MULTISCALE INVESTIGATION OF RANDOM HETEROGENEOUS MEDIA IN MATERIALS AND EARTH SCIENCES

MULTISCALE INVESTIGATION OF RANDOM HETEROGENEOUS
MEDIA IN MATERIALS AND EARTH SCIENCES

By Andrew J. Goupee
Dissertation Advisor: Dr. Senthil S. Vel
A Lay Abstract of the Dissertation Presented
in Partial Fulfillment of the Requirements for the
Degree of Doctor of Philosophy
(in Mechanical Engineering)
May, 2010

This dissertation is concerned with three major areas pertaining to the characterization and analysis of specific types of composite materials.. The first is focused on the computer modeling of composite materials in which the material components of the composite have random shapes and sizes. The computer modeling effort aims to understand the physical properties of these types of composite materials as well as develop methods to accurately model and analyze larger components comprised of this class of composite material. Novel methods are developed which allow the easy creation of realistic random composite material microstructure geometries which closely resemble those made by actual manufacturing procedures. Advanced computer analysis tools are developed and employed to obtain the desired physical properties of the random composite material,  including stiffness, strength and a host of other properties related to the behavior of the material when subjected to changes in temperature.

The second area addressed in this dissertation involves an extensive development of the computer tools necessary to analyze complex composite material structures called functionally graded materials. These composite materials have smoothly varying ratios of the composite material phase ingredient volumetric amounts as well as spatially varying microstructure geometries. Sophisticated computer tools for analyzing functionally
graded components subjected to dynamic mechanical and high temperature loads are created. Example problems are studied to illustrate the effectiveness of the developed analysis tools. The last area of this dissertation is concerned with determining the role of certain rock features, coined rock fabrics, on the speed of seismic waves traveling through Earth’s crust. Since rocks can be analyzed as complex, multiphase composite materials, similar computer modeling techniques to those employed in the first portion of this dissertation are used to determine the effective stiffness of the rock fabrics which are in turn used to compute the seismic wave speeds of the bulk rock material. Through a systematic study of various rock fabric types, important findings are discovered regarding the influence of rock fabric features on the speed of seismic waves traveling
through Earth’s crust.