The properties of composite materials with random microstructures are often defined by homogenizing the properties of a representative volume element (RVE). This results in the effective properties of an equivalent homogeneous material. This approach is useful for predicting a global response but smooths the underlying variability of the composite's properties resulting from the random microstructure. Statistical volume elements (SVEs) are partitions of an RVE. Homogenization of individual SVEs produces a population of apparent properties. While not as rigorously defined as RVEs, SVEs can still provide a repeatable framework to characterize mesoscale variability in composite properties. In particular, their statistical properties can be used as the basis for simulation studies. For this work, Voronoi tessellation was used to partition RVEs into SVEs and apparent properties developed for each SVE. The resulting field of properties is characterized with respect to its spatial autocorrelation and distribution. These autocorrelation and distribution functions (PDFs) are then used as target fields to simulate additional property fields, with the same probabilistic characteristics. Simulations based on SVEs may provide a method of further exploring the uncertainty within the underlying approximations or of highlighting effects that might be experimentally measurable or used to validate the use of an SVE mesoscale analysis in a specific predictive model. This work presents an update to an existing simulation technique developed by Joshi (1975, “A Class of Stochastic Models for Porous Media,” Ph.D. thesis, University of Kansas, Lawrence, KS) and initially extended by Adler et al. (1990, “Flow in Simulated Porous Media,” Int. J. Multiphase Flow, 16(4), pp. 691–712). The simulation methodology is illustrated for three random microstructures and two SVE partitioning sizes.

References

References
1.
Shinozuka
,
M.
, and
Deodatis
,
G.
,
1991
, “
Simulation of Stochastic Processes by Spectral Representation
,”
ASME Appl. Mech. Rev.
,
44
(
4
), pp.
191
204
.
2.
Shinozuka
,
M.
, and
Deodatis
,
G.
,
1996
, “
Simulation of Multi-Dimensional Gaussian Stochastic Fields by Spectral Representation
,”
ASME Appl. Mech. Rev.
,
49
(
1
), pp.
29
53
.
3.
Roberts
,
A. P.
, and
Teubner
,
M.
,
1995
, “
Transport Properties of Heterogeneous Materials Derived From Gaussian Random Fields: Bounds and Simulation
,”
Phys. Rev. E
,
51
(
5
), pp.
4141
4154
.
4.
Roberts
,
A. P.
,
1997
, “
Statistical Reconstruction of Three-Dimensional Porous Media From Two-Dimensional Images
,”
Phys. Rev. E
,
56
(
3
), p.
3203
.
5.
Cule
,
D.
, and
Torquato
,
S.
,
1999
, “
Generating Random Media From Limited Microstructural Information Via Stochastic Optimization
,”
J. Appl. Phys.
,
86
(
6
), pp.
3428
3437
.
6.
Sheehan
,
N.
, and
Torquato
,
S.
,
2001
, “
Generating Microstructures With Specified Correlation Functions
,”
J. Appl. Phys.
,
89
(
1
), pp.
53
60
.
7.
Koutsourelakis
,
P. S.
, and
Deodatis
,
G.
,
2005
, “
Simulation of Binary Random Fields With Applications to Two-Phase Random Media
,”
J. Eng. Mech.
,
131
(
4
), pp.
397
412
.
8.
Joshi
,
M. Y.
,
1975
, “
A Class of Stochastic Models for Porous Media
,” Ph.D. thesis, University of Kansas, Lawrence, KS.
9.
Adler
,
P. M.
,
Jacquin
,
C. G.
, and
Quiblier
,
J. A.
,
1990
, “
Flow in Simulated Porous Media
,”
Int. J. Multiphase Flow
,
16
(
4
), pp.
691
712
.
10.
Quiblier
,
J. A.
,
1984
, “
A New Three-Dimensional Modeling Technique for Studying Porous Media
,”
J. Colloid Interface Sci.
,
98
(
1
), pp.
84
102
.
11.
Fenton
,
G. A.
, and
Vanmarcke
,
E. H.
,
1990
, “
Simulation of Random Fields Via Local Average Subdivision
,”
J. Eng. Mech.
,
116
(
8
), pp.
1733
1749
.
12.
Guilleminot
,
J.
,
Soize
,
C.
