Multiscale Investigation of Random Heterogenous Media in Materials and Earth Sciences

This dissertation is concerned with three major areas pertaining to the characterization and analysis of heterogeneous materials. The first is focused on the modeling of heterogeneous materials with random microstructure and understanding their thermomechanical properties as well as developing a methodology for the multiscale thermoelastic analysis of random heterogeneous materials. Realistic random microstructures are generated for computational analyses using random morphology description functions. The simulated microstructures closely resemble actual micrographs of random heterogeneous materials. The simulated random microstructures are characterized using statistical techniques and their homogenized material properties computed using the asymptotic expansion homogenization method. The failure response of random media is investigated via a direct micromechanical failure analysis which utilizes stresses at the microstructural level coupled with appropriate phase material failure models to generate initial failure envelopes. The homogenized material properties and failure envelopes are employed to perform accurate coupled macroscale and microscale analyses of random heterogeneous material components. The second area addressed in this dissertation involves the transient multiscale analysis of two-phase functionally graded materials within the framework of linearized thermoelasticity. The two-phase material microstructures, which are created using a morphology description function, have smoothly varying microstructure morphologies that depend on the volume fractions of the constituent phases. The multiscale problem is analyzed using asymptotic expansion homogenization coupled with the finite element method. Model problems are studied to illustrate the versatility of the multiscale analysis procedure which incorporates a direct micromechanical failure analysis to accurately compute the factors of safety for functionally graded components. The last area of this dissertation is concerned with determining the role of heterogeneous rock fabric features in quartz/muscovite rich rocks on seismic wave speed anisotropy. The bulk elastic properties and corresponding wave velocities are calculated for synthetic heterogeneous rock microstructures with varying material and geometric features to investigate their influence on seismic wave speed anisotropy. The asymptotic expansion homogenization method is employed to calculate precise bulk stiffness tensors for representative rock volumes and the wave speed velocities are obtained from the Christoffel equation. The obtained results are also used to assess the performance of analytic homogenization schemes currently used in the geophysics community

Integrated Analytical-Computational Analysis of Microstructural Influences on Seismic Anisotropy

The magnitudes, orientations and spatial distributions of elastic anisotropy in Earth\u27s crust and mantle carry valuable information about gradients in thermal, mechanical and kinematic parameters arising from mantle convection, mantle-crust coupling and tectonic plate interactions. Relating seismic signals to deformation regimes requires knowledge of the elastic signatures (bulk stiffnesses) of different microstructures that characterize specific deformation environments, but the influence of microstructural heterogeneity on bulk stiffness has not been comprehensively evaluated. The objectives of this project are to: (1) scale up a preliminary method to determine the bulk stiffness of rocks using integrated analytical (electron backscatter diffraction) and computational (asymptotic expansion homogenization) approaches that fully account for the grain-scale elastic interactions among the different minerals in the sample; (2) apply this integrated framework to investigate the effect on elastic anisotropy of several common crustal microstructures; (3) integrate time-dependent microstructure modeling with bulk stiffness calculations to investigate the effects of strain- and process-dependent microstructure evolution on elastic anisotropy in mantle rocks; and (4) disseminate open-source software for the calculation of bulk stiffnesses from electron backscatter diffraction data and creation of synthetic (computer generated) microstructures that can be used in sensitivity analyses among other applications. Because commonly used methods, such as the Voigt, Reuss and Voigt-Reuss-Hill averages, for calculating bulk rock stiffnesses do not account for elastic interactions among the constituent minerals, they exhibit marked, non-systematic differences from stiffnesses obtained using asymptotic expansion homogenization. These objectives are important because the results would substantially improve understanding of the nature of seismic anisotropy in the Earth\u27s crust, which is composed of rocks dominated by low symmetry minerals with complex structures. Traditional methods for performing these calculations do not easily incorporate these effects. This project will develop an elegant, easily-implemented alternative method for anisotropic materials. The scientific results and computational tools that result from this project will have global application across a number of solid Earth and engineering disciplines. Open-source codes developed in this project will made available through existing open-source ELLE platform. Classroom exercises developed for Earth Science and Mechanical Engineering courses that employ this software will be make available to the community, probably through the Science Education Resource Center website at Carleton College

Comparison of Extreme Wind and Waves Using Different Statistical Methods in 40 Offshore Wind Energy Lease Areas Worldwide

With the ongoing global drive towards renewable energy, several potential offshore wind energy lease areas worldwide have come into focus. This study aims to estimate the extreme wind and wave conditions across several newly designated offshore wind lease sites spanning six continents that are crucial for risk assessment and the design of offshore wind turbines. Firstly, the raw data of wind speeds and wave heights prevailing in these different lease areas were obtained. Following this, an in-depth extreme value analysis was performed over different return periods. Two principal methodologies were applied for this comparative study: the block-maxima and the peaks-over-threshold (POT) approaches. Various statistical techniques, including the Gumbel method of moments, Gumbel maximum likelihood, Gumbel least-squares, and the three-parameter GEV, were employed under the block-maxima approach to obtain the distribution parameters. The threshold for the POT approach was defined using the mean residual life method, and the distribution parameters were obtained using the maximum likelihood method. The Gumbel least-squares method emerged as the most conservative estimator of extreme values in the majority of cases, while the POT approach generally yielded lower extreme values compared to the block-maxima approach. However, the results from the POT approach showed large variations based on the selected threshold. This comprehensive study’s findings will provide valuable input for the efficient planning, design, and construction of future offshore wind farms.publishedVersio

Importance of Second-Order Difference-Frequency Wave-Diffraction Forces in the Validation of a Fast Semi-Submersible Floating Wind Turbine Model: Preprint

To better access the abundant offshore wind resource, efforts across the world are being undertaken to develop and improve floating offshore wind turbine technologies. A critical aspect of creating reliable, mature floating wind turbine technology is the development, verification, and validation of efficient computer-aided-engineering (CAE) tools that can be relied upon in the design process. The National Renewable Energy Laboratory (NREL) has created a comprehensive, coupled analysis CAE tool for floating wind turbines, FAST, which has been verified and utilized in numerous floating wind turbine studies. Several efforts are currently underway that leverage the extensive 1/50th-scale DeepCwind wind/wave basin model test dataset, obtained at the Maritime Research Institute Netherlands (MARIN) in 2011, to validate the floating platform functionality of FAST to complement its already validated aerodynamic and structural simulation capabilities. In this paper, further work is undertaken to continue this validation. In particular, the ability of FAST to replicate global response behaviors associated with dynamic wind forces, second-order difference-frequency wave-diffraction forces and their interaction with one another are investigated

Date: MULTISCALE INVESTIGATION OF RANDOM HETEROGENEOUS MEDIA IN MATERIALS AND EARTH SCIENCES

In presenting this thesis in partial fulfillment of the requirements for an advanced degree at The University of Maine, I agree that the Library shall make it freely available for inspection. I further agree that permission for “fair use ” copying of this thesis for scholarly purposes may be granted by the Librarian. It is understood that any copying or publication of this thesis for financial gain shall not be allowed without my written permission. Signature

Methodology for the Thermomechanical Simulation and Optimization of Functionally Graded Materials

Functionally graded materials are comprised of two or more material ingredients whose relative volume fractions and microstructure are engineered to have a continuous spatial variation. finctionally graded materials permit tailoring of the material volume fractions to extract maximum benefit from their inhomogeneity. Such materials offer great potential for components which operate under severe thermal or mechanical loadings, such as spacecraft heat shields, plasma facings for fusion reactors, crucial jet fighter structures and engine components. However, the performance of a functionally graded component is not just a function of the properties and mass of its material constituents alone, but is directly related to the ability of the designer to utilize the materials in the most optimal fashion. Therefore, we propose a methodology for the two-dimensional simulation and optimization of material distribution of functionally graded materials undergoing thermomechanical processes or free vibration. We first present the two-dimensional quasi-static heat conduction and thermoelasticity problems and analyze them using a meshless method, namely the element-free Galerkin method. The element-free Galerkin code is validated by comparing the results with known exact solutions, one for a homogeneous beam subjected to a distributed load and the other for a thermally loaded, simply supported functionally graded plate. Subsequently, we show the steady-state vibration problem and the corresponding element-free Galerkin formulation. The meshless code is compared to the exact solution for the free vibration of a simply supported, functionally graded plate and good agreement is obtained between the two. The spatial distribution of constituent volume fraction, which is to be optimized for various loading and boundary conditions, is obtained by piecewise bicubic interp* lation of volume fractions defined at a finite number of grid points. The effective material properties at a point in the domain are estimated from the local volume fractions of the material constituents using the Mori-Tanaka, self-consistent and Hashin- Shtrikman lower estimate homogenization schemes. The volume fraction distribution is optimized using real-coded genetic algorithms for both single and multi-objective problems. Lastly, the proposed methodology is applied to several example problems to illustrate its effectiveness in designing superior functionally graded components. The method is utilized to minimize the residual stress due to cooling from a high fabrication temperature of a functionally graded material as well as minimize the mass of a functionally graded material under imposed nonlinear temperature and effective stress constraints. The methodology is also demonstrated for the maximization and tuning of natural frequencies for functionally graded structures. Multi-objective optimization of volume fraction distribution is also performed for functionally graded material experiencing intense heat fluxes. The example problems demonstrate that the proposed methodology is robust and is well suited for designing functionally graded materials with superior thermomechanical and dynarnical response

Floating Wind Turbine Technology Development at the University of Maine

The State of Maine possesses a substantial offshore wind resource that if harnessed, could yield several benefits including job generation and a reduction in Maine’s dependence on fossil fuels. Most of this wind resource is located in waters that are too deep to employ conventional fixed-bottom offshore wind technology commonly found in Europe, and as such, requires the use of novel floating technology. Over the last decade, the University of Maine has worked to develop a floating offshore wind technology that can take advantage of Maine’s abundant offshore wind resource and be competitive with other forms of energy generation. In this presentation, an overview of the major research activities undertaken at the University of Maine in the development of its floating offshore wind turbine technology, dubbed VolturnUS, will be discussed. This research encompasses 1:50-scale model testing in a wind/wave basin, validation of coupled aero-hydro-servo-elastic floating offshore wind turbine simulation tools, demonstration of the VolturnUS technology in the field at a 1:8-scale as well as engineering design and component testing in support of the U.S. Department of Energy-funded Aqua Ventus I Demonstration Project which aims to deploy two 6 MW floating wind turbines off the coast of Maine. Various lessons learned through this technology development process will be discussed using supporting experimental data and numerical simulation results. The talk will conclude with the current status of floating wind turbine technology development at the University of Maine. Presenter Bio Dr. Andrew Goupee is the Libra Assistant Professor of Mechanical Engineering at the University of Maine. Andy received his bachelor\u27s, master\u27s, and Ph.D. in Mechanical Engineering from the University of Maine and immediately began working at the UMaine Composites Center. When he first started, Andy was in charge of the DeepCwind Model Test Program and went on to work on design and modeling of the VolturnUS 1:8