Date of Award


Level of Access Assigned by Author

Open-Access Dissertation

Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering


Senthil S. Vel

Second Committee Member

Zhihe Jin

Third Committee Member

Alireza S. Sarvestani


This dissertation is concerned with three major areas pertaining to the characterization and analysis of heterogeneous materials. The first is focused on the modeling of heterogeneous materials with random microstructure and understanding their thermomechanical properties as well as developing a methodology for the multiscale thermoelastic analysis of random heterogeneous materials. Realistic random microstructures are generated for computational analyses using random morphology description functions. The simulated microstructures closely resemble actual micrographs of random heterogeneous materials. The simulated random microstructures are characterized using statistical techniques and their homogenized material properties computed using the asymptotic expansion homogenization method. The failure response of random media is investigated via a direct micromechanical failure analysis which utilizes stresses at the microstructural level coupled with appropriate phase material failure models to generate initial failure envelopes. The homogenized material properties and failure envelopes are employed to perform accurate coupled macroscale and microscale analyses of random heterogeneous material components. The second area addressed in this dissertation involves the transient multiscale analysis of two-phase functionally graded materials within the framework of linearized thermoelasticity. The two-phase material microstructures, which are created using a morphology description function, have smoothly varying microstructure morphologies that depend on the volume fractions of the constituent phases. The multiscale problem is analyzed using asymptotic expansion homogenization coupled with the finite element method. Model problems are studied to illustrate the versatility of the multiscale analysis procedure which incorporates a direct micromechanical failure analysis to accurately compute the factors of safety for functionally graded components. The last area of this dissertation is concerned with determining the role of heterogeneous rock fabric features in quartz/muscovite rich rocks on seismic wave speed anisotropy. The bulk elastic properties and corresponding wave velocities are calculated for synthetic heterogeneous rock microstructures with varying material and geometric features to investigate their influence on seismic wave speed anisotropy. The asymptotic expansion homogenization method is employed to calculate precise bulk stiffness tensors for representative rock volumes and the wave speed velocities are obtained from the Christoffel equation. The obtained results are also used to assess the performance of analytic homogenization schemes currently used in the geophysics community.