Date of Award

Spring 1993

Degree Type

Thesis - Restricted

Degree Name

Master of Science (MS)



First Advisor

Day, Art

Second Advisor

Mendelson, Kenneth S.


In this thesis we have developed a model which will enable us to study the elastic properties of two dimensional composites with an arbitrary microstructure, for all physically allowed values of Poisson's ratio. As a test case we to study randomly oriented elliptical holes in a sheet. This is an extension of previous work on circular holes by Day et al [5] but does not have the restrictions on Poisson's ratio of the model used in their work. Furthermore, it allows us to compare two competing effective medium theories developed by Thorpe and Sen [14J. The two theories give identical results for circles (i.e. for ellipses with aspect ratio alb = 1) but give different results when the aspect ratio alb 1= 1. Lastly, our simulation results allow us to confirm the observation of Day et al. [5] that, for a given geometry, the relative Young's modulus for a two dimensional sheet containing holes is independent of the initial Poisson's ratio of the sheet. This result has been proved analytically by Cherkov, Laurie and Milton [15], and so it is a stringent check on our results.