Hypoplastic left heat syndrome (HLHS) is a complex cardiac malformation in neonates suffering from congenital heart disease and occurs in nearly 1 per 5000 births. HLHS is uniformly fatal within the first hours or days after birth as the severly malformed anatomies of the left ventricle, mitral, and aortic valves, and ascending aorta are not compatable with life. The regularly implemented treatment, the Norwood operation, is a complex open heart procedure that attempts to establish univenticular circulation by removing the atrial septum ( communicating the right and left ventricle), reconstructing the malformed aortic arch, and connecting the main pulmonary artery into the reconstructed arch to allow direct perfusion from the right ventricle into the systemic circulation. A relatively new treatment being utilized,the Hybrid Norwood procedure, involves a less invasive strategy to establish univentricular circulation that avoids a cardiopulmonary bypass (heart-lung machine), deliberate cardiac arrest, and circulatroy arrest of the patient during the procedure. The resulting systemic-pulmonary circulation is unconventional; blood is pumped simotaneously and in parallel to the systemic and pulmonary arteries after the procedure. Cardiac surgeons are deeply interested in understanding the global and local hemodynamics of this anotomical configuration. To this end, a multiscale model of the entire circulatory system was developed utilizing an electrical lumped parameter model for the peripheralor distal circulation coupled with a #D Computational Fluid Dynamics (CFD) model to understand the local hemodynamics. The lumped parameter (LP) model is mainly a closed loop circut comprised of RLC comartments that model cardiac function as well as the viscous drag, flow intertia, and compliance of the different atrial and venous beds in the body. A system of 32 first-order differential equations is formulated and solved for the LP model using a fourth-order adaptive Runge-Kutta solver. The output pressure and flow waveforms obtained from the LP model are imposed as boundary conditions on the CFD model. Coupling of the two models is done through an iterative process where the parameters in the LP model are adjusted to match the CFD solution. The CFD model domain is a representative HLHS anatomy of an infant after undergoing the Hybrid Norwood procedure and is comprised of the neo-aorta, pulmonary roots, aortic arch with branching arteries, and pulmonary arteries. The flow field is solved over several cardiac cycles using an implicit-unsteady RANS equation solver with the k-epsilon turbulence model.; Hypoplastic left heart syndrome (HLHS) is a complex cardiac malformation in neonates suffering from congenital heart disease and occurs in nearly 1 per 5000 births. HLHS is uniformly fatal within the first hours or days after birth as the severely malformed anatomies of the left ventricle, mitral and aortic valves, and ascending aorta are not compatible with life. The regularly implemented treatment, the Norwood operation, is a complex open heart procedure that attempts to establish univentricular circulation by removing the atrial septum (communicating the right and left ventricle), reconstructing the malformed aortic arch, and connecting the main pulmonary artery into the reconstructed arch to allow direct perfusion from the right ventricle into the systemic circulation. A relatively new treatment being utilized, the Hybrid Norwood procedure, involves a less invasive strategy to establish univentricular circulation that avoids a cardiopulmonary bypass (heart-lung machine), deliberate cardiac arrest, and circulatory arrest of the patient during the procedure. The resulting systemic-pulmonary circulation is unconventional; blood is pumped simultaneously and in parallel to the systemic and pulmonary arteries after the procedure. Cardiac surgeons are deeply interested in understanding the global and local hemodynamics of this anatomical configuration. To this end, a multiscale model of the entire circulatory system was developed utilizing an electrical lumped parameter model for the peripheral or distal circulation coupled with a 3D Computational Fluid Dynamics (CFD) model to understand the local hemodynamics. The lumped parameter (LP) model is mainly a closed loop circuit comprised of RLC compartments that model cardiac function as well as the viscous drag, flow inertia, and compliance of the different arterial and venous beds in the body.

