Committee Chair

Newman, James C., III

Committee Member

Anderson, William K.; Arabshahi, Abdollah; Matthews, John V., III


Dept. of Computational Engineering


College of Engineering and Computer Science


University of Tennessee at Chattanooga

Place of Publication

Chattanooga (Tenn.)


In this dissertation, a computational structural mechanics capability is developed for the simulation of biological tissues. These tissues may exhibit either linear or nonlinear material responses and, therefore, the resultant theory and computational implementation are presented. Various discretization methods of the systems of equations are possible, and in the current work Continuous Galerkin (CG) and the Discontinuous Galerkin (DG) approaches are employed. Additionally, due to natural variations in biophysical properties from person to person, uncertainty quantification may be used to ascertain the impact on deterministic simulation results when assuming mean values of these properties. To this end, a hyper elastic formulation for the nonlinear, transversely isotropic behavior of soft and hard tissue is utilized for the simulation and failure analysis of the proximal femur. Both linear and nonlinear material results are compared. The uncertainty in the failure analysis due to the selected biophysical properties is then examined using the First-Order Second-Moment (FOSM) method. Additionally, within Computational Fluid Dynamics (CFD) it is often necessary to adaptively move the mesh (e.g. moving boundary simulations, shape design optimization, generation of higher-order grids near curved boundaries, etc.). In these regards, linear elasticity is commonly used for adaptation by viewing the mesh as a solid. In some cases, such as for anisotropic meshes or for extremely large boundary movement, this approach to mesh movement has experienced difficulties in producing valid grids for simulation purposes. Thus, using the developed capability, the potential benefits of utilizing nonlinear material behavior for mesh movement is additionally examined.


I use this opportunity to express my gratitude to my adviser, Dr. James C. Newman, for his friendly guidance and support during my research. Besides my advisor, I would like to express my deepest appreciation to Dr. Timothy W. Swafford who provided me the possibility to work at the SimCenter. I would like to thank the rest of my thesis committee, Dr. William Kyle Anderson, Dr. Mat Matthews, and Dr. Abi Arabshahi, for their insightful comments and encouragement. I thank my fellow friends Dr. Arash Ghasemi and Dr. Ethan Hereth for the stimulating discussions and the good times we had. Also I thank my wife Dr. Faranak Behzadi for all the support she provided for me during my research and my life. I would like to thank Dr. Georg N. Duda from Julius Wolff Institute and Berlin-Brandenburg, Center for Regenerative Therapies, for proving the loading data of femur during the gait cycle.


Ph. D.; A dissertation submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Doctor of Philosophy.




Biomedical engineering -- Computer simulation


Uncertainty quantification; Hyper elasticity; Biological tissues; Finite element methods

Document Type

Doctoral dissertations




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