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Full-domain multiscale analyses of unidirectional AS4/H3502 open-hole composite tensile specimens were performed to assess the effect of microscale progressive fiber failures in regions with large stress/strain gradients on macroscale composite strengths. The effect of model discretization at the microscale and macroscale on the calculated composite strengths and analysis times was investigated. Multiple sets of microscale analyses of repeating unit cells, each containing varying numbers of fibers with a distinct statistical distribution of fiber strengths and fiber volume fractions, were used to establish the microscale discretization for use in multiscale calculations. In order to improve computational times, multiscale analyses were performed over a reduced domain of the open-hole specimen. The calculated strengths obtained using reduced domain analyses were comparable to those for full-domain analyses, but at a fraction of the computational cost. Such reduced domain analyses likely are an integral part of efficient adaptive multiscale analyses of large all-composite air vehicles.

A modified Weibull cumulative distribution function, which accounts for the effect of fiber length on the probability of failure, was used to characterize the variation in fiber tensile strength in a SCS-6/ TIMETAL 21S material system and was implemented within the framework of the NASA code MAC/GMC. A parametric study investigating the effect of repeating unit cell architecture and fiber strength distribution on the RUC-averaged ultimate composite strength and failure was performed. Multiscale progressive failure analyses of a tensile dogbone specimen were performed using FEAMAC/ ABAQUS to assess the effect of local variations in fiber strength on the global response. The effect of the RUC architecture, fiber strength distribution, and microscale/ macroscale discretization on the global response was determined. The methodology developed in this work for accounting for statistical variations in microscale properties that feed into macroscale progressive failure analyses can readily be applied to other composite material systems.

The study of hemodynamic patterns in large blood vessels, such as the ascending aortic artery, brachiocephalic trunk, right carotid artery and right subclavian artery presents the challenging complexity of vessel wall compliance induced by the high levels of shear stress gradients and blood flow pulsatility. Accurate prediction of hemodynamics in such conditions requires a complete Fluid Structure Interaction (FSI) analysis that couples the fluid flow behavior throughout the cardiac cycle with the structural response of the vessel walls. This research focuses on the computational study of a Multiscale Fluid-Structure Interaction on the arterial wall by coupling Finite Volumes Method (FVM) predictions of the Fluid Dynamics within the artery with Finite Elements Method (FEM) predictions of the Elasto-Dynamics response of the arterial walls and 1-D closed loop electrical circuit system to generate the dynamic pressure pulse. To this end, a commercial FVM Computational Fluid Dynamics (CFD) code (STAR-CCM+ 7.09.012) will be coupled through an external interface with a commercial FEM Elasto-Dynamics code (ABAQUS V6.12). The coupling interface is written in such a way that the wall shear stresses and pressures predicted by the CFD analysis will be passed as boundary conditions to the FEM structural solver. The deformations predicted by the FEM structural solver will be passed to the CFD solver to update the geometry in an implicit manner before the following iteration step. The coupling between the FSI and the 1-D closed loop lump parameter circuit updated the pressure pulse and mass flow rates generated by the circuit in an explicit manner after the periodic solution in the FSI analysis had settled. The methodology resulting from this study will be incorporated in a larger collaborative research program between UCF and ORHS that entails optimization of surgical implantation of Left Ventricular Assist iv Devices (LVAD) cannulae and bypass grafts with the aim to minimize thrombo-embolic events. Moreover, the work proposed will also be applied to another such collaborative project focused on the computational fluid dynamics modeling of the circulation of congenitally affected cardiovascular systems of neonates, specifically the Norwood and Hybrid Norwood circulation of children affected by the hypoplastic left heart syndrome.

We observe a stochastic process 𝑌 on [0,1]^𝑑 (𝑑 ≥ 1) satisfying 𝑑𝑌(𝑡)=𝑛¹/²𝑓(𝑡)𝑑𝑡 + 𝑑𝑊(𝑡), 𝑡 ∈ [0,1]^𝑑, where 𝑛 ≥ 1 is a given scale parameter (`sample size'), 𝑊 is the standard Brownian sheet on [0,1]^𝑑 and 𝑓 ∈ L₁([0,1]^𝑑) is the unknown function of interest. We propose a multivariate multiscale statistic in this setting and prove that the statistic attains a subexponential tail bound; this extends the work of 'Dumbgen and Spokoiny (2001)' who proposed the analogous statistic for 𝑑=1. In the process, we generalize Theorem 6.1 of 'Dumbgen and Spokoiny (2001)' about stochastic processes with sub-Gaussian increments on a pseudometric space, which is of independent interest. We use the proposed multiscale statistic to construct optimal tests (in an asymptotic minimax sense) for testing 𝑓 = 0 versus (i) appropriate Hölder classes of functions, and (ii) alternatives of the form 𝑓 = 𝜇_𝑛𝕀_{𝐵_𝑛}$, where 𝐵_𝑛 is an axis-aligned hyperrectangle in [0,1]^𝑑 and 𝜇_𝑛 ∈ ℝ; 𝜇_𝑛 and 𝐵_𝑛 unknown. In Chapter 3 we use this proposed multiscale statistics to construct honest confidence bands for multivariate shape-restricted regression including monotone and convex functions.