Iron-based ferritic alloys are used for a plethora of industrial applications. These alloys contain foreign atoms purposely employed to improve certain properties as well as some unwanted impurities introduced during fabrication. Materials properties are decisively influenced by diffusion processes. Very often diffusion cannot be avoided during fabrication and application. Therefore, many efforts are made to understand the underlying atomic-level mechanisms by both experimental and theoretical investigations. In this thesis work a multiscale modelling approach is used to study oxygen and vacancy diffusion in dilute ferritic iron alloys. Due to the extremely low solubility of oxygen the measurement of oxygen diffusion in iron is difficult. Only few experimental data are available. Experimental investigation of vacancy migration is still more complicated. The lack of reliable experimental data is therefore an important motivation for theoretical investigations. Gaining fundamental data on oxygen and vacancy diffusion in dilute iron alloys is essential for many applications. Oxygen plays a crucial role in the corrosion of iron-based alloys. Oxygen and the vacancy are also important in the formation and evolution of Y-Ti-O nanoclusters in oxide dispersion strengthened ferritic Fe-Cr alloys, which are considered as promising candidates for structural materials of future fusion and fission reactors. Furthermore, vacancies are formed during neutron and ion irradiation and their diffusion affects radiation-induced nanostructure formation in ferritic alloys. In the first part of this thesis work, the diffusion of interstitial oxygen under the influence of substitutional atoms or solutes (Al, Si, P, S, Ti, Cr, Mn, Ni, Y, Mo and W) in bcc Fe is investigated by the combination of Density Functional Theory (DFT) and Atomistic Kinetic Monte Carlo (AKMC) simulations. The substitutional atoms are assumed to be immobile because oxygen diffusion is much faster than that of the solutes. DFT is applied to gain data on binding energies between interstitial oxygen and the substitutional foreign atoms, and to calculate the migration barriers for oxygen in the environment of the solutes. Using the migration barriers obtained by DFT, the diffusion coefficient of oxygen is determined by AKMC simulation. It is found that Si, P, Ni, Mo, and W have negligible influence on the oxygen diffusion coefficient. Al, Cr, Mn, S, Ti, and Y cause a considerable reduction of oxygen mobility. In these cases, the temperature dependence of oxygen diffusivity shows deviations from Arrhenius behavior. This is explained in detail by the significant temperature dependence of the ratio between residence times in the respective states. In the second part of the work a method is presented which allows for an efficient calculation of the diffusion coefficient of oxygen and other interstitial atoms in dilute alloys. The method is applied to examples considered in the first part of the work. The calculation procedure is based on the separation of the diffusion path into a contribution related to migration in the interaction region between the mobile interstitial and the substitutional solute and another part related to diffusion in perfect bcc Fe. In this manner AKMC simulation must be performed only for one concentration of the substitutional solute, and the obtained results can be employed to obtain data for other concentrations using analytical expressions containing binding energies between the interstitial and the substitutional solute. The focus of third part of the work is on the mutual dependence of oxygen and vacancy diffusion in bcc Fe and dilute iron alloys. Here both O and v must be considered as mobile while the substitutional atoms are assumed to be immobile. DFT is applied to determine the binding energy between O and v for different distances, the migration barriers for O in the environment of v, and the corresponding barriers of v in the vicinity of O. In agreement with previous work O and v have a very strong binding at the 1st neighbor distance. On the other hand, the calculations show that the Ov pair at the 6th neighbor distance is instable. The newly found simultaneous or coupled jumps of both O and v compensate the lack of jump paths that would occur due to this instability. The DFT results are employed to determine the diffusion coefficient of O and v using the scheme of the AKMC-based calculation method presented in the second part of the thesis work. At first a model system with fixed O and v concentrations is studied. It is found that a small v content of some ppm can already lead to a strong reduction of the O diffusivity. A similar effect is obtained for v diffusion under the influence of O. Furthermore, investigations on the interdependence of O and v diffusion during thermal processing of oxide dispersion strengthened iron alloys are performed, and the influence of the substitutional atoms Y and Ti is studied. A simple thermodynamic model is employed to determine the concentration of O, Y, and Ti monomers as well as the total v concentration, for a typical total content of O, Y, and Ti. These results are used in calculations of the diffusion coefficients of O and v. Not only a strong mutual dependence but also a significant influence of Y on O diffusion is found. Finally, O and v diffusivities in a system with a total O content close to the thermal solubility are calculated. The monomer O concentration as well as the total v concentration was determined using two different models considering equilibrium of O and v with Ov, or equilibrium of O and v with Ov and O2v or Ov2. Despite the very small value of thermal solubility of O in bcc Fe, both the O and v diffusion coefficient are very different from that in pure iron. Even for such a low amount of O in the alloy the diffusion coefficients differ strongly from those in perfect bcc Fe. The results of the present work have important consequences for planning and performing new experiments on O and v diffusion in dilute iron alloys. In particular, a very precise knowledge of the concentrations of O and v, as well as of other foreign atoms and traps such as dislocations is required.

