Application of Numerical Methods to Study Arrangement and Fracture of Lithium-Ion Microstructure

The focus of this work is to develop and employ numerical methods that provide characterization of granular microstructures, dynamic fragmentation of brittle materials, and dynamic fracture of three-dimensional bodies.

We first propose the fabric tensor formalism to describe the structure and evolution of lithium-ion electrode microstructure during the calendaring process. Fabric tensors are directional measures of particulate assemblies based on inter-particle connectivity, relating to the structural and transport properties of the electrode. Applying this technique to X-ray computed tomography of cathode microstructure, we show that fabric tensors capture the evolution of the inter-particle contact distribution and are therefore good measures for the internal state of and electronic transport within the electrode.

We then shift focus to the development and analysis of fracture models within finite element simulations. A difficult problem to characterize in the realm of fracture modeling is that of fragmentation, wherein brittle materials subjected to a uniform tensile loading break apart into a large number of smaller pieces. We explore the effect of numerical precision in the results of dynamic fragmentation simulations using the cohesive element approach on a one-dimensional domain. By introducing random and non-random field variations, we discern that round-off error plays a significant role in establishing a mesh-convergent solution for uniform fragmentation problems. Further, by using differing magnitudes of randomized material properties and mesh discretizations, we find that employing randomness can improve convergence behavior and provide a computational savings.

The Thick Level-Set model is implemented to describe brittle media undergoing dynamic fragmentation as an alternative to the cohesive element approach. This non-local damage model features a level-set function that defines the extent and severity of degradation and uses a length scale to limit the damage gradient. In terms of energy dissipated by fracture and mean fragment size, we find that the proposed model reproduces the rate-dependent observations of analytical approaches, cohesive element simulations, and experimental studies.

Lastly, the Thick Level-Set model is implemented in three dimensions to describe the dynamic failure of brittle media, such as the active material particles in the battery cathode during manufacturing. The proposed model matches expected behavior from physical experiments, analytical approaches, and numerical models, and mesh convergence is established. We find that the use of an asymmetrical damage model to represent tensile damage is important to producing the expected results for brittle fracture problems.

The impact of this work is that designers of lithium-ion battery components can employ the numerical methods presented herein to analyze the evolving electrode microstructure during manufacturing, operational, and extraordinary loadings. This allows for enhanced designs and manufacturing methods that advance the state of battery technology. Further, these numerical tools have applicability in a broad range of fields, from geotechnical analysis to ice-sheet modeling to armor design to hydraulic fracturing.

A New Method for Modeling Free Surface Flows and Fluid-structure Interaction with Ocean Applications

The computational modeling of ocean waves and ocean-faring devices poses numerous challenges. Among these are the need to stably and accurately represent both the fluid-fluid interface between water and air as well as the fluid-structure interfaces arising between solid devices and one or more fluids. As techniques are developed to stably and accurately balance the interactions between fluid and structural solvers at these boundaries, a similarly pressing challenge is the development of algorithms that are massively scalable and capable of performing large-scale three-dimensional simulations on reasonable time scales. This dissertation introduces two separate methods for approaching this problem, with the first focusing on the development of sophisticated fluid-fluid interface representations and the second focusing primarily on scalability and extensibility to higher-order methods.

We begin by introducing the narrow-band gradient-augmented level set method (GALSM) for incompressible multiphase Navier-Stokes flow. This is the first use of the high-order GALSM for a fluid flow application, and its reliability and accuracy in modeling ocean environments is tested extensively. The method demonstrates numerous advantages over the traditional level set method, among these a heightened conservation of fluid volume and the representation of subgrid structures.

Next, we present a finite-volume algorithm for solving the incompressible Euler equations in two and three dimensions in the presence of a flow-driven free surface and a dynamic rigid body. In this development, the chief concerns are efficiency, scalability, and extensibility (to higher-order and truly conservative methods). These priorities informed a number of important choices: The air phase is substituted by a pressure boundary condition in order to greatly reduce the size of the computational domain, a cut-cell finite-volume approach is chosen in order to minimize fluid volume loss and open the door to higher-order methods, and adaptive mesh refinement (AMR) is employed to focus computational effort and make large-scale 3D simulations possible. This algorithm is shown to produce robust and accurate results that are well-suited for the study of ocean waves and the development of wave energy conversion (WEC) devices.

A Search for a New Particle Decaying to Pairs of Weak Gauge Bosons with the ATLAS Detector

A search for new heavy resonances decaying to boson pairs (WZ, WW or ZZ) using 20.3 inverse femtobarns of proton-proton collision data at a center of mass energy of 8 TeV is presented. The data were recorded by the ATLAS detector at the Large Hadron Collider (LHC) in 2012. The analysis combines several search channels with the leptonic, semi-leptonic and fully hadronic final states. The diboson invariant mass spectrum is studied for local excesses above the Standard Model background prediction, and no significant excess is observed for the combined analysis. 95$\%$ confidence limits are set on the cross section times branching ratios for three signal models: an extended gauge model with a heavy W boson, a bulk Randall-Sundrum model with a spin-2 graviton, and a simplified model with a heavy vector triplet. Among the individual search channels, the fully-hadronic channel is predominantly presented where boson tagging technique and jet substructure cuts are used. Local excesses are found in the dijet mass distribution around 2 TeV, leading to a global significance of 2.5 standard deviations. This deviation from the Standard Model prediction results in many theory explanations, and the possibilities could be further explored using the LHC Run 2 data.

Bridging the Scale Gap from Leaf to Canopy in Biosphere-Atmosphere Gas and Particle Exchanges

Terrestrial ecosystems, occupying more than 25% of the Earth's surface, can serve as

`biological valves' in regulating the anthropogenic emissions of atmospheric aerosol

particles and greenhouse gases (GHGs) as responses to their surrounding environments.

While the signicance of quantifying the exchange rates of GHGs and atmospheric

aerosol particles between the terrestrial biosphere and the atmosphere is

hardly questioned in many scientic elds, the progress in improving model predictability,

data interpretation or the combination of the two remains impeded by

the lack of precise framework elucidating their dynamic transport processes over a

wide range of spatiotemporal scales. The diculty in developing prognostic modeling

tools to quantify the source or sink strength of these atmospheric substances

can be further magnied by the fact that the climate system is also sensitive to the

feedback from terrestrial ecosystems forming the so-called `feedback cycle'. Hence,

the emergent need is to reduce uncertainties when assessing this complex and dynamic

feedback cycle that is necessary to support the decisions of mitigation and

adaptation policies associated with human activities (e.g., anthropogenic emission

controls and land use managements) under current and future climate regimes.

With the goal to improve the predictions for the biosphere-atmosphere exchange

of biologically active gases and atmospheric aerosol particles, the main focus of this

dissertation is on revising and up-scaling the biotic and abiotic transport processes

from leaf to canopy scales. The validity of previous modeling studies in determining

iv

the exchange rate of gases and particles is evaluated with detailed descriptions of their

limitations. Mechanistic-based modeling approaches along with empirical studies

across dierent scales are employed to rene the mathematical descriptions of surface

conductance responsible for gas and particle exchanges as commonly adopted by all

operational models. Specically, how variation in horizontal leaf area density within

the vegetated medium, leaf size and leaf microroughness impact the aerodynamic attributes

and thereby the ultrane particle collection eciency at the leaf/branch scale

is explored using wind tunnel experiments with interpretations by a porous media

model and a scaling analysis. A multi-layered and size-resolved second-order closure

model combined with particle

uxes and concentration measurements within and

above a forest is used to explore the particle transport processes within the canopy

sub-layer and the partitioning of particle deposition onto canopy medium and forest

oor. For gases, a modeling framework accounting for the leaf-level boundary layer

eects on the stomatal pathway for gas exchange is proposed and combined with sap

ux measurements in a wind tunnel to assess how leaf-level transpiration varies with

increasing wind speed. How exogenous environmental conditions and endogenous

soil-root-stem-leaf hydraulic and eco-physiological properties impact the above- and

below-ground water dynamics in the soil-plant system and shape plant responses

to droughts is assessed by a porous media model that accommodates the transient

water

ow within the plant vascular system and is coupled with the aforementioned

leaf-level gas exchange model and soil-root interaction model. It should be noted

that tackling all aspects of potential issues causing uncertainties in forecasting the

feedback cycle between terrestrial ecosystem and the climate is unrealistic in a single

dissertation but further research questions and opportunities based on the foundation

derived from this dissertation are also brie

y discussed.