 RVE: Representative Volume Element 
Explanation:  A Voronoi cell
generator is able to
create a
polycrystalline
volume model. In
order to guarantee a
representative
volume, the model is
periodic in each
geometric direction.
The cubic mesh is
generated by means
of raster space
discretization. All
elements are
arranged by the
nearest neighbor
sweep circle method,
which aligns all
elements within an
incrementally
growing circle to a
specific seed point
within the RVE.
Another method is to
calculate the
minimum distance
between an element
and all seeds, which
is more accurate but
inefficient due to
the explicit
calculation. An
improved method for
tessellating a space
is the Delaunay
triangulation. This
method is an exact
Voronoi diagram in
vector
representation. This
method is applied
for RVE with
tetragonal mesh. 
Picture / Figure / Diagram: 

RVE and microstructural model for high Mn steels.


SFBLink:  The developed microstructural model is able to describe the material morphology of high manganese steels by means of Voronoi tessellation. The grain size and chemical distribution within the polycrystalline aggregate can be modeled according to microscopy investigations and XRD measurements. Beside the temperature, the locally varied chemical composition is the main factor controlling the stacking fault energy (→SFE). The variables in the RVE are used for calculation of the SFE is a direct link to the material model, which describes the hardening behavior. A microstructural model for flow curve and failure modeling based on the RVE approach is developed for high Mn steels. The polycrystalline structure is generated by discrete Voronoi tessellation. The RVE tool can also be used for generating the microstructure for other advanced high strength steels (→AHSS) and can also be used for generating banded microstructure. 
References:  R. Twardowski, PhD Thesis, Mikrostrukturelle Beschreibung von Verformung und Schädigung hochmanganhaltiger Stähle mit TRIP und TWIPEffekt. R. Twardowski, D. Steinmetz, and U. Prahl. Flow curve and failure modelling for highMn steels on a microstructural scale. SRI 2012 

