I found this reference very helpful in building a solid base for learning the foundamentals of Homogenization methods and up to now, is the only reference that addresses the difference between Homogenization and Averaging methods.

I will put more references in this entry and will be happy if you share your links with me.

G.A. Pavliotis and A.M. Stuart, "Multiscale Methods: Averaging and Homogenization," Springer, 2008

Dear All,

Could somebody indicate me some literature about the topic "2D
approximation of heterogeneous 3D media"?

In particular I am interested to address following issues:

1) Under which conditions averaging thermal conductivity and young
modulus (or more general, mechanical behaviour) on multiple 2D crossections of an heterogeneous "random"
material can be a good approximation for the behaviour of the real 3D
microstructure

2) Is there any theorem which shows the equivalence between averaging
on n 2D crossections of a certain media and taking the single
real 3D structure for n sufficiently large?

Thank you very much in advance.

Phu