On the Uncertainty Quantification and Non-Linear Hyper Elastic Simulation of Biological Tissues
A Dissertation Presented for the Doctor of Philosophy in Computational Engineering, The University of Tennessee at Chattanooga
Behrouz Shamsaei, August 2016
Abstract:
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.
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