Glasses are amorphous materials. Nevertheless, as far as I know, in some areas of Condensed Matter, they consider that the glass is isotropic. Under what restrictions they can do this assumption?
Mathematically, the assumption that glasses are isotropic make the calculations, in my imagination, dramatically simpler. In what they are simplied?
And, finally, there are some good references in this subject?
Probably the simplest, yet best model to understand many things about glasses and amorphous materials is the hard sphere model. Consider a system of hard particles, impenetrable billiard balls that you are trying to pack in a box. If you just shake those particles in such a way that you do not allow formation of a periodic structure (the ground state of hard spheres is a FCC lattice) but make them reasonably dense, then those particles will resist shearing and the system will behave like a solid (in this case, a glass!).
The property of being "isotropic" means that, although the particles have random configuration and the system is definitely NOT HOMOGENEOUS, the characteristics of the system have no special direction. In other words, if you have a big enough system and calculate properties (e.g., electrical conductivity) in one specific direction, those properties should not differ considerably from those measured in another direction. The reason is exactly that, given the randomness of the particle positions, the differences will average out. From this, it is clear that the mathematics will become simpler, once one will not need to worry about characterizing the material in each different direction, there will be no need to worry about non-linear terms in the tensors, etc.
Regarding a good source on the subject, glassy materials is actually a very controverse subject and different 'schools' propose different views and explanations. You can find a recent overview on Physics 4, 42 (2011)
