Mohr–Coulomb criterion follows the log normal distribution. The elastic modulus is used to reflect the anisotropy of rock, and the weak patches stiffness model is verified and employed to depict the variation of elastic modulus with different inclination angle. Based on basic damage mechanics theory and statistical method, a nonlinear statistical empirical model for transversely isotropic rocks is proposed under uniaxial compressive condition. In order to verify the correctness of the proposed model, comparison analyses between predicted results and experimental data taken from published literature are carried out, which have good consistency. Finally, the discussions on the influences of the distribution parameters ��, �� and elastic modulus with different inclination angle, ����, on proposed model is offered.