In 1998, the United States National Committee on Biomechanics (USNCB) established an evolving discipline called Functional Tissue Engineering (FTE). In establishing this discipline, the goals of the USNCB were to advance FTE by increasing awareness among tissue engineers about the importance of restoring function when engineering tissue constructs. Another goal was to encourage tissue engineers to incorporate these functional criteria in the design, manufacturing and optimization of tissue engineered constructs. Based on this motivation, an investigation of the structure and mechanical properties of the rabbit patellar tendon will be executed, with the ultimate goal of creating a multiscale soft tissue model based on internal state variable (ISV) theory. Many continuum scale models, mostly phenomenological and microstrucutral, have been created to contribute to the understanding of the complex functional properties of the tendon, such as its anisotropy, inhomogeneity, nonlinearity, and viscoelasticity. However, none of these models have represented the mechanical behavior of the tendon in the presence of internal structural change on a multiscale level. The development of a multiscale ISV model will allow the capture of the irreversible, path history dependent aspects of the material behavior. The objective of this study is to contribute to the multiscale ISV model development by quantifying the structure- property relations. In particular, the fibril distribution at the microstructural level and the resultant multiaxial stress states (longitudinal and transverse compression and longitudinal tension) will be examined).

One of the main goals of ecological research is to understand the factors that determine how communities are structured over both space and time. However, our understanding of any system is largely a function of the scale at which we make our observations. Thus, the mechanisms that determine patterns in community structure are likely to change depending on the scale of observation. This thesis explores how environmental variability affects community structure and species performance, and how the resulting patterns change as a function of scale. Specifically, I asses the role of variability in temperature, oxygen, pH, and chloride, on species richness, abundance, diversity, and species performance, at three observational scales: micro-spatial, local temporal, and landscape-temporal scales, in 49 natural erosional rock pool microcosms, located on the northern coast of Jamaica. I found that while environmental variability was not a primary determinant of species richness or abundance, it did play a role in determining species compositions in the pools. I also show that community patterns are strongly affected by the scale of observation. Recognizing scale-dependent changes in community patterns is a prerequisite for predicting the consequences of changes in ecological systems induced by variability in abiotic factors. / Thesis / Master of Science (MS)

Transport phenomena at the nanoscale can differ from that at the continuum because the large surface area to volume ratio significantly influences material properties. While the modeling of many such transport processes have been reported in the literature, a few examples exist that integrate molecular approaches into the more typical macroscale perspective. This thesis extends the understanding of nanoscale transport governed by charge, mass and energy transfer, comparing these phenomena with the corresponding continuum behavior where applicable. For instance, molecular simulations enable us to predict the solvation structure around ions and describe the diffusion of water in salt solutions. In another case, we find that in the absence of interfacial effects, the stagnation flow produced by two opposing nanojets can be suitably described using continuum relations. We also examine heat conduction within solids of nanometer dimensions due to both the ballistic propagation of lattice vibrations in small confined dimensions and a diffusive behavior that is observed at larger length scales. Our simulations determine the length dependence of thermal conductivity for these cases as well as effects of isotope substitution in a material. We find that a temperature discontinuity at interfaces between dissimilar materials arises due to interfacial thermal resistance. We successfully incorporate these interfacial nanoscale effects into a continuum model through a modified heat conduction approach and also by a multiscale computational scheme. Finally, our efforts at integrating research with education are described through our initiative for developing and implementing a nanotechnology module for freshmen, which forms the first step of a spiral curriculum. / Ph. D.

