The generalized Cauchy relation as an universal property of the amorphous state

From the structural point of view a simple Cauchy relation is not expected to hold for isotropic materials. Such a Cauchy relation would imply the reduction of independent elastic stiffness constants for the isotropic state from two to one. However, high frequency elastic data of glasses and viscous liquids show a linear transformation between the shear and the longitudinal elastic stiffness which is called a generalized Cauchy relation. It seems, that the parameters of the linear transformation are related to the global and local symmetry and/or order. Brillouin investigations on the elastic stiffness coefficients of a consolidated nano-crystalline material (CeO 2 ) and of DGEBA/SiO 2 nano-composites are used in order to elucidated the role of the discrepancy between local and global symmetry and/or order.