Date of Award


Document Type

Masters Thesis

Degree Name


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


Effective properties, Heterogeneous, Percolation


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


Received from ProQuest

File Format




File Size

116 p.


Mechanical engineering, Materials Science