Multiscale constitutive modeling of polymer materials

Materials are inherently multi-scale in nature consisting of distinct characteristics at various length scales from atoms to bulk material. There are no widely accepted predictive multi-scale modeling techniques that span from atomic level to bulk relating the effects of the structure at the nanometer (10-9 meter) on macro-scale properties. Traditional engineering deals with treating matter as continuous with no internal structure. In contrast to engineers, physicists have dealt with matter in its discrete structure at small length scales to understand fundamental behavior of materials. Multiscale modeling is of great scientific and technical importance as it can aid in designing novel materials that will enable us to tailor properties specific to an application like multi-functional materials. Polymer nanocomposite materials have the potential to provide significant increases in mechanical properties relative to current polymers used for structural applications. The nanoscale reinforcements have the potential to increase the effective interface between the reinforcement and the matrix by orders of magnitude for a given reinforcement volume fraction as relative to traditional micro- or macro-scale reinforcements. To facilitate the development of polymer nanocomposite materials, constitutive relationships must be established that predict the bulk mechanical properties of the materials as a function of the molecular structure. A computational hierarchical multiscale modeling technique is developed to study the bulk-level constitutive behavior of polymeric materials as a function of its molecular chemistry. Various parameters and modeling techniques from computational chemistry to continuum mechanics are utilized for the current modeling method. The cause and effect relationship of the parameters are studied to establish an efficient modeling framework. The proposed methodology is applied to three different polymers and validated using experimental data available in literature.

MODELING DYNAMICS OF OZONE AND NITROGEN OXIDES AT SUMMIT, GREENLAND WITH A 1-D PROCESS-SCALE MODEL

This work presents a 1-D process scale model used to investigate the chemical dynamics and temporal variability of nitrogen oxides (NOx) and ozone (O3) within and above snowpack at Summit, Greenland for March-May 2009 and estimates surface exchange of NOx between the snowpack and surface layer in April-May 2009. The model assumes the surface of snowflakes have a Liquid Like Layer (LLL) where aqueous chemistry occurs and interacts with the interstitial air of the snowpack. Model parameters and initialization are physically and chemically representative of snowpack at Summit, Greenland and model results are compared to measurements of NOx and O3 collected by our group at Summit, Greenland from 2008-2010. The model paired with measurements confirmed the main hypothesis in literature that photolysis of nitrate on the surface of snowflakes is responsible for nitrogen dioxide (NO2) production in the top ~50 cm of the snowpack at solar noon for March – May time periods in 2009. Nighttime peaks of NO2 in the snowpack for April and May were reproduced with aqueous formation of peroxynitric acid (HNO4) in the top ~50 cm of the snowpack with subsequent mass transfer to the gas phase, decomposition to form NO2 at nighttime, and transportation of the NO2 to depths of 2 meters. Modeled production of HNO4 was hindered in March 2009 due to the low production of its precursor, hydroperoxy radical, resulting in underestimation of nighttime NO2 in the snowpack for March 2009. The aqueous reaction of O3 with formic acid was the major sync of O3 in the snowpack for March-May, 2009. Nitrogen monoxide (NO) production in the top ~50 cm of the snowpack is related to the photolysis of NO2, which underrepresents NO in May of 2009. Modeled surface exchange of NOx in April and May are on the order of 1011 molecules m-2 s-1. Removal of measured downward fluxes of NO and NO2 in measured fluxes resulted in agreement between measured NOx fluxes and modeled surface exchange in April and an order of magnitude deviation in May. Modeled transport of NOx above the snowpack in May shows an order of magnitude increase of NOx fluxes in the first 50 cm of the snowpack and is attributed to the production of NO2 during the day from the thermal decomposition and photolysis of peroxynitric acid with minor contributions of NO from HONO photolysis in the early morning.

