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2D approximation of heterogeneous 3D media

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

Comments

Wenbin Yu's picture

I don't know whether I understand your problem. If your 3D heterogeneous media, such as fiber reinforced composites, can be considered as periodic or random along two directions and uniform along one direction. Then you can obtain the effective properties by analysis a 2D microstructure, the results will be the same as using the original 3D microstructure if you use a right micromehcanics mehtod, such as VAMUCH . If your 3D media is random or peroidic along three directions, such as partical reinforced composites, then I don't know a good approach to reduce the 3D analysis to a 2D analysis.

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