Mechanically stable effective isotropic media for all crystal classes: Construction of the third-order elastic constants

The simplest kind of mutual interactions of long-wavelength acoustic phonon s in crystalline elastic media is characterized by sets of components of te nsors of the third-order elastic constants. Averaging these components over all directions of axes of a laboratory frame we obtained elastic constants for effective isotropic media corresponding to anisotropic media that belo ng to all crystal classes. In regions of stability of anisotropic media the corresponding tensors of effective second-order elastic constants are posi tive, i.e., effective isotropic media are mechanically stable. The obtained sets of elastic constants for effective isotropic media can be used in com puter experiments on nonequilibrium gases of long-wavelength acoustic phono ns.