Contribution to the theory of the second gradient for isotropic media (Q800174)

The theory of the second gradient could provide a correct model of surface and interfacial phenomena. The energy is assumed to be distributed in the fluid and expressed as a function of the density and its spatial derivatives. In the theory of the second gradient, the most general expression of specific energy requires 300 coefficients. For an isotropic medium, the linear representations of the group SO(3) (rotations in \({\mathbb{R}}^ 3)\) reveal eigenspaces and eigenvalues of the linear mapping expressing the ''generalized stress'' as a function of the ''generalized deformation''. The number of coefficients is thereby reduced to 8.