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<p>The rapid growth of fields such as metamaterials, composites, architected materials, porous solids, and micro/nano materials, along with the continuing advancements in design and fabrication procedures have led to the synthesis of complex structures having intricate material distributions and non-trivial geometries. These materials find important applications including biomedical implants and devices, aerospace and naval structures, and micro/nano-electromechanical devices. Theoretical and experimental evidences have shown that these structures exhibit size-dependent (or, nonlocal) effects. This implies that the response of a point within the solid is affected by a collection of points; ultimately a manifestation of the multiscale deformation process. Broadly speaking, at a continuum level, the mathematical description of these multiscale phenomena leads to integral constitutive models, that account for the long-range interactions via nonlocal kernels. </p> <p><br></p> <p>Despite receiving considerable attention, the existing class of approaches to nonlocal elasticity are predominantly phenomenological in nature, following from their definition of the material parameters of the nonlocal kernel based on 'representative volume element' (RVE)-based statistical homogenization of the heterogeneous microstructure. The size of the RVE required for practical simulation, does not achieve a full-resolution of the intricate heterogeneous microstructure, and also implicitly enforces the use of symmetric nonlocal kernels to achieve thermodynamic consistency and mathematically well-posedness. The latter restriction directly limits the application of existing approaches only to the linear deformation analysis of either periodic or isotropic nonlocal structures. Additionally, the lack of a consistent characterization of the nonlocal effects, often results in inconsistent (also labeled as 'paradoxical') predictions depending on the nature of the external loading. In order to address these fundamental theoretical gaps, this dissertation develops a fractional-order kinematic approach to nonlocal elasticity by leveraging cutting-edge mathematical operators derived from the field of fractional calculus.</p> <p><br></p> <p>In contrast to the class of existing class of approaches that adopt an integral stress-strain constitutive relation derived from the equilibrium of the RVE, the fractional-order approach is predicated on a differ-integral (fractional-order) strain-displacement relation. The latter relation is derived from a fractional-order deformation-gradient mapping between deformed and undeformed configurations, and this approach naturally localizes and captures the effect of nonlocality at the root of the deformation phenomena. The most remarkable consequence of this reformulation consists in its ability to achieve thermodynamic and mathematical consistency, irrespective of the nature of the nonlocal kernel. The convex and positive-definite nature of the formulation enabled the use of variational principles to formulate well-posed governing equations, the incorporation of nonlinear effects, and enabled the development of accurate finite element simulation methods. The aforementioned features, when combined with a variable-order extension of the fractional-order continuum theory, enabled the physically consistent application of the nonlocal formulation to general continua exhibiting asymmetric interactions; ultimately a manifestation of material heterogeneity. Indeed, a rigorous theoretical analysis was conducted to demonstrate the natural ability of the variable-order in capturing the role of microstructure in the deformation of heterogeneous porous solids. These advantages allowed the application of the fractional-order kinematic approach to accurately and efficiently model the response of porous beams and plates, with random microstructural descriptions. Results derived from multiphysical loading conditions, as well as nonlinear deformation regimes, are used to demonstrate the causal relation between the kinematics-based fractional-order characterization of nonlocal effects and the natural role of microstructure in determining the macroscopic response of heterogeneous solids. The potential implications of the developed formalism on scientific discovery of material laws are examined in-depth, and different areas for further research are identified.</p>

Photocarriers in semiconductors excited by modulated laser sources give rise to charge diffusion waves that can be used to study and characterize the electronic transport properties of materials and devices. In this talk the concept of carrier diffusion waves (CDW) will be introduced for continuous-band semiconductors (e.g. Si); and of hopping diffusion waves in nanolayers (e.g. colloidal quantum dot (CQD) excitonic ensembles).