Parameter estimation for transformer modeling

Large Power transformers, an aging and vulnerable part of our energy infrastructure, are at choke points in the grid and are key to reliability and security. Damage or destruction due to vandalism, misoperation, or other unexpected events is of great concern, given replacement costs upward of $2M and lead time of 12 months. Transient overvoltages can cause great damage and there is much interest in improving computer simulation models to correctly predict and avoid the consequences. EMTP (the Electromagnetic Transients Program) has been developed for computer simulation of power system transients. Component models for most equipment have been developed and benchmarked. Power transformers would appear to be simple. However, due to their nonlinear and frequency-dependent behaviors, they can be one of the most complex system components to model. It is imperative that the applied models be appropriate for the range of frequencies and excitation levels that the system experiences. Thus, transformer modeling is not a mature field and newer improved models must be made available. In this work, improved topologically-correct duality-based models are developed for three-phase autotransformers having five-legged, three-legged, and shell-form cores. The main problem in the implementation of detailed models is the lack of complete and reliable data, as no international standard suggests how to measure and calculate parameters. Therefore, parameter estimation methods are developed here to determine the parameters of a given model in cases where available information is incomplete. The transformer nameplate data is required and relative physical dimensions of the core are estimated. The models include a separate representation of each segment of the core, including hysteresis of the core, λ-i saturation characteristic, capacitive effects, and frequency dependency of winding resistance and core loss. Steady-state excitation, and de-energization and re-energization transients are simulated and compared with an earlier-developed BCTRAN-based model. Black start energization cases are also simulated as a means of model evaluation and compared with actual event records. The simulated results using the model developed here are reasonable and more correct than those of the BCTRAN-based model. Simulation accuracy is dependent on the accuracy of the equipment model and its parameters. This work is significant in that it advances existing parameter estimation methods in cases where the available data and measurements are incomplete. The accuracy of EMTP simulation for power systems including three-phase autotransformers is thus enhanced. Theoretical results obtained from this work provide a sound foundation for development of transformer parameter estimation methods using engineering optimization. In addition, it should be possible to refine which information and measurement data are necessary for complete duality-based transformer models. To further refine and develop the models and transformer parameter estimation methods developed here, iterative full-scale laboratory tests using high-voltage and high-power three-phase transformer would be helpful.

Physical modeling of air injection as a scour remediation technique near gated weir stilling basins

The South Florida Water Management District (SFWMD) manages and operates numerous water control structures that are subject to scour. In an effort to reduce scour downstream of these gated structures, laboratory experiments were performed to investigate the effect of active air-injection downstream of the terminal structure of a gated spillway on the depth of the scour hole. A literature review involving similar research revealed significant variables such as the ratio of headwater-to-tailwater depths, the diffuser angle, sediment uniformity, and the ratio of air-to-water volumetric discharge values. The experimental design was based on the analysis of several of these non-dimensional parameters. Bed scouring at stilling basins downstream of gated spillways has been identified as posing a serious risk to the spillway’s structural stability. Although this type of scour has been studied in the past, it continues to represent a real threat to water control structures and requires additional attention. A hydraulic scour channel comprised of a head tank, flow straightening section, gated spillway, stilling basin, scour section, sediment trap, and tail-tank was used to further this analysis. Experiments were performed in a laboratory channel consisting of a 1:30 scale model of the SFWMD S65E spillway structure. To ascertain the feasibility of air injection for scour reduction a proof-of-concept study was performed. Experiments were conducted without air entrainment and with high, medium, and low air entrainment rates for high and low headwater conditions. For the cases with no air entrainment it was found that there was excessive scour downstream of the structure due to a downward roller formed upon exiting the downstream sill of the stilling basin. When air was introduced vertically just downstream of, and at the same level as, the stilling basin sill, it was found that air entrainment does reduce scour depth by up to 58% depending on the air flow rate, but shifts the deepest scour location to the sides of the channel bed instead of the center. Various hydraulic flow conditions were tested without air injection to verify which scenario caused more scour. That scenario, uncontrolled free, in which water does not contact the gate and the water elevation in the stilling basin is lower than the spillway crest, would be used for the remainder of experiments testing air injection. Various air flow rates, diffuser elevations, air hole diameters, air hole spacings, diffuser angles and widths were tested in over 120 experiments. Optimal parameters include air injection at a rate that results in a water-to-air ratio of 0.28, air holes 1.016mm in diameter the entire width of the stilling basin, and a vertically orientated injection pattern. Detailed flow measurements were collected for one case using air injection and one without. An identical flow scenario was used for each experiment, namely that of a high flow rate and upstream headwater depth and a low tailwater depth. Equilibrium bed scour and velocity measurements were taken using an Acoustic Doppler Velocimeter at nearly 3000 points. Velocity data was used to construct a vector plot in order to identify which flow components contribute to the scour hole. Additionally, turbulence parameters were calculated in an effort to help understand why air-injection reduced bed scour. Turbulence intensities, normalized mean flow, normalized kinetic energy, and anisotropy of turbulence plots were constructed. A clear trend emerged that showed air-injection reduces turbulence near the bed and therefore reduces scour potential.

