Date of Award

Winter 12-2016

Level of Access

Open-Access Dissertation

Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering


Senthil Vel

Second Committee Member

Scott Johnson

Third Committee Member

Christopher Gerbi

Additional Committee Members

Michael Peterson

Zhihe Jin

Quan Guo


This dissertation is concerned with the development of robust numerical solution procedures for the generalized micromechanical analysis of linear and nonlinear constitutive behavior in heterogeneous materials. Although the methods developed are applicable in many engineering, geological, and materials science fields, three main areas are explored in this work. First, a numerical methodology is presented for the thermomechanical analysis of heterogeneous materials with a special focus on real polycrystalline microstructures obtained using electron backscatter diffraction techniques. Asymptotic expansion homogenization and finite element analysis are employed for micromechanical analysis of polycrystalline materials. Effective thermoelastic properties of polycrystalline materials are determined and compared with existing analytical estimates. Distributions in microscale stresses resulting from different applied loading scenarios are compared and analyzed. Second, the aforementioned methodology is adapted within an iterative numerical framework in order to study nonlinear creep in polyphase aggregates. The proposed solution procedure is capable of analyzing aggregates composed of phases whose constitutive behavior may take the form of any nonlinear relationship between stress and strain-rate. In the studies presented herein, phases deforming by power-law relations are considered. Analytical approximations of bulk aggregate behavior are assessed through comparison with results from the proposed rigorous methodology, yielding significant geological implications. In the final study of this dissertation, a generalized methodology is developed for the analysis of pervasive cracking in heterogeneous brittle materials. The methodology incorporates the multidirectional smeared crack concept in a sequentially linear analysis framework. The proposed model allows for the initiation, propagation, and coalescence of multiple cracks existing within a microstructure composed of generally anisotropic phases. Validation studies are performed in order to demonstrate the objectivity of finite element results. Model problems are presented for heterogeneous concrete and polycrystalline alumina. Results for bulk constitutive behavior are compared with those in the literature, along with the corresponding constituent-level crack patterns.