In a cubic crystal system, the elastic properties can be described using two shear moduli: the maximum shear modulus, denoted as Gmax, and the minimum shear modulus, denoted as Gmin. These shear moduli correspond to the directions of maximum and minimum resistance to shear deformation, respectively.

In a cubic system, the crystallographic axes are all equal in length, and the angles between them are 90 degrees. The elastic anisotropy curves can be plotted by varying the orientation of the crystallographic axes with respect to the applied stress.

The equations for Gmax and Gmin in terms of other elastic constants are as follows:

Gmax = (C11 - C12) / 2 Gmin = (C44)

Here, C11, C12, and C44 are the elastic constants associated with the cubic crystal system. C11 and C12 represent the stiffness constants related to axial deformation, and C44 represents the stiffness constant associated with shear deformation.

Please note that the values of the elastic constants C11, C12, and C44 depend on the specific material you are considering. These constants are typically experimentally determined or obtained from material databases.

To plot the elastic anisotropy curves, you would need to evaluate Gmax and Gmin for various orientations of the crystallographic axes and then plot the variation of these shear moduli as a function of crystallographic orientation.

You can see it in more detail, for example, in the book Theory of Elasticity - Timoshenko & J. N. Goodier

Firstly, thank you "Andrii Velychkovych" very much for your detailed answer.

I used the equations you gave me to plot the elastic anisotropy of the shear modulus in spherical coordinates using data from the paper of wang et al: "First-Principles Study on the Elastic Mechanical Properties and Anisotropies of Gold–Copper Intermetallic Compounds" https://doi.org/10.3390/met12060959, but the result I got is very different from the one in the mentioned article. The attached images show the results obtained.

I recommend that you ask the authors of the article you mentioned about it. The article contains the postal addresses of all authors.