Optimal game theoretic distributed control methodologies in small scale power systems

This dissertation presents the competitive control methodologies for small-scale power system (SSPS). A SSPS is a collection of sources and loads that shares a common network which can be isolated during terrestrial disturbances. Micro-grids, naval ship electric power systems (NSEPS), aircraft power systems and telecommunication system power systems are typical examples of SSPS. The analysis and development of control systems for small-scale power systems (SSPS) lacks a defined slack bus. In addition, a change of a load or source will influence the real time system parameters of the system. Therefore, the control system should provide the required flexibility, to ensure operation as a single aggregated system. In most of the cases of a SSPS the sources and loads must be equipped with power electronic interfaces which can be modeled as a dynamic controllable quantity. The mathematical formulation of the micro-grid is carried out with the help of game theory, optimal control and fundamental theory of electrical power systems. Then the micro-grid can be viewed as a dynamical multi-objective optimization problem with nonlinear objectives and variables. Basically detailed analysis was done with optimal solutions with regards to start up transient modeling, bus selection modeling and level of communication within the micro-grids. In each approach a detail mathematical model is formed to observe the system response. The differential game theoretic approach was also used for modeling and optimization of startup transients. The startup transient controller was implemented with open loop, PI and feedback control methodologies. Then the hardware implementation was carried out to validate the theoretical results. The proposed game theoretic controller shows higher performances over traditional the PI controller during startup. In addition, the optimal transient surface is necessary while implementing the feedback controller for startup transient. Further, the experimental results are in agreement with the theoretical simulation. The bus selection and team communication was modeled with discrete and continuous game theory models. Although players have multiple choices, this controller is capable of choosing the optimum bus. Next the team communication structures are able to optimize the players’ Nash equilibrium point. All mathematical models are based on the local information of the load or source. As a result, these models are the keys to developing accurate distributed controllers.

Molecular Modeling of PMR-15 Polyimide

PMR-15 polyimide is a polymer that is used as a matrix in composites. These composites with PMR-15 matrices are called advanced polymer matrix composite that is abundantly used in the aerospace and electronics industries because of its high temperature resistivity. Apart from having high temperature sustainability, PMR-15 composites also display good thermal-oxidative stability, mechanical properties, processability and low costs, which makes it a suitable material for manufacturing aircraft structures. PMR-15 uses the reverse Diels-Alder (RDA) method for crosslinking which provides it with the groundwork for its distinctive thermal stability and a range of 280-300 degree Centigrade use temperature. Regardless of such desirable properties, this material has a number of limitations that compromises its application on a large scale basis. PMR-15 composites has been known to be very vulnerable to micro-cracking at inter and intra-laminar cracking. But the major factor that hinders its demand is PMR-15's carcinogenic constituent, methylene dianilineme (MDA), also a liver toxin. The necessity of providing a safe working environment during its production adds up to the cost of this material. In this study, Molecular Dynamics and Energy Minimization techniques are utilized to simulate a structure of PMR-15 at a given density of 1.324 g/cc and an attempt to recreate the polyimide to reduce the number of experimental testing and hence subdue the health hazards as well as the cost involved in its production. Even though this study does not involve in validating any mechanical properties of the model, it could be used in future for the validation of its properties and further testing for different properties like aging, microcracking, creep etc.

