Date of Award
1-1-2009
Document Type
Masters Thesis
Degree Name
M.S.
Organizational Unit
Daniel Felix Ritchie School of Engineering and Computer Science
First Advisor
Yun-Bo Yi, Ph.D.
Second Advisor
Siavash Pourkamali Anaraki
Third Advisor
Paul Rullkoetter
Keywords
Effective properties, Heterogeneous, Percolation
Abstract
The effective elastic modulus and conductivity of a two phase material system are investigated computationally using a Monte Carlo scheme. The continuum contains circular, spherical or ellipsoidal inclusions that are either uniformly or randomly embedded in the matrix. The computed results are compared to the applicable effective medium theories. It is found that the random distribution, permeability and particle aspect ratio have non-negligible effects on the effective material properties. For spherical inclusions, the effective medium approximations agree well with the simulation results in general, but the analytical predictions on void or non-spherical inclusions are much less reliable. It is found that the results for overlapping and nonoverlapping inclusions do not differ very much at the same volume fraction. The effect of the particle morphology is also investigated in the context of prolate and oblate ellipsoidal particles.
The geometric percolation thresholds for circular, elliptical, square and triangular disks in the three-dimensional space are determined precisely by Monte Carlo simulations. These geometries represent oblate particles in the limit of zero thickness. The normalized percolation points, which are estimated by extrapolating the data to zero radius, are &eta c=0.9614 ± 0.0005, 0.8647 ± 0.0006 and 0.7295 ± 0.0006 for circles, squares and equilateral triangles, respectively. These results show that the noncircular shapes and corner angles in the disk geometry tend to increase the interparticle connectivity and therefore reduce the percolation point. For elliptical plate, the percolation threshold is found to decrease moderately when the aspect ratio &epsilon is between 1 and 1.5 but decrease rapidly for &epsilon greater than 1.5. For the binary dispersion of circular disks with two different radii, &eta c is consistently larger than that of equisized plates, with the maximum value located at around r_1/r_2 =0.5.
Publication Statement
Copyright is held by the author. User is responsible for all copyright compliance.
Rights Holder
Elyas El Arbi Tawerghi
Provenance
Received from ProQuest
File Format
application/pdf
Language
en
File Size
116 p.
Recommended Citation
Tawerghi, Elyas El Arbi, "Computational Studies on the Effective Properties of Two-Phase Heterogeneous Media" (2009). Electronic Theses and Dissertations. 642.
https://digitalcommons.du.edu/etd/642
Copyright date
2009
Discipline
Mechanical engineering, Materials Science