Analysis of stresses at the center of transversely isotropic Brazilian disk

This article presents the stresses at the center of a Brazilian disk (BD) for transversely isotropic rocks. It is shown that the solution of stresses at the center of an anisotropic disk is a function of the disk radius and the magnitude of applied load, as well as the material orientation with respect to the load axis and two dimensionless ratios with specific physical meanings and limitations. These two dimensionless parameters are the ratios of Young's modulus and apparent shear modulus, although the ratio of apparent shear modulus will be eliminated if the Saint-Venant assumption is considered. Considerable finite element simulations are carried out to find the stresses at the disk center concerning the material orientation and the two dimensionless parameters. Also, an approximate formula obtained from analytical results, previously proposed in the literature for solving the tensile and compressive stresses at the disk center, is re-written and simplified based on these new definitions. The results of the approximate formula fitted to the analytical results are compared to those obtained from numerical solutions, suggesting a good agreement between the numerical and analytical methods. An approximate equation for the shear stress at the disk center is also formulated based on the numerical results. Finally, the influence of the assumptions for simplification of the proposed formula for the tensile, compressive, and shear stresses at the disk center is discussed, and simple and practical equations are proposed as estimations for the stresses at the center of the BD specimen for low to moderate anisotropic rocks. For highly anisotropic rocks, the reference plots can be used for more accuracy.

Automated summary

This article studies the stresses at the center of a disk made of transversely isotropic rocks in Brazil. It finds that the solution for these stresses depends on the radius of the disk, the applied load, the material orientation, and two dimensionless ratios related to Young's modulus and apparent shear modulus. Finite element simulations are conducted to determine the stresses at the disk center, and an approximate formula is derived from analytical results. The formula is compared to numerical solutions, and simple and practical equations are proposed for estimating the stresses at the center of the disk specimen.