The basic assumption of RVE modeling is that the overall geometry is obtained by an infinite repetition of the RVE in all allowed (depending on specific BCs) directions. You need to tile (fill) the 2D (3D) space by infinitely repeating the RVE without gaps.

Thus, the RVE shape does not need to be regular per se, but it must be such that, when repeated infinite times, it fills the space without gaps. The simplest such geometries are the square, the rectangle and the hexagon. More are available, with different degrees of regularity (a term that should be better specified, we are using it with a quite vague meaning), and one has to look into the research on tessellations. It would be interesting to study how different patterns affect the calculated mechanical behavior. However, you cannot use arbitrary "irregular" shapes or even purely random geometries. It is not compatible with the homogenization method's assumptions.

Furthermore, geometries and size of RVE do affect the mechanical homogenized behavior, especially for composites (and any material with structure at multiple scales). The RVE should in theory be independent of geometry, but in practice you need to investigate which configuration is best to model the homogenized material.

I feel there are some methods like MOC, GMC, HFGMC, FVDAM defined for RVE's in cartesian co-ordinate. Is it possible to implement for RVE's in cylindrical coordinate system.

Marcio A. A. Cavalcante

Rami Haj-Ali , Marek-Jerzy Pindera

Yes. You can consider RVEs in the longitudinal direction or in the cross-section. In the latter the RVE should most probably has the shape of a circular sector. Then the detailed BCs depend on the specific features of the model.

Recently we published article on the homogenization with cylindrically periodic microstructure.

See this link

https://rdcu.be/5tj8