Yes / This study investigated the impact of sedimentation on rainwater storage system using a case study at the Ikorodu area of Lagos state, a rural area in Nigeria. In this investigation, the proportions of Escherichia coli (E. coli) that were settleable (due to sedimentation) and those that were at the free phase have been studied. Water samples were collected from different depths in the inspected rainwater storage tank at two different periods (i.e. rainy and dry periods) for 20 days. The samples collected from these periods have been analysed for physical and microbial measures before passing it through the serial filters with pore sizes of 500 μm, 100 μm, 10 μm and 1.5 μm to measure the retained particle mass. From the results, it was observed that: (1) the water quality at the free-phase zone was better than that at the tank’s bottom; (2) the settleable bacteria rapidly sinked to bottom; (3) the correlation of turbidity, E. coli and total suspended solids (TSS) for all the rain events showed a relatively high Pearson’s coefficient of 0.9 to one another; and (4) over 70% of settling TSS occurred within first 36 hours. Finally, it has been found that the physical sedimentation process can significantly reduce the microbial measures.

A numerical model based on fundamental engineering principles was developed and validated to establish a relationship between process parameters and the final properties of woodbased composite boards. The model simulates the mat formation, then compresses the reconstituted mat to its final thickness in a virtual press. The number of interacting variables during the hot-compression process is prohibitively large to assess a wide variety of data by experimental means. Therefore, the main advantage of the model based approach that the effect of the hot-compression parameters on the final properties of wood-based composite boards can be monitored without extensive experimentation. The mat formation part of the model is based on the Monte Carlo simulation technique to reproduce the spatial structure of the mat. The dimensions and the density of each flake are considered as random variables in the model, which follow certain probability density distributions. The parameters of these distributions are derived from data collected on industrial flakes by using an image analysis technique. The model can simulate the structure of a threelayer oriented strandboard (OSB) mat as well as the structure of random fiber networks. A grid is superimposed on the simulated mat and the number of flakes, the thickness, and the density of the mat at each grid point are computed. Additionally, the model predicts the change in several void volume fractions within the mat and the contact area between the flakes during consolidation. The void volume fractions are directly related to the physical properties of the mat, such as thermal conductivity, diffusivity, and permeability, and the contact area is an indicator of the effectively bonded area within the mat. The heat and mass transfer part of the model predicts the change of air content, moisture content, and temperature at designated mesh points in the cross section of the mat during the hotcompression. The water content is subdivided into vapor and bound water components. The free water component is not considered in the model due to the low (typically 6-7 %) initial moisture content of the flakes. The gas phase (air and vapor) moves by bulk flow and diffusion, while the bound water only moves by diffusion across the mat. The heat flow occurs by conduction and convection. The spatial derivatives of the resulting coupled partial differential equations are discretized by finite differences. The resulting ordinary differential equation in time is solved by a differential-algebraic system solver (DDASSL). The internal environment within the mat can be predicted among different initial and boundary conditions by this part of the hot-compression model. In the next phase of the research, the viscoelastic (time, temperature, and moisture dependent) response of the flakes was modeled using the time-temperature-moisture superposition principle of polymers. A master curve was created from data available in the literature, which describes the changing relaxation modulus of the flakes as a function of moisture and temperature at different locations in the mat. Then the flake mat was compressed in a virtual press. The stress-strain response is highly nonlinear due to the cellular structure of the mat. Hooke's Law was modified with a nonlinear strain function to account for the behavior of the flake mat in transverse compression. This part of the model gives insight into the vertical density profile formation through the thickness of the mat. Laboratory boards were produced to validate the model. A split-plot experimental design, with three different initial mat moisture contents (5, 8.5, 12 %), three final densities (609, 641, 673 kg êm3 or 38, 40, 42 lb ê ft3), two press platen temperatures (150, 200 °C), and three different press closing times (40, 60, 80 s) was applied to investigate the effect of production parameters on the internal mat conditions and the formation of the vertical density profile. The temperature and gas pressure at six locations in the mat, and the resultant density profiles of the laboratory boards, were measured. Adequate agreement was found between the model predicted and the experimentally measured temperature, pressure, and vertical density profiles. The complete model uses pressing parameters (press platen temperature, press schedule) and mat properties (flake dimensions and orientation, density distribution, initial moisture content and temperature) to predict the resulting internal conditions and vertical density profile formation within the compressed board. The density profile is related to all the relevant mechanical properties (bending strength, modulus of elasticity, internal bond strength) of the final board. The model can assist in the optimization of the parameters for hot-pressing woodbased composites and improve the performance of the final panel. / Ph. D.

