{"id":{"repo_id":"utc","oai_identifier":"oai:scholar.utc.edu:theses-1613"},"canonical_url":"https://search.dev.ndltd.org/etd/utc/oai:scholar.utc.edu:theses-1613","repository":{"repo_id":"utc","name":"University of Tennessee - Chattanooga","base_url":"https://scholar.utc.edu/do/oai/"},"display":{"title":"On the uncertainty quantification and non-linear hyper elastic simulation of biological tissues","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Shamsaei, Behrouz"],"institution":"University of Tennessee at Chattanooga","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Newman, James C., III","Anderson, William K.; Arabshahi, Abdollah; Matthews, John V., III","College of Engineering and Computer Science"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T05:46:28Z","subjects":["Biomedical engineering -- Computer simulation"],"languages":["English","eng"],"rights":[],"rights_urls":["https://rightsstatements.org/page/InC/1.0/?language=en"],"identifier_entries":[]},"links":{"outbound_url":"https://scholar.utc.edu/theses/471","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Newman, James C., III","Anderson, William K.; Arabshahi, Abdollah; Matthews, John V., III","College of Engineering and Computer Science"]},{"key":"dc:creator","label":"Author","values":["Shamsaei, Behrouz"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2016-08-01T07:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["University of Tennessee at Chattanooga","Chattanooga (Tenn.)"]},{"key":"dc:relation","label":"Dc Relation","values":["Masters Theses and Doctoral Dissertations"]},{"key":"dc:type","label":"Dc Type","values":["Doctoral dissertations","Text"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Biomedical engineering -- Computer simulation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["https://rightsstatements.org/page/InC/1.0/?language=en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholar.utc.edu/theses/471"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Dept. of Computational Engineering","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."]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["On the uncertainty quantification and non-linear hyper elastic simulation of biological tissues"]}]}],"canonical_facts":{"dc:contributor":["Newman, James C., III","Anderson, William K.; Arabshahi, Abdollah; Matthews, John V., III","College of Engineering and Computer Science"],"dc:creator":["Shamsaei, Behrouz"],"dc:date":["2016-08-01T07:00:00Z"],"dc:description":["Dept. of Computational Engineering","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."],"dc:description.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."],"dc:identifier":["https://scholar.utc.edu/theses/471"],"dc:language":["English","eng"],"dc:publisher":["University of Tennessee at Chattanooga","Chattanooga (Tenn.)"],"dc:relation":["Masters Theses and Doctoral Dissertations"],"dc:rights":["https://rightsstatements.org/page/InC/1.0/?language=en"],"dc:subject":["Biomedical engineering -- Computer simulation"],"dc:title":["On the uncertainty quantification and non-linear hyper elastic simulation of biological tissues"],"dc:type":["Doctoral dissertations","Text"]},"updated_at":"2026-07-24T05:46:28Z"}