Effective isotropic media for all Laue symmetry classes - construction of second and third order elastic constants

Dispersion law and mutual interactions of long wavelength acoustic phonons in crystalline elastic media depend on sets of components of tensors of the second and 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 which belo ng to all symmetry classes. In regions of stability of anisotropic media th e corresponding tensors of effective second order elastic constants are pos itive, i.e. effective isotropic media are mechanically stable. The obtained elastic constants can be used in computer experiments on nonequilibrium ga ses of long wavelength acoustic phonons. (C) 1999 Elsevier Science B.V. All rights reserved.