MULTISCALE EXAMINATION AND MODELING OF ELECTRON TRANSPORT IN NANOSCALE MATERIALS AND DEVICES

For half a century the integrated circuits (ICs) that make up the heart of electronic devices have been steadily improving by shrinking at an exponential rate. However, as the current crop of ICs get smaller and the insulating layers involved become thinner, electrons leak through due to quantum mechanical tunneling. This is one of several issues which will bring an end to this incredible streak of exponential improvement of this type of transistor device, after which future improvements will have to come from employing fundamentally different transistor architecture rather than fine tuning and miniaturizing the metal-oxide-semiconductor field effect transistors (MOSFETs) in use today. Several new transistor designs, some designed and built here at Michigan Tech, involve electrons tunneling their way through arrays of nanoparticles. We use a multi-scale approach to model these devices and study their behavior. For investigating the tunneling characteristics of the individual junctions, we use a first-principles approach to model conduction between sub-nanometer gold particles. To estimate the change in energy due to the movement of individual electrons, we use the finite element method to calculate electrostatic capacitances. The kinetic Monte Carlo method allows us to use our knowledge of these details to simulate the dynamics of an entire device— sometimes consisting of hundreds of individual particles—and watch as a device ‘turns on’ and starts conducting an electric current. Scanning tunneling microscopy (STM) and the closely related scanning tunneling spectroscopy (STS) are a family of powerful experimental techniques that allow for the probing and imaging of surfaces and molecules at atomic resolution. However, interpretation of the results often requires comparison with theoretical and computational models. We have developed a new method for calculating STM topographs and STS spectra. This method combines an established method for approximating the geometric variation of the electronic density of states, with a modern method for calculating spin-dependent tunneling currents, offering a unique balance between accuracy and accessibility.

STATE-AND-TRANSITION MODELING AND ADAPTIVE MANAGEMENT: TOOLS FOR FUTURE CO-DEVELOPMENT OF MADAGASCAR’S NATURAL RESOURCES AND PEOPLE

Madagascar’s terrestrial and aquatic ecosystems have long supported a unique set of ecological communities, many of whom are endemic to the tropical island. Those same ecosystems have been a source of valuable natural resources to some of the poorest people in the world. Nevertheless, with pride, ingenuity and resourcefulness, the Malagasy people of the southwest coast, being of Vezo identity, subsist with low development fishing techniques aimed at an increasingly threatened host of aquatic seascapes. Mangroves, sea grass bed, and coral reefs of the region are under increased pressure from the general populace for both food provisions and support of economic opportunity. Besides purveyors and extractors, the coastal waters are also subject to a number of natural stressors, including cyclones and invasive, predator species of both flora and fauna. In addition, the aquatic ecosystems of the region are undergoing increased nutrient and sediment runoff due, in part, to Madagascar’s heavy reliance on land for agricultural purposes (Scales, 2011). Moreover, its coastal waters, like so many throughout the world, have been proven to be warming at an alarming rate over the past few decades. In recognizing the intimate interconnectedness of the both the social and ecological systems, conservation organizations have invoked a host of complimentary conservation and social development efforts with the dual aim of preserving or restoring the health of both the coastal ecosystems and the people of the region. This paper provides a way of thinking more holistically about the social-ecological system within a resiliency frame of understanding. Secondly, it applies a platform known as state-and-transition modeling to give form to the process. State-and-transition modeling is an iterative investigation into the physical makeup of a system of study as well as the boundaries and influences on that state, and has been used in restorative ecology for more than a decade. Lastly, that model is sited within an adaptive management scheme that provides a structured, cyclical, objective-oriented process for testing stakeholders cognitive understanding of the ecosystem through a pragmatic implementation and monitoring a host of small-scale interventions developed as part of the adaptive management process. Throughout, evidence of the application of the theories and frameworks are offered, with every effort made to retool conservation-minded development practitioners with a comprehensive strategy for addressing the increasingly fragile social-ecological systems of southwest Madagascar. It is offered, in conclusion, that the seascapes of the region would be an excellent case study worthy of future application of state-and-transition modeling and adaptive management as frameworks for conservation-minded development practitioners whose multiple projects, each with its own objective, have been implemented with a single goal in mind: preserve and protect the state of the supporting environment while providing for the basic needs of the local Malagasy people.