<p>Long-acting injectables (LAI) offer many practical benefits for patients in improving drug adherence to therapies for chronic diseases. LAI, administered either subcutaneously (SC) or intramuscularly (IM), can improve drug bioavailability, and reduce frequency of administration as well as regimen complexity. SC also has additional benefits over IM injections as being safer, less painful, and able to be administered at home. However, development and translation of these products into the clinic is often limited because of physiological complexity at injection site, such that absorption rate mechanisms are not well understood. Common predictive and correlative methods used in oral formulations, such as <em>in vitro-in vivo </em>correlations, are not well suited for SC physiology and are only capable of measuring a few parameters at a time, meaning relationships between parameters cannot be discriminately measured.</p> <p><br></p> <p>This project seeks to address this gap in knowledge by using computation to bridge the gap between suboptimal preclinical testing methods and human pharmacokinetic data. A Multiscale framework was developed by integrating a first-principles Multiphysics model of the SC space to experimental plasma concentration profiles using simulated absorption rates. First, our lab’s previous framework for lymphatic absorption of monoclonal antibodies (mAbs) was converted into small molecule absorption into the capillaries. Drug and formulation critical quality attributes (CQA) were determined for a solution injection of methotrexate, and a nanocrystal formulation of medroxyprogesterone acetate (MPA, Depo-SubQ Provera). Two dissolution models were incorporated to compare the difference between using average particle size (Noyes-Whitney) and particle size distributions (Population Balance Model, PBM) as CQA for nanocrystal LAI specifically. Absorption rates were validated using compartmental pharmacokinetic models, and sensitivity analyses were conducted to determine model parametric sensitivity. Overall, the modeling framework was able to determine the importance of and discriminate the effect of parameters on SC absorption rates. </p>

Many experiments demonstrate that the effects of hydrogen solutes decrease macroscopic fracture stresses and strains in ductile materials. Hydrogen-related failures have occurred in nearly all industries involving hydrogen-producing environments. The financial losses incurred from those failures reaches millions if not billions of dollars annually. With the ever-urgent needs for alternative energy sources, there is a strong push for a hydrogen economy from government and private sectors. Safe storage and transportation of hydrogen increases the momentum for studying hydrogen-related failures, especially in ductile materials. To quantify ductile material damage with the effects of hydrogen embrittlement, it is necessary to add hydrogen effects into the void nucleation, void growth, and void coalescence equations. In this research, hydrogen-enhanced void nucleation is our focus, with hydrogen-enhanced void growth and void coalescence t be studied in the future. Molecular Dynamic (MD) and Monte Carlo (MC) simulations with Embedded Atom Method (EAM) potentials were performed to study how hydrogen affects dislocation nucleation, dislocation structure formation and nanovoid nucleation at nickel grain boundaries. The results were inserted into the continuum void nucleation model by Horstemeyer and Gokhale, and the relationships between stress triaxiality-driven void nucleation, grain boundary hydrogen concentrations and local grain geometries were extracted. MD and MC simulations with EAM potentials were also performed to study how hydrogen interstitials affect the dislocation nucleation, dislocation structure formation and subsequent anovoid nucleation of single crystal nickel in different hydrogen-charging conditions. Evolutions of dislocation structures of nickel single crystal with different hydrogen concentrations were compared. The effects of nanovoid nucleation stress and strain at different hydrogen concentrations were quantified. The results were also inserted into the Horstemeyer and Gokhale model and the relationship between stress triaxiality-driven void nucleation and hydrogen concentration caused by stress gradient, which showed similar trends as the grain boundary studies. From nanoscale studies and existing experimental observations, a continuum void nucleation model with hydrogen effects was proposed and used in a continuum damage model based upon Bammann and coworkers. The damage model was implemented into user material code in FEA code ABAQUS. Finite element analyses were performed and the results were compared to the experimental data by Kwon and Asaro.

No description available.

No description available.

In this research, a first-principles, non-equilibrium thermodynamic-ensemble approach applicable across all temporal and spatial scales is developed based on steepest-entropy-ascent quantum thermodynamics (SEAQT). The SEAQT framework provides an equation of motion consisting of both reversible mechanical dynamics and irreversible relaxation dynamics, which is able to describe the evolution of any state of any system, equilibrium or non-equilibrium. Its key feature is that the irreversible dynamics is based on a gradient dynamics in system state space instead of the microscopic mechanics of more traditional approaches. System energy eigenstructure and density operator (or ensemble probability distribution) describe the system and system thermodynamic state, respectively. Extensive properties (i.e., energy, entropy, and particle number) play a key role in formulating the equation of motion and in describing non-equilibrium state evolutions. All the concepts involved in this framework (i.e., eigentstructure, density operator, and extensive properties) are well defined at all temporal and spatial scales leading to the extremely broad applicability of SEAQT. The focus of the present research is that of developing non-equilibrium thermodynamic models based specifically on the irreversible part of the equation of motion of SEAQT and applying these to the study of pure relaxation processes of systems in non-equilibrium states undergoing chemical reactions and heat and mass diffusion. As part of the theoretical investigation, the new concept of hypo-equilibrium state is introduced and developed. It is able to describe any non-equilibrium state going through a pure relaxation process and is a generalization of the concept of stable equilibrium of equilibrium thermodynamics to the non-equilibrium realm. Using the concept of hypo-equilibrium state, it is shown that non-equilibrium intensive properties can be fundamentally defined throughout the relaxation process. The definition of non-equilibrium intensive properties also relies on various ensemble descriptions of system state. In this research, three SEAQT ensemble descriptions, i.e., the canonical, grand canonical, and isothermal-isobaric, are derived corresponding, respectively, to the definition of temperature, chemical potential, and pressure. To computationally and not just theoretically permit the application of the SEAQT framework across all scales, a density of states method is developed, which is applicable to solving the SEAQT equation of motion for all types of non-equilibrium relaxation processes. In addition, a heterogeneous multiscale method (HMM) algorithm is also applied to extend the application of the SEAQT framework to multiscale modeling. Applications of this framework are given for systems involving chemical kinetics, the heat and mass diffusion of indistinguishable particles, power cycles, and the complex, coupled reaction-diffusion pathways of a solid oxide fuel cell (SOFC) cathode. / Ph. D.

Most engineering systems have some degree of uncertainty in their input and operating parameters. The interaction of these parameters leads to the uncertain nature of the system performance and outputs. In order to quantify this uncertainty in a computational model, it is necessary to include the full range of uncertainty in the model. Currently, there are two major technical barriers to achieving this: (1) in many situations -particularly those involving multiscale phenomena-the stochastic nature of input parameters is not well defined, and is usually approximated by limited experimental data or heuristics; (2) incorporating the full range of uncertainty across all uncertain input and operating parameters via conventional techniques often results in an inordinate number of computational scenarios to be performed, thereby limiting uncertainty analysis to simple or approximate computational models. This first objective is addressed through combining molecular and macroscale modeling where the molecular modeling is used to quantify the stochastic distribution of parameters that are typically approximated. Specifically, an adsorption separation process is used to demonstrate this computational technique. In this demonstration, stochastic molecular modeling results are validated against a diverse range of experimental data sets. The stochastic molecular-level results are then shown to have a significant role on the macro-scale performance of adsorption systems. The second portion of this research is focused on reducing the computational burden of performing an uncertainty analysis on practical engineering systems. The state of the art for uncertainty analysis relies on the construction of a meta-model (also known as a surrogate model or reduced order model) which can then be sampled stochastically at a relatively minimal computational burden. Unfortunately these meta-models can be very computationally expensive to construct, and the complexity of construction can scale exponentially with the number of relevant uncertain input parameters. In an effort to dramatically reduce this effort, a novel methodology "QUICKER (Quantifying Uncertainty In Computational Knowledge Engineering Rapidly)" has been developed. Instead of building a meta-model, QUICKER focuses exclusively on the output distributions, which are always one-dimensional. By focusing on one-dimensional distributions instead of the multiple dimensions analyzed via meta-models, QUICKER is able to handle systems with far more uncertain inputs. / Ph. D.

The goal of this research is developing a computational framework to study mechanical fatigue and fracture at different length scales for a broad range of materials. The developed multiscale framework is utilized to study the details of fracture and fatigue for the rolling contact in rails, additively manufactured alloys, and bio-inspired hierarchical materials. Rolling contact fatigue (RCF) is a major source of failure and a dominant cause of maintenance and replacements in many railways around the world. The highly-localized stress in a relatively small contact area at the wheel-rail interface promotes micro-crack initiation and propagation near the surface of the rail. 2D and 3D microstructural-based computational frameworks are developed for studying the rolling contact fatigue in rail materials. The method can predict RCF life and simulate crack initiation sites under various conditions. The results obtained from studying RCF behavior in different conditions will help better maintenance of the railways and increase the safety of trains. The developed framework is employed to study the fracture and fatigue behavior in 3D printed metallic alloys fabricated by selective laser melting (SLM) method. SLM method as a part of metal additive manufacturing (AM) technologies is revolutionizing the manufacturing sector and is being utilized across a diverse array of industries, including biomedical, automotive, aerospace, energy, consumer goods, and many others. Since experiments on 3D printed alloys are considerably time-consuming and expensive, computational analysis is a proper alternative to reduce cost and time. In this research, a computational framework is developed to study fracture and fatigue in different scales in 3D printed alloys fabricated by the SLM method. Our method for studying the fatigue at the microstructural level of 3D printed alloys is pioneering with no similar work being available in the literature. Our studies can be used as a first step toward establishing comprehensive numerical frameworks to investigate fracture and fatigue behavior of 3D metallic devices with complex geometries, fabricated by 3D printing. Composite materials are fabricated by combining the attractive mechanical properties of materials into one system. A combination of materials with different mechanical properties, size, geometry, and order of different phases can lead to fabricating a new material with a wide range of properties. A fundamental problem in engineering is how to find the design that exhibits the best combination of these properties. Biological composites like bone, nacre, and teeth attracted much attention among the researchers. These materials are constructed from simple building blocks and show an uncommon combination of high strength and toughness. By inspiring from simple building blocks in bio-inspired materials, we have simulated fracture behavior of a pre-designed composite material consisting of soft and stiff building blocks. The results show a better performance of bio-inspired composites compared to their building blocks. Furthermore, an optimization methodology is implemented into the designing the bio-inspired composites for the first time, which enables us to perform the bio-inspired material design with the target of finding the most efficient geometries that can resist defects in their structure. This study can be used as an effective reference for creating damage-tolerant structures with improved mechanical behavior. / Doctor of Philosophy / The goal of this research is developing a multiscale framework to study the details of fracture and fatigue for the rolling contact in rails, additively manufactured alloys, and bio-inspired hierarchical materials. Rolling contact fatigue (RCF) is a major source of failure and a dominant cause of maintenance and replacements in many railways around the world. Different computational models are developed for studying rolling contact fatigue in rail materials. The method can predict RCF life and simulate crack initiation sites under various conditions and the results will help better maintenance of the railways and increase the safety of trains. The developed model is employed to study the fracture and fatigue behavior in 3D printed metals created by the selective laser melting (SLM) method. SLM method as a part of metal additive manufacturing (AM) technologies is revolutionizing industries including biomedical, automotive, aerospace, energy, and many others. Since experiments on 3D printed metals are considerably time-consuming and expensive, computational analysis is a proper alternative to reduce cost and time. Our method for studying the fatigue at the microstructural level of 3D printed alloys can help to create more fatigue and fracture resistant materials. In the last section, we have studied fracture behavior in bio-inspired materials. A fundamental problem in engineering is how to find the design that exhibits the best combination of mechanical properties. Biological materials like bone, nacre, and teeth are constructed from simple building blocks and show a surprising combination of high strength and toughness. By inspiring from these materials, we have simulated fracture behavior of a pre-designed composite material consisting of soft and stiff building blocks. The results show a better performance of bio-inspired structure compared to its building blocks. Furthermore, an optimization method is implemented into the designing the bio-inspired structures for the first time, which enables us to perform the bio-inspired material design with the target of finding the most efficient geometries that can resist defects in their structure.

For simple fluids, or Newtonian fluids, the study of the Navier-Stokes equations in the high Reynolds number limit brings about two fundamental research subjects, the Euler equations and the Prandtl's system. The consideration of infinite Reynolds number reduces the Navier-Stokes equations to the Euler equations, both of which are dealing with the entire flow region. Prandtl's system consists of the governing equations of the boundary layer, a thin layer formed at the wall boundary where viscosity cannot be neglected. In this dissertation, we investigate the upper convected Maxwell(UCM) model for complex fluids, or non-Newtonian fluids, in the high Weissenberg number limit. This is analogous to the Newtonian fluids in the high Reynolds number limit. We present two well-posedness results. The first result is on an initial-boundary value problem for incompressible hypoelastic materials which arise as a high Weissenberg number limit of viscoelastic fluids. We first assume the stress tensor is rank-one and develop energy estimates to show the problem is locally well-posed. Then we show the more general case can be handled in the same spirit. This problem is closely related to the incompressible ideal magneto-hydrodynamics (MHD) system. The second result addresses the formulation of a time-dependent elastic boundary layer through scaling analysis. We show the well-posedness of this boundary layer by transforming to Lagrangian coordinates. In contrast to the possible ill-posedness of Prandtl's system in Newtonian fluids, we prove that in non-Newtonian fluids the stress boundary layer problem is well-posed. / Ph. D.