Extracting material response from simple mechanical tests on hardening-softening-hardening viscoplastic solids

Compliant foams are usually characterized by a wide range of desirable mechanical properties. These properties include viscoelasticity at different temperatures, energy absorption, recoverability under cyclic loading, impact resistance, and thermal, electrical, acoustic and radiation-resistance. Some foams contain nano-sized features and are used in small-scale devices. This implies that the characteristic dimensions of foams span multiple length scales, rendering modeling their mechanical properties difficult. Continuum mechanics-based models capture some salient experimental features like the linear elastic regime, followed by non-linear plateau stress regime. However, they lack mesostructural physical details. This makes them incapable of accurately predicting local peaks in stress and strain distributions, which significantly affect the deformation paths. Atomistic methods are capable of capturing the physical origins of deformation at smaller scales, but suffer from impractical computational intensity. Capturing deformation at the so-called meso-scale, which is capable of describing the phenomenon at a continuum level, but with some physical insights, requires developing new theoretical approaches.

A fundamental question that motivates the modeling of foams is ‘how to extract the intrinsic material response from simple mechanical test data, such as stress vs. strain response?’ A 3D model was developed to simulate the mechanical response of foam-type materials. The novelty of this model includes unique features such as the hardening-softening-hardening material response, strain rate-dependence, and plastically compressible solids with plastic non-normality. Suggestive links from atomistic simulations of foams were borrowed to formulate a physically informed hardening material input function. Motivated by a model that qualitatively captured the response of foam-type vertically aligned carbon nanotube (VACNT) pillars under uniaxial compression [2011,“Analysis of Uniaxial Compression of Vertically Aligned Carbon Nanotubes,” J. Mech.Phys. Solids, 59, pp. 2227–2237, Erratum 60, 1753–1756 (2012)], the property space exploration was advanced to three types of simple mechanical tests: 1) uniaxial compression, 2) uniaxial tension, and 3) nanoindentation with a conical and a flat-punch tip. The simulations attempt to explain some of the salient features in experimental data, like
1) The initial linear elastic response.
2) One or more nonlinear instabilities, yielding, and hardening.

The model-inherent relationships between the material properties and the overall stress-strain behavior were validated against the available experimental data. The material properties include the gradient in stiffness along the height, plastic and elastic compressibility, and hardening. Each of these tests was evaluated in terms of their efficiency in extracting material properties. The uniaxial simulation results proved to be a combination of structural and material influences. Out of all deformation paths, flat-punch indentation proved to be superior since it is the most sensitive in capturing the material properties.

On the transport properties of fluid-particle flow

The hydrodynamic forces acting on a solid particle in a viscous, incompressible fluid medium at low Reynolds number flow is investigated mathematically as a prerequisite to the understanding of transport processes in two-phase flow involving solid particles and fluid. Viscous interaction between a small number of spherical particles and continuous solid boundaries as well as fluid interface are analyzed under a “point-force” approximation. Non-spherical and elastic spherical particles in a simple shear flow area are then considered. Non-steady motion of a spherical particle is briefly touched upon to illustrate the transient effect of particle motion.

A macroscopic continuum description of particle-fluid flow is formulated in terms of spatial averages yielding a set of particle continuum and bulk fluid equations. Phenomenological formulas describing the transport processes in a fluid medium are extended to cases where the volume concentration of solid particles is sufficiently high to exert an important influence. Hydrodynamic forces acting on a spherical solid particle in such a system, e.g. drag, torque, rotational coupling force, and viscous collision force between streams of different sized particles moving relative to each other are obtained. Phenomenological constants, such as the shear viscosity coefficient, and the diffusion coefficient of the bulk fluid, are found as a function of the material properties of the constituents of the two-phase system and the volume concentration of solid. For transient heat conduction phenomena, it is found that the introduction of a complex conductivity for the bulk fluid permits a simple mathematical description of this otherwise complicated process. The rate of heat transfer between particle continuum and bulk fluid is also investigated by means of an Oseen-type approximation to the energy equation.

Diffusion in glassy polymers

Fluid diffusion in glassy polymers proceeds in ways that are not explained by the standard diffusion model. Although the reasons for the anomalous effects are not known, much of the observed behavior is attributed to the long times that polymers below their glass transition temperature take to adjust to changes in their condition. The slow internal relaxations of the polymer chains ensure that the material properties are history-dependent, and also allow both local inhomogeneities and differential swelling to occur. Two models are developed in this thesis with the intent of accounting for these effects in the diffusion process.

In Part I, a model is developed to account for both the history dependence of the glassy polymer, and the dual sorption which occurs when gas molecules are immobilized by the local heterogeneities. A preliminary study of a special case of this model is conducted, showing the existence of travelling wave solutions and using perturbation techniques to investigate the effect of generalized diffusion mechanisms on their form. An integral averaging method is used to estimate the penetrant front position.