Although enormous potential benefits are envisioned with the application of nanotechnology in conjunction with biological systems, interactions of nano particulate materials with biological materials is not well understood. The focus of this dissertation is to determine the mathematical relationships of the forces between nanoparticles and biological agents. The systems under investigation are the alpha-SiC/H2O/LGG polar based systems. The mathematical analysis for the surface forces, based on the attractive van der Waals forces for the alpha-SiC/H2O/alpha-SiC and alpha-SiC/H2O/LGG polar solvent based systems are presented and discussed. The rheological parameters including pH, zeta potential, shear rate, shear stress and viscosity that alter the dispersion mechanisms are also presented and discussed. The concurrence of the experimental analysis with the mathematical modeling is also presented. The rheological analysis in these systems for determining of the optimum amounts of dispersant, binder, plasticizer and solids loading using the Krieger-Dougherty fit and Liu's model are presented and discussed. Alpha-SiC/H2O/alpha-SiC and alpha-SiC/H2O/LGG polar solvent based samples were also fabricated to test for an application area of nano-bio technology: A novel nano and micro porous materials fabrication process. Porous materials are used for a variety of applications including insulation, filtration, catalytic substrates, textiles and consumer goods and accounts for billions of dollars in sales annually. Results from the alpha-SiC/H2O/alpha-SiC and alpha-SiC/H2O/LGG polar solvent based slip and freeze cast samples and their characterization using digital and electron microscopy are presented and discussed. Finally, the green and sintered density, porosity and strength of the alpha-SiC/H2O/alpha-SiC and alpha-SiC/H2O/LGG polar solvent based dispersion samples are determined and discussed. / Ph. D.

While the structure and mechanical properties of natural cellular solids such as wood and trabecular bone have been extensively studied in the past, the structural design and underlying deformation mechanisms of natural cellular solids with very high mineral contents (> 90 wt%), which we term as natural ceramic cellular solids, are largely unexplored. Many of these natural ceramic cellular solids, despite their inherent brittle constituent biominerals (e.g., calcite or aragonite), exhibit remarkable mechanical properties, such as high stiffness and damage tolerance. In this thesis, by carefully selecting three biomineralized skeletal models with distinctly different cellular morphologies, including the honeycomb-like structure in cuttlefish bone (or cuttlebone), the stochastic open-cell structure in sea urchin spines, and the periodic open-cell structure in starfish ossicles, I systematically investigate the mechanical design strategies of these natural ceramic cellular solids. The three model systems are cuttlefish Sepia officinalis, sea urchin Heterocentrotus mammillatus, and starfish Protoreaster nodosus, respectively. By investigating the relationship between their mechanical properties and structural characteristics, this thesis reveals some novel structural design strategies for developing lightweight, tough, strong, and stiff ceramic cellular solids. The internal skeleton of S. officinalis, also known as cuttlebone, has a porosity of 93 vol% (constituent material: 90 wt% aragonite), which is a multichambered structure consisting of horizontal septa and thin vertical walls with corrugated cross-sectional profiles. Through systematic ex-situ and synchrotron-based in-situ mechanical measurements and collaborative computational modeling, we reveal that the vertical walls in the cuttlebone exhibit an optimal waviness gradient, which leads to compression-dominant deformation and asymmetric wall fracture, accomplishing both high stiffness (8.4 MN∙m/kg) and high energy absorption (4.4 kJ/kg). Moreover, the distribution of walls reduces stress concentrations within the horizontal septa, facilitating a larger chamber crushing stress and more significant densification. For the stochastic open-cell foam-like structure, also known as stereom (porosity: 60-80 vol%, constituent material: 99 wt% calcite) in H. mammillatus, we first developed a computer vision-based algorithm that allows for quantitative analysis of the cellular network of these structures at both local individual branch and node level as well as the global network level. This open-source algorithm could be used for analyzing both biological and engineering open-cell foams. I further show that the smooth, highly curved branch morphology with near-constant surface curvature in stereom results in low-stress concentration, which further leads to dispersed crack formation upon loading. Combined synchrotron in-situ analysis, electron microscopic analysis, and computational modeling further reveal that the fractured