Browsing by Subject "Subdomain"
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Item Coupled theoretical and experimental methods to characterize heterogeneous, anisotropic, nonlinear materials: application to cardiovascular tissues(2014-10) Witzenburg, Colleen M.The Generalized Anisotropic Inverse Mechanics (GAIM) method is able to provide general tissue characteristics in terms of stiffness, anisotropy strength, and preferred orientation. It allows for the computational dissection of samples, capturing regional differences within a single sample nondestructively. However, the linear assumption implicit in GAIM limited its utility, particularly in the case of cardiovascular soft tissues, which exhibit markedly nonlinear behavior when operating at physiologic strain levels. Therefore, GAIM was extended to consider large-deformation kinematics, a nonlinear closed-form structural model of planar fibrous tissue mechanics was utilized to describe the nonlinear behavior of a cardiovascular soft tissue (rat ventricle wall), and the partitioning method utilized by GAIM was replaced with a more robust partitioning scheme. Then, GAIM was applied in a stepwise fashion (NGAIM) in order to capture the full nonlinear kinetics of cardiovascular soft tissues. Finally, experiments characterizing the three-dimensional loading and failure of healthy porcine ascending aorta were discussed. The work presented in this thesis marks the development and use of novel theoretical and experimental approaches for the analysis of complex cardiovascular soft tissues. An analysis method was developed, NGAIM, that can be applied to examine regional mechanical differences in planar, nonlinear, anisotropic, heterogeneous, tissue samples from all over the body which yields full-field stress. Finally, a partnering was proposed which exploits the characterization capacity of NGAIM with the predictive capacity of the multiscale model to create full three-dimensional simulations of cardiovascular soft tissue behavior.Item A Novel Computational Framework Integrating Different Space Discretization and Time Discretization Methods with Multiple Subdomains and Reduced Order Modeling(2020-09) Tae, DavidThis thesis presents advances and developments in the field of spatial discretization and time integration. Along with the growth of the FEM, there has been a steady development of particle discretization methods such as Moving Particle Semi-implicit method or Smoothed Particle Hydrodynamics method. We propose a novel generalized approach to describe numerous existing particle methods by exploiting Taylor series expansion and the weighted residual method. The method is then validated through various problems in first and second order systems. The FEM and the particle methods have their own strengths and weaknesses. With the concept of subdomains and Differential Algebraic Equations (DAE) framework, we can divide a body and implement different methods in different regions of the body targeting an area with a specific method which can fully utilize its best features. We propose an implementation of multi-spatial method, multi-time scheme subdomain DAE framework allowing a mix of different space discretization methods and different time schemes on a single body analysis. This is not possible in the current state of the technology as it shows limitations in order of accuracy, and consistency. Various combinations of spatial methods and time schemes between subdomains are tested in linear and nonlinear problems for first and second order systems. Lastly, we introduced reduced order modeling via Proper Orthogonal Decomposition (POD) which decreases the size of the system based on its eigenvalues. The snapshot data are used to establish the reduced order basis. We additionally propose the integration of POD into the subdomain DAE framework. As the required amount of snapshot data are unknown and problem specific, we present an iterative process to ensure the snapshot data to accurately capture the physics of the system. In addition, the iteration approach is extended to include the convergence check in time on the solution for implicit time schemes. The proposed DAE POD framework is tested on numerous linear and nonlinear problems for first and second order systems. In all cases, we see time savings in computational effort.