Long-Range Pollution Transport: Trans-Atlantic Mechanisms and Lagrangian Modeling Methods

Over the past several decades, it has become apparent that anthropogenic activities have resulted in the large-scale enhancement of the levels of many trace gases throughout the troposphere. More recently, attention has been given to the transport pathway taken by these emissions as they are dispersed throughout the atmosphere. The transport pathway determines the physical characteristics of emissions plumes and therefore plays an important role in the chemical transformations that can occur downwind of source regions. For example, the production of ozone (O3) is strongly dependent upon the transport its precursors undergo. O3 can initially be formed within air masses while still over polluted source regions. These polluted air masses can experience continued O3 production or O3 destruction downwind, depending on the air mass's chemical and transport characteristics. At present, however, there are a number of uncertainties in the relationships between transport and O3 production in the North Atlantic lower free troposphere. The first phase of the study presented here used measurements made at the Pico Mountain observatory and model simulations to determine transport pathways for US emissions to the observatory. The Pico Mountain observatory was established in the summer of 2001 in order to address the need to understand the relationships between transport and O3 production. Measurements from the observatory were analyzed in conjunction with model simulations from the Lagrangian particle dispersion model (LPDM), FLEX-PART, in order to determine the transport pathway for events observed at the Pico Mountain observatory during July 2003. A total of 16 events were observed, 4 of which were analyzed in detail. The transport time for these 16 events varied from 4.5 to 7 days, while the transport altitudes over the ocean ranged from 2-8 km, but were typically less than 3 km. In three of the case studies, eastward advection and transport in a weak warm conveyor belt (WCB) airflow was responsible for the export of North American emissions into the FT, while transport in the FT was governed by easterly winds driven by the Azores/Bermuda High (ABH) and transient northerly lows. In the fourth case study, North American emissions were lofted to 6-8 km in a WCB before being entrained in the same cyclone's dry airstream and transported down to the observatory. The results of this study show that the lower marine FT may provide an important transport environment where O3 production may continue, in contrast to transport in the marine boundary layer, where O3 destruction is believed to dominate. The second phase of the study presented here focused on improving the analysis methods that are available with LPDMs. While LPDMs are popular and useful for the analysis of atmospheric trace gas measurements, identifying the transport pathway of emissions from their source to a receptor (the Pico Mountain observatory in our case) using the standard gridded model output, particularly during complex meteorological scenarios can be difficult can be difficult or impossible. The transport study in phase 1 was limited to only 1 month out of more than 3 years of available data and included only 4 case studies out of the 16 events specifically due to this confounding factor. The second phase of this study addressed this difficulty by presenting a method to clearly and easily identify the pathway taken by only those emissions that arrive at a receptor at a particular time, by combining the standard gridded output from forward (i.e., concentrations) and backward (i.e., residence time) LPDM simulations, greatly simplifying similar analyses. The ability of the method to successfully determine the source-to-receptor pathway, restoring this Lagrangian information that is lost when the data are gridded, is proven by comparing the pathway determined from this method with the particle trajectories from both the forward and backward models. A sample analysis is also presented, demonstrating that this method is more accurate and easier to use than existing methods using standard LPDM products. Finally, we discuss potential future work that would be possible by combining the backward LPDM simulation with gridded data from other sources (e.g., chemical transport models) to obtain a Lagrangian sampling of the air that will eventually arrive at a receptor.

SYSTEM DYNAMICS MODELING AS A QUANTITATIVE-QUALITATIVE FRAMEWORK FOR SUSTAINABLE WATER RESOURCES MANAGEMENT: INSIGHTS FOR WATER QUALITY POLICY IN THE GREAT LAKES REGION

Early water resources modeling efforts were aimed mostly at representing hydrologic processes, but the need for interdisciplinary studies has led to increasing complexity and integration of environmental, social, and economic functions. The gradual shift from merely employing engineering-based simulation models to applying more holistic frameworks is an indicator of promising changes in the traditional paradigm for the application of water resources models, supporting more sustainable management decisions. This dissertation contributes to application of a quantitative-qualitative framework for sustainable water resources management using system dynamics simulation, as well as environmental systems analysis techniques to provide insights for water quality management in the Great Lakes basin. The traditional linear thinking paradigm lacks the mental and organizational framework for sustainable development trajectories, and may lead to quick-fix solutions that fail to address key drivers of water resources problems. To facilitate holistic analysis of water resources systems, systems thinking seeks to understand interactions among the subsystems. System dynamics provides a suitable framework for operationalizing systems thinking and its application to water resources problems by offering useful qualitative tools such as causal loop diagrams (CLD), stock-and-flow diagrams (SFD), and system archetypes. The approach provides a high-level quantitative-qualitative modeling framework for "big-picture" understanding of water resources systems, stakeholder participation, policy analysis, and strategic decision making. While quantitative modeling using extensive computer simulations and optimization is still very important and needed for policy screening, qualitative system dynamics models can improve understanding of general trends and the root causes of problems, and thus promote sustainable water resources decision making. Within the system dynamics framework, a growth and underinvestment (G&U) system archetype governing Lake Allegan's eutrophication problem was hypothesized to explain the system's problematic behavior and identify policy leverage points for mitigation. A system dynamics simulation model was developed to characterize the lake's recovery from its hypereutrophic state and assess a number of proposed total maximum daily load (TMDL) reduction policies, including phosphorus load reductions from point sources (PS) and non-point sources (NPS). It was shown that, for a TMDL plan to be effective, it should be considered a component of a continuous sustainability process, which considers the functionality of dynamic feedback relationships between socio-economic growth, land use change, and environmental conditions. Furthermore, a high-level simulation-optimization framework was developed to guide watershed scale BMP implementation in the Kalamazoo watershed. Agricultural BMPs should be given priority in the watershed in order to facilitate cost-efficient attainment of the Lake Allegan's TP concentration target. However, without adequate support policies, agricultural BMP implementation may adversely affect the agricultural producers. Results from a case study of the Maumee River basin show that coordinated BMP implementation across upstream and downstream watersheds can significantly improve cost efficiency of TP load abatement.

MOLECULAR MODELING OF EPON 862-DETDA / CARBON COMPOSITES

The thermoset epoxy resin EPON 862, coupled with the DETDA hardening agent, are utilized as the polymer matrix component in many graphite (carbon fiber) composites. Because it is difficult to experimentally characterize the interfacial region, computational molecular modeling is a necessary tool for understanding the influence of the interfacial molecular structure on bulk-level material properties. The purpose of this research is to investigate the many possible variables that may influence the interfacial structure and the effect they will have on the mechanical behavior of the bulk level composite. Molecular models are established for EPON 862-DETDA polymer in the presence of a graphite surface. Material characteristics such as polymer mass-density, residual stresses, and molecular potential energy are investigated near the polymer/fiber interface. Because the exact degree of crosslinking in these thermoset systems is not known, many different crosslink densities (degrees of curing) are investigated. It is determined that a region exists near the carbon fiber surface in which the polymer mass density is different than that of the bulk mass density. These surface effects extend ~10 Å into the polymer from the center of the outermost graphite layer. Early simulations predict polymer residual stress levels to be higher near the graphite surface. It is also seen that the molecular potential energy in polymer atoms decreases with increasing crosslink density. New models are then established in order to investigate the interface between EPON 862-DETDA polymer and graphene nanoplatelets (GNPs) of various atomic thicknesses. Mechanical properties are extracted from the models using Molecular Dynamics techniques. These properties are then implemented into micromechanics software that utilizes the generalized method of cells to create representations of macro-scale composites. Micromechanics models are created representing GNP doped epoxy with varying number of graphene layers and interfacial polymer crosslink densities. The initial micromechanics results for the GNP doped epoxy are then taken to represent the matrix component and are re-run through the micromechanics software with the addition of a carbon fiber to simulate a GNP doped epoxy/carbon fiber composite. Micromechanics results agree well with experimental data, and indicate GNPs of 1 to 2 atomic layers to be highly favorable. The effect of oxygen bonded to the surface of the GNPs is lastly investigated. Molecular Models are created for systems with varying graphene atomic thickness, along with different amounts of oxygen species attached to them. Models are created for graphene containing hydroxyl groups only, epoxide groups only, and a combination of epoxide and hydroxyl groups. Results show models of oxidized graphene to decrease in both tensile and shear modulus. Attaching only epoxide groups gives the best results for mechanical properties, though pristine graphene is still favored.

ADVANCED COMPUTATIONAL MODELING OF THE INTERNAL STRUCTURE OF SMART WIND-TURBINE BLADES

Implementation of stable aeroelastic models with the ability to capture the complex features of Multi concept smartblades is a prime step in reducing the uncertainties that come along with blade dynamics. The numerical simulations of fluid structure interaction can thus be used to test a realistic scenarios comprising of full-scale blades at a reasonably low computational cost. A code which was a combination of two advanced numerical models was designed and was run with the help of paralell HPC supercomputer platform. The first model was based on a variation of dimensional reduction technique proposed by Hodges and Yu. This model was the one to record the structural response of heterogenous composite blades. This technique reduces the geometrical complexities of the heterogenous blade section into a stiffness matrix for an equivalent beam. This derived equivalent 1-D strain energy matrix is similar to the actual 3-D strain energy matrix in an asymptotic sense. As this 1-D matrix helps in accurately modeling the blade structure as a 1-D finite element problem, this substantially redues the computational effort and subsequently the computational cost that are required to model the structural dynamics at each step. Second model comprises of implementation of the Blade Element Momentum Theory. In this approach we map all the velocities and the forces with the help of orthogonal matrices that help in capturing the large deformations and the effects of rotations in calculating the aerodynamic forces. This ultimately helps us to take into account the complex flexo torsional deformations. In this thesis we have succesfully tested these computayinal tools developed by MTU’s research team lead by for the aero elastic analysis of wind-turbine blades. The validation in this thesis is majorly based on several experiments done on NREL-5MW blade, as this is widely accepted as a benchmark blade in the wind industry. Along with the use of this innovative model the internal blade structure was also changed to add up to the existing benefits of the already advanced numerical models.

DIFFUSE-INTERFACE FIELD APPROACH TO MODELING SELF-ASSEMBLY OF HETEROGENEOUS COLLOIDAL SYSTEMS AND RELATED DIPOLE-DIPOLE INTERACTION PHENOMENA

Colloid self-assembly under external control is a new route to fabrication of advanced materials with novel microstructures and appealing functionalities. The kinetic processes of colloidal self-assembly have attracted great interests also because they are similar to many atomic level kinetic processes of materials. In the past decades, rapid technological progresses have been achieved on producing shape-anisotropic, patchy, core-shell structured particles and particles with electric/magnetic charges/dipoles, which greatly enriched the self-assembled structures. Multi-phase carrier liquids offer new route to controlling colloidal self-assembly. Therefore, heterogeneity is the essential characteristics of colloid system, while so far there still lacks a model that is able to efficiently incorporate these possible heterogeneities. This thesis is mainly devoted to development of a model and computational study on the complex colloid system through a diffuse-interface field approach (DIFA), recently developed by Wang et al. This meso-scale model is able to describe arbitrary particle shape and arbitrary charge/dipole distribution on the surface or body of particles. Within the framework of DIFA, a Gibbs-Duhem-type formula is introduced to treat Laplace pressure in multi-liquid-phase colloidal system and it obeys Young-Laplace equation. The model is thus capable to quantitatively study important capillarity related phenomena. Extensive computer simulations are performed to study the fundamental behavior of heterogeneous colloidal system. The role of Laplace pressure is revealed in determining the mechanical equilibrium of shape-anisotropic particles at fluid interfaces. In particular, it is found that the Laplace pressure plays a critical role in maintaining the stability of capillary bridges between close particles, which sheds light on a novel route to in situ firming compact but fragile colloidal microstructures via capillary bridges. Simulation results also show that competition between like-charge repulsion, dipole-dipole interaction and Brownian motion dictates the degree of aggregation of heterogeneously charged particles. Assembly and alignment of particles with magnetic dipoles under external field is studied. Finally, extended studies on the role of dipole-dipole interaction are performed for ferromagnetic and ferroelectric domain phenomena. The results reveal that the internal field generated by dipoles competes with external field to determine the dipole-domain evolution in ferroic materials.