SERVE-Boundary Conditions
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Fig. 15 (a) Voronoi tessellation of the polydispersed microstructural volume element (MVE) with
gray-scale shading corresponding to the local volume fraction (coordinates x (or 1) and y (or
2) correspond to transverse directions in the section, while z (or 3) corresponds to the longitudinal
direction of the fibers); probability distribution functions of (b) volume fraction ; (c) fiber size,
and (d) the radial distance and orientation-dependent 2-point correlation function S 2 (r, θ) of the
polydispersed MVE
5.3 Creating Statistically Equivalent MVEs from Experimental
Micrographs
Prior to conducting DNS of the SERVE for effective properties, it is important to
create statistically equivalent microstructural volume elements (SE-MVEs) that are
representative of the entire experimental micrograph as in Fig. 1a with identical
statistical distributions. The SE-MVE forms the parent domain from which SERVEs
may be extracted. The SE-MVEs are obtained by a Monte Carlo-type reconstruction
method using the 2-point correlation function S 1 , 2-point correlation function S 2 ,
and the probability distribution of fiber radius in the PMC micrograph, depicted