, and
Kondo
,
D.
,
2009
, “
Mesoscale Probabilistic Models for the Elasticity Tensor of Fiber Reinforced Composites: Experimental Identification and Numerical Aspects
,”
Mech. Mater.
,
41
(
12
), pp.
1309
1322
.
13.
Rahman
,
S.
, and
Chakraborty
,
A.
,
2007
, “
A Stochastic Micromechanical Model for Elastic Properties of Functionally Graded Materials
,”
Mech. Mater.
,
39
(
6
), pp.
548
563
.
14.
Acton
,
K. A.
, and
Baxter
,
S. C.
,
2017
, “
Characterization of Random Composite Properties Based on Statistical Volume Element Partitioning
,”
J. Eng. Mech.
,
144
(
2
), p.
04017168
.
15.
Acton
,
K. A.
,
Baxter
,
S. C.
,
Bahmani
,
B.
,
Clarke
,
P. L.
, and
Abedi
,
R.
,
2018
, “
Voronoi Tessellation Based Statistical Volume Element Characterization for Use in Fracture Modeling
,”
Comput. Methods Appl. Mech. Eng.
,
336
, pp.
135
155
.
16.
Tran
,
V. P.
,
Guilleminot
,
J.
,
Brisard
,
S.
, and
Sab
,
K.
,
2016
, “
Stochastic Modeling of Mesoscopic Elasticity Random Field
,”
Mech. Mater.
,
93
, pp.
1
12
.
17.
Stabler
,
B.
, and
Guilleminot
,
J.
,
2017
, “
Stochastic Modeling and Generation of Random Fields of Elasticity Tensors: A Unified Information-Theoretic Approach
,”
C.-R. Mec.
,
345
, pp.
399
416
.
18.
Malyarenko
,
A.
, and
Ostoja-Starzewski
,
M.
,
2017
, “
A Random Field Formulation of Hooke's Law in All Elasticity Classes
,”
J. Elasticity
,
127
(
2
), pp.
269
302
.
19.
Baxter
,
S. B.
, and
Acton
,
K. A.
,
2018
, “
Distributions of Wave Velocities in Heterogeneous Media Based on the Apparent Properties of Statistical Volume Elements
,”
Eighth International Conference on Computational Stochastic Mechanics
,
G.
Deodatis
and
P.
Spanos
, eds., Paros, Greece (in press).
20.
Ostoja-Starzewski
,
M.
,
2006
, “
Material Spatial Randomness: From Statistical to Representative Volume Element
,”
Probab. Eng. Mech.
,
21
(
2
), pp.
112
132
.
21.
Shannon
,
C. E.
,
2001
, “
A Mathematical Theory of Communication
,”
ACM SIGMOBILE Mobile Comput. Commun. Rev.
,
5
(
1
), pp.
3
55
.
22.
Soize
,
C.
,
2008
, “
Tensor-Valued Random Fields for Meso-Scale Stochastic Model of Anisotropic Elastic Microstructure and Probabilistic Analysis of Representative Volume Element Size
,”
Probab. Eng. Mech.
,
23
(
2–3
), pp.
307
323
.
23.
Sobczyk
,
K.
,
2003
, “
Reconstruction of Random Material Microstructures: Patterns of Maximum Entropy
,”
Probab. Eng. Mech.
,
18
(
4
), pp.
279
287
.
24.
Bourn
,
R.
,
Fralick
,
B. S.
, and
Baxter
,
S. C.
,
2013
, “
Distributions of Elastic Moduli in Mechanically Percolating Composites
,”
Probab. Eng. Mech.
,
34
, pp.
67
72
.
25.
Jaynes
,
E. T.
,
2003
,
Probability Theory: The Logic of Science
,
G. L.
Bretthorst
, ed.,
Cambridge University Press
,
Cambridge, UK
.
26.
Beltzer
,
A. I.
, and
Sato
,
T.
,
2003
, “
Probability Distribution of Wave Velocity in Heterogeneous Media Due to Random Phase Configuration
,”
Wave Motion
,
38
(
3
), pp.
221
227
.
27.
Broste
,
N.
,
1971
, “
Digital Generation of Random Sequences
,”
IEEE Trans. Autom. Control
,
16
(
2
), pp.
213
214
.
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