In Part II, a model is developed for particle diffusion along with displacements in isotropic viscoelastic materials. The nonlinear dependence of the materials on the fluid concentration is taken into account, while pure displacements are assumed to remain in the range of linear viscoelasticity. A fairly general model is obtained for three-dimensional irrotational movements, with the development of the model being based on the assumptions of irreversible thermodynamics. With the help of some dimensional analysis, this model is simplified to a version which is proposed to be studied for Case II behavior.

Analysis and optimization of stress wave propagation in two-dimensional granular crystals with defects

Granular crystals are compact periodic assemblies of elastic particles in Hertzian contact whose dynamic response can be tuned from strongly nonlinear to linear by the addition of a static precompression force. This unique feature allows for a wide range of studies that include the investigation of new fundamental nonlinear phenomena in discrete systems such as solitary waves, shock waves, discrete breathers and other defect modes. In the absence of precompression, a particularly interesting property of these systems is their ability to support the formation and propagation of spatially localized soliton-like waves with highly tunable properties. The wealth of parameters one can modify (particle size, geometry and material properties, periodicity of the crystal, presence of a static force, type of excitation, etc.) makes them ideal candidates for the design of new materials for practical applications. This thesis describes several ways to optimally control and tailor the propagation of stress waves in granular crystals through the use of heterogeneities (interstitial defect particles and material heterogeneities) in otherwise perfectly ordered systems. We focus on uncompressed two-dimensional granular crystals with interstitial spherical intruders and composite hexagonal packings and study their dynamic response using a combination of experimental, numerical and analytical techniques. We first investigate the interaction of defect particles with a solitary wave and utilize this fundamental knowledge in the optimal design of novel composite wave guides, shock or vibration absorbers obtained using gradient-based optimization methods.

Aseismic deformation in subduction megathrusts : central Andes and north-east Japan

We aim to characterize fault slip behavior during all stages of the seismic cycle in subduction megathrust environments with the eventual goal of understanding temporal and spatial variations of fault zone rheology, and to infer possible causal relationships between inter-, co- and post-seismic slip, as well as implications for earthquake and tsunami hazard. In particular we focus on analyzing aseismic deformation occurring during inter-seismic and post-seismic periods of the seismic cycle. We approach the problem using both Bayesian and optimization techniques. The Bayesian approach allows us to completely characterize the model parameter space by searching a posteriori estimates of the range of allowable models, to easily implement any kind of physically plausible a priori information and to perform the inversion without regularization other than that imposed by the parameterization of the model. However, the Bayesian approach computational expensive and not currently viable for quick response scenarios. Therefore, we also pursue improvements in the optimization inference scheme. We present a novel, robust and yet simple regularization technique that allows us to infer robust and somewhat more detailed models of slip on faults. We apply such methodologies, using simple quasi-static elastic models, to perform studies of inter- seismic deformation in the Central Andes subduction zone, and post-seismic deformation induced by the occurrence of the 2011 Mw 9.0 Tohoku-Oki earthquake in Japan. For the Central Andes, we present estimates of apparent coupling probability of the subduction interface and analyze its relationship to past earthquakes in the region. For Japan, we infer high spatial variability in material properties of the megathrust offshore Tohoku. We discuss the potential for a large earthquake just south of the Tohoku-Oki earthquake where our inferences suggest dominantly aseismic behavior.

Planar reflection of gaseous detonations

Pipes containing flammable gaseous mixtures may be subjected to internal detonation. When the detonation normally impinges on a closed end, a reflected shock wave is created to bring the flow back to rest. This study built on the work of Karnesky (2010) and examined deformation of thin-walled stainless steel tubes subjected to internal reflected gaseous detonations. A ripple pattern was observed in the tube wall for certain fill pressures, and a criterion was developed that predicted when the ripple pattern would form. A two-dimensional finite element analysis was performed using Johnson-Cook material properties; the pressure loading created by reflected gaseous detonations was accounted for with a previously developed pressure model. The residual plastic strain between experiments and computations was in good agreement.

During the examination of detonation-driven deformation, discrepancies were discovered in our understanding of reflected gaseous detonation behavior. Previous models did not accurately describe the nature of the reflected shock wave, which motivated further experiments in a detonation tube with optical access. Pressure sensors and schlieren images were used to examine reflected shock behavior, and it was determined that the discrepancies were related to the reaction zone thickness extant behind the detonation front. During these experiments reflected shock bifurcation did not appear to occur, but the unfocused visualization system made certainty impossible. This prompted construction of a focused schlieren system that investigated possible shock wave-boundary layer interaction, and heat-flux gauges analyzed the boundary layer behind the detonation front. Using these data with an analytical boundary layer solution, it was determined that the strong thermal boundary layer present behind the detonation front inhibits the development of reflected shock wave bifurcation.

