links

http://technopress.kaist.ac.kr/samplejournal/pdf/cac0901003.pdf

http://dl.acm.org/citation.cfm?id=2983148

http://www.sciencedirect.com/science/article/pii/S0020768312002193

http://framcos.org/FraMCoS-5/Gitman.Representative.pdf

http://pbc.gda.pl/Content/12856/phd_skarzynski_lukasz.pdf

thanks a lot william

it was very helpful.

Dear Alireza, 

We usually use RVE to obtain homogenized properties of a non-homogeneous material e.g. concrete. In fact, RVE is a sample of the micro or meso-structure that needs to be enough large to includes all heterogeneity of the subscale. However, this definition does not help us with the determination of the RVE size. Of course, more large more accurate results. Even in periodic materials, a large RVE gives more accurate results than the small one. This is due to the boundary conditions that we impose on RVEs. 

Therefore, it is the accuracy that choose the size of RVE. If you want more accurate results you need to consider a larger RVE. 

Please find below some useful papers:

Kouznetsova, V. G., Brekelmans, W. a. M. and Baaijens, F. P. T. [2001], `An approach to micro-macro modeling of heterogeneous materials', Computational Mechanics 27(1), 37{48. 2, 36

Kouznetsova, V. G., Geers, M. G. D. and Brekelmans, W. a. M. [2002], `Multi-scale constitutive modelling of heterogeneous materials with a gradient enhanced computational homogenization scheme', International Journal for Numerical Methods in Engineering 54(8), 1235{1260

A Akbari Rahimabadi, P Kerfriden, S Bordas, Scale selection in nonlinear fracture mechanics of heterogeneous materials, Philosophical Magazine 95 (28-30), 3328-3347

All the best,

A