branches are efficiently jammed by the small throat openings within the cellular structure. This further leads to the formation of damage bands with densely packed fracture pieces. The continuous widening of the damage bands through progressive microfracture of branches at the boundaries contributes to the observed high plateau stress during compression, thereby contributing to its high energy absorption (17.7 kJ/kg), which is comparable and even greater than many synthetic metal- and polymer-based foams. Lastly, this thesis leads to the discovery of a unique dual-scale single-crystalline porous lattice structure (porosity: 50 vol%, constituent material: 99 wt% calcite) in the ossicles of P. nodosus. At the atomic level, the ossicle is composed of single-crystal biogenic calcite. At the lattice level, the ossicle's microstructure organizes as a diamond-triply periodic minimal surface (TPMS) structure. Moreover, the crystallographic axes at atomic and lattice levels are aligned, i.e., the c-axis of calcite is aligned with the [111] direction of the diamond-TPMS lattice. This single crystallinity co-alignment at two levels mitigates the compliance of calcite in the c-axis direction by utilizing the stiff <111> direction of the diamond-TPMS lattice. Furthermore, 3D in-situ mechanical characterizations reveal that the presence of crystal defects such as 60° and screw dislocations at the lattice level suppresses slip-like fracture along the {111} planes of the calcitic diamond-TPMS lattice upon loading, achieving an enhanced energy absorption capability. Even though the skeleton of echinoderm is made up of single-crystal calcite, the structure fractures in a conchoidal manner rather than along the clipping plane, which can continuously fracture the fragments into small pieces and enhance energy dissipation. / Doctor of Philosophy / The application of engineering ceramic cellular solids as structural components is limited by their brittleness and flaw sensitivity. In contrast, nature has evolved ceramic cellular materials such as sea sponge, sea urchin spine, and diatom shells that are simultaneously lightweight, strong, and damage-tolerant. These properties are thought to be achieved by the structure design of the component of those materials. Learning design strategies from these natural ceramic cellular solids is significant for developing lightweight bio-inspired ceramic materials with improved mechanical performance. In this thesis, I investigated mechanical design strategies from natural ceramic cellular solids in three model systems, i.e., cuttlebone from cuttlefish Sepia officinalis, spines from sea urchin Heterocentrotus mammillatus, ossicles from starfish Protoreaster nodosus. These three natural ceramic porous solids have high mineral content in the constituent materials (> 90 wt%) and have a highly porous structure (porosity: 50 vol%-93 vol%). These three model systems are selected to represent the analogs of three typical structure forms of synthetic cellular solids, i.e., honeycomb-like structures, stochastic and periodic open-cell structures, respectively. This thesis aims to establish a quantitative relationship between the 3D multiscale structure and deformation/toughening behavior for these selected natural ceramic cellular solids via a combination of different experimental and computational approaches.

Various combinations of multi-stage thermophilic and/or mesophilic anaerobic sludge digestion systems were studied to evaluate their solids reduction, odor generation after centrifugal dewatering and indicator organism reduction in comparison to single-stage thermophilic and/or mesophilic anaerobic digestion systems. Pre-aeration of sludge in a thermophilic temperature was also tested followed by single or multi-stage anaerobic digestion systems. It was found that multi stage systems were capable of greater solids removal and placing thermophilic system in multi stage system enhanced indicator organism destruction below EPA Class A biosolids requirement. However, all the digestion systems in the study showed less than 3 log reduction of indicator organism DNA/g solids, which was much smaller than indicator organism reduction measured by standard culturing method. It was also found that the thermophilic anaerobic digestion system could increase organic sulfur-based odors from dewatered biosolids while placing a mesophilic digester reduced odors. It was exclusively observed from sludges containing high sulfate such as ones in this study. A combined anaerobic and aerobic sludge digestion system was also studied to evaluate their solids and nitrogen reduction efficiencies. The aerobic digester was continuously aerated to maintain dissolved oxygen level below 1 ppm and intermittently aerated. It was found that 90 % or more nitrogen removal was possible at the aerobic SRT greater than 3 days and the optimum aeration ratio could be determined. / Ph. D.