Date of Award

Spring 2004

Project Type


Program or Major

Engineering: Mechanical

Degree Name

Doctor of Philosophy

First Advisor

Igor Tsukrov


This work investigates the effective elastic properties of two-dimensional solids with inhomogeneities of various shapes. We develop a special procedure to evaluate the contribution of irregularly shaped inhomogeneities to these properties. The method can also be used to investigate the stress concentrations around the inhomogeneities. The procedure is based on the analysis of a representative volume element. We express the contribution of each inhomogeneity to the overall moduli of the composite in terms of the compliance contribution tensor. To calculate the components of this tensor, we devise a method that combines analytical and numerical approaches: Kolosov-Muskhelishvili complex variable technique and numerical conformal mapping. Application of this method to regularly shaped elastic inclusions, holes and rigid inclusions produces results that correspond well with the available analytical predictions. In the case of holes, the applicability of the finite element method is also investigated. The expressions for the effective elastic properties are first derived in the approximation of non-interacting inhomogeneities. Then the results for interacting inhomogeneities incorporating the first order approximate schemes are presented.

To demonstrate the application of the method, we analyze a carbon fiber reinforced composite containing pores of irregular shapes. A two-step micromechanical procedure utilizing the concept of the compliance contribution tensor is used. We derive the closed form formulae for the contribution of fibers into the effective moduli and apply the procedure to determine the effective in-situ properties of pyrolytic carbon---a matrix phase formed during a densification process by chemical vapor infiltration.