Microstructure properties and data analysis.

1. Microstructure-Property
Relationship in Randomly
Packed Mono-sized Structures
ME-8883
TEAM MEMBER: Mahdi Roozbahani, Jie(Jessie) Cao
Nov 5, 2014

2. STRUCTURE DATASETS
Full Datasets --- Gravitational Sphere Packing Simulation
Samples --- 200 Non-overlapping Random Volumes of 60×60×60 Voxels

3. TWO POINT STATISTICS
Visualization 2-point Statistics in 2D
2-point statistics of void phase – central slice
(N0. 200 Volume)

4. TWO POINT STATISTICS
2-point statistics of particle phase – central slice
(N0. 200 Volume)
Visualization 2-point Statistics in 2D

5. TWO POINT STATISTICS
Visualization 2-point Statistics
Void Phase
(N0. 200 Volume)

6. TWO POINT STATISTICS
Visualization 2-point Statistics
Solid Phase
(N0. 200 Volume)

7. PCA ANALYSIS
Evaluate Eigenvalue Results
Cumulative Eigenvalue Explanation
95%

8. PCA ANALYSIS
Two Point Statistics in PCA Space
First 2 components
First 3 components

9. STRUCTURE PROPERTY DATA
Permeability --- Transport Property
Permeability Datasets --- Computed using FVM in MATLAB (Ahmet)
Pressure Gradient for Simulation

10. STRUCTURE PROPERTY DATA
Permeability k --- Transport Property
Hydraulic Conductivity K --- K = kρg/μ, assume fluid is water
(m/s)

11. MICROSTRUCTURE - PROPERTY CORRELATION
Microstructure --- Randomly Packed Mono-sized Structure (loose)
Property --- Hydraulic Conductivity K, assume fluid is water
Hydraulic Conductivity (m/s)
PC1
Linear model: f(x,y) = p00 + p10*PC1 + p01*PC2
Coefficients (with 95% confidence bounds):
p00 = 0.2595 (0.2583, 0.2606)
p10 = 0.002132 (0.001976, 0.002287)
p01 = 0.0002297 (-0.0002588, 0.0007181)
Goodness of fit
SSE: 0.01297
R-square: 0.788
Adjusted R-square: 0.7858
RMSE: 0.008114

12. PROBLEMS
1. PCA Analysis
Cumulative Eigenvalue Explanation
95%
2. Additional Analysis on Binary-sized Structure ?

13. REAL MICRO-STRUCTURE

14. STRUCTURE PROPERTY DATA

15. STRUCTURE PROPERTY DATA

16. REFERENCES
• Roozbahani, M. M., Graham‐Brady, L., & Frost, J. D. (2014). Mechanical trapping
of fine particles in a medium of mono‐sized randomly packed spheres.
International Journal for Numerical and Analytical Methods in Geomechanics.
• Çeçen, A., Fast, T., Kumbur, E. C., & Kalidindi, S. R. (2014). A data-driven
approach to establishing microstructure–property relationships in porous
transport layers of polymer electrolyte fuel cells. Journal of Power Sources,
245, 144-153.
• Mönkeberg, F., & Hiptmair, R. (2012). Finite volume methods for fluid flow in
porous media.
• Aarnes, J. E., Gimse, T., & Lie, K. A. (2007). An introduction to the numerics of
flow in porous media using Matlab. In Geometric Modelling, Numerical
Simulation, and Optimization (pp. 265-306). Springer Berlin Heidelberg.
• Santamarina, J. C., Klein, A., & Fam, M. A. (2001). Soils and Waves: Particulate
Materials Behavior, Characterization and Process Monitoring.
• Spatial Statistics Code From Tony.
• FVM Code From Ahmet.