It has been observed that carbon nanotube (CNT)-polymer nanocomposite material has observable piezoresistive effect, that is to say that changes in applied strain may induce measurable changes in resistance. The first focus of the work is on modeling the piezoresistive response of the CNT-polymer nanocomposites by using computational micromechanics techniques based on finite element analysis. The in-plane, axial, the three dimensional piezoresistive responses of the CNT-polymer nanocomposites are studied by using 2D, axisymmetric, and 3D electromechanically coupled and multiscale finite element models. The microscale mechanisms that may have a substantial influence on the overall piezoresistivity of the nanocomposites, i.e. the electrical tunneling effect and the inherent piezoresistivity of the CNT, are included in microscale RVEs in order to understand their influence on macroscale piezoresistive response in terms of both the normalized change in effective resistivity and the corresponding effective gauge factor under applied strain. The computational results are used to better understand the driving mechanisms for the observed piezoresistive response of the material. The second focus of the work is on modeling the piezoresistive response of fuzzy fiber reinforced polymer composites by applying a 3D multiscale micromechanics model based on finite element analysis. Through explicitly accounting for the local piezoresistive response of the anisotropic interphase region, the piezoresistive responses of the overall fuzzy fiber reinforced polymer composites are obtained. The modeling results not only provide a possible explanation for the small gauge factors as observed in experiments, but also give guidance for the manufacture of fuzzy fiber reinforced polymer composites in order to achieve large, consistent, and predictable gauge factors. The third focus of the work is on modeling the coupled effect between continuum damage and piezoresistivity in the CNT-polymer nanocomposites by using computational micromechanics techniques based on a concurrent multiscale finite element analysis. The results show that there is a good correlation between continuum damage and piezoresistive response of the nanocomposites, which gives theoretical and modeling support for the use of CNT-polymer nanocomposites in structural health monitoring (SHM) applications for damage detections. / Ph. D.

Incentives are an effective mechanism to align the interests of decision-makers. For example, employers use incentives to motivate their employees to take actions that benefit both the employers and the employees. Incentives also play a role in the interaction between firms, for example in a supply chain network. The prevalent approach to analyzing interactions between decision-makers is through principal-agent models. Due to mathematical intractability, the majority of these models are restricted to the interaction between two decision-makers. However, modern organizations have many decision-makers that interact with each other in a network. Therefore, effective incentive mechanisms for systems with many decision-makers (agents) must account for the numerous network interdependencies. The objective of this dissertation is to design incentive mechanisms for systems with many agents, with a focus on teams and multi-firm networks. Methodologically, our approach applies and builds upon multiscale decision theory (MSDT). MSDT can effectively and efficiently model the interdependencies between decision-makers and their optimal response to incentives. This dissertation consists of three parts. The first part focuses on incentives in teams, where multiple subordinates work under a single supervisor. The contribution of the team model to MSDT is the introduction of continuous decision variables; prior MSDT models have only used discrete decision variables. In the second and third part of this dissertation, we analyze a network of collaborating firms in a systems engineering project and focus on verification decisions. We introduce a belief-based model, which is a novel approach for both MSDT and verification modeling in systems engineering. Using MSDT, we determine how incentives can be used by a contractor to motivate a subcontractor to verify its design when the subcontractor prefers not to do so. We extend this two-firm model to a general multi-firm network model for verification coordination and incentivization. This firm network resembles the inter-firm collaboration present in most large-scale system engineering projects. Through better aligned verification activities, system-wide verification costs decrease, while the reliability of the final system improves. / Ph. D. / Incentives are often used to align the interests of decision-makers in modern organizations. Employers use incentives to motivate their employees to take actions that benefit both the employers and the employees. Incentives also play a role in the interaction between multiple firms, for example in a supply chain network. The prevalent approach to analyzing interactions between decision-makers is through the so-called principal-agent models. Due to mathematical intractability, the majority of these models are restricted to the interaction between two decision-makers. However, modern organizations have many decision-makers that interact with each other in a network. Therefore, effective incentive mechanisms for systems with many decision-makers (agents) must account for the numerous interdependencies that arise due to the organizational structure. The objective of this dissertation is to design incentive mechanisms for systems with many agents, with a focus on teams and multi-firm networks. Methodologically, our approach applies and builds upon multiscale decision theory (MSDT). MSDT can effectively and efficiently model the interdependencies between decision-makers and derive optimal organization-wide incentives. This dissertation consists of three parts. The first part focuses on incentives in teams, where multiple employees work under a single manager. The contribution of the team model to MSDT is the introduction of continuous decision variables; prior MSDT models have only used discrete decision variables. In the second and third part of this dissertation, we analyze a network of collaborating contractors in a systems engineering project and focus on design verification strategies. We introduce a belief-based model, which is a novel approach for both MSDT and verification modeling in systems engineering. Using MSDT, we determine how incentives can be used by a contractor to motivate a subcontractor to verify its design when the subcontractor prefers not to do so. We extend this two-firm model to a general multi-firm network model for verification coordination and incentivization. This firm network resembles the inter-firm collaboration present in most large-scale system engineering projects. Through better aligned verification activities, system-wide verification costs decrease, while the reliability of the final system improves.