Three-dimensional nonlinear inelastic analysis of steel moment-frame buildings damaged by earthquake excitations

The Northridge earthquake of January 17, 1994, highlighted the two previously known problems of premature fracturing of connections and the damaging capabilities of near-source ground motion pulses. Large ground motions had not been experienced in a city with tall steel moment-frame buildings before. Some steel buildings exhibited fracture of welded connections or other types of structural degradation.

A sophisticated three-dimensional nonlinear inelastic program is developed that can accurately model many nonlinear properties commonly ignored or approximated in other programs. The program can assess and predict severely inelastic response of steel buildings due to strong ground motions, including collapse.

Three-dimensional fiber and segment discretization of elements is presented in this work. This element and its two-dimensional counterpart are capable of modeling various geometric and material nonlinearities such as moment amplification, spread of plasticity and connection fracture. In addition to introducing a three-dimensional element discretization, this work presents three-dimensional constraints that limit the number of equations required to solve various three-dimensional problems consisting of intersecting planar frames.

Two buildings damaged in the Northridge earthquake are investigated to verify the ability of the program to match the level of response and the extent and location of damage measured. The program is used to predict response of larger near-source ground motions using the properties determined from the matched response.

A third building is studied to assess three-dimensional effects on a realistic irregular building in the inelastic range of response considering earthquake directivity. Damage levels are observed to be significantly affected by directivity and torsional response.

Several strong recorded ground motions clearly exceed code-based levels. Properly designed buildings can have drifts exceeding code specified levels due to these ground motions. The strongest ground motions caused collapse if fracture was included in the model. Near-source ground displacement pulses can cause columns to yield prior to weaker-designed beams. Damage in tall buildings correlates better with peak-to-peak displacements than with peak-to-peak accelerations.

Dynamic response of tall buildings shows that higher mode response can cause more damage than first mode response. Leaking of energy between modes in conjunction with damage can cause torsional behavior that is not anticipated.

Various response parameters are used for all three buildings to determine what correlations can be made for inelastic building response. Damage levels can be dramatically different based on the inelastic model used. Damage does not correlate well with several common response parameters.

Realistic modeling of material properties and structural behavior is of great value for understanding the performance of tall buildings due to earthquake excitations.

High fidelity probe and mitigation of mirror thermal fluctuations

Thermal noise arising from mechanical loss in high reflective dielectric coatings is a significant source of noise in precision optical measurements. In particular, Advanced LIGO, a large scale interferometer aiming to observed gravitational wave, is expected to be limited by coating thermal noise in the most sensitive region around 30–300 Hz. Various theoretical calculations for predicting coating Brownian noise have been proposed. However, due to the relatively limited knowledge of the coating material properties, an accurate approximation of the noise cannot be achieved. A testbed that can directly observed coating thermal noise close to Advanced LIGO band will serve as an indispensable tool to verify the calculations, study material properties of the coating, and estimate the detector’s performance.

This dissertation reports a setup that has sensitivity to observe wide band (10Hz to 1kHz) thermal noise from fused silica/tantala coating at room temperature from fixed-spacer Fabry–Perot cavities. Important fundamental noises and technical noises associated with the setup are discussed. The coating loss obtained from the measurement agrees with results reported in the literature. The setup serves as a testbed to study thermal noise in high reflective mirrors from different materials. One example is a heterostructure of Al_xGa_1−xAs (AlGaAs). An optimized design to minimize thermo–optic noise in the coating is proposed and discussed in this work.

Dynamic rupture simulation integrated with earthquake observations

Dynamic rupture simulations are unique in their contributions to the study of earthquake physics. The current rapid development of dynamic rupture simulations poses several new questions: Do the simulations reflect the real world? Do the simulations have predictive power? Which one should we believe when the simulations disagree? This thesis illustrates how integration with observations can help address these questions and reduce the effects of non-uniqueness of both dynamic rupture simulations and kinematic inversion problems. Dynamic rupture simulations with observational constraints can effectively identify non-physical features inferred from observations. Moreover, the integrative technique can also provide more physical insights into the mechanisms of earthquakes. This thesis demonstrates two examples of such kinds of integration: dynamic rupture simulations of the M_w 9.0 2011 Tohoku-Oki earthquake and of earthquake ruptures in damaged fault zones:

(1) We develop simulations of the Tohoku-Oki earthquake based on a variety of observations and minimum assumptions of model parameters. The simulations provide realistic estimations of stress drop and fracture energy of the region and explain the physical mechanisms of high-frequency radiation in the deep region. We also find that the overridding subduction wedge contributes significantly to the up-dip rupture propagation and large final slip in the shallow region. Such findings are also applicable to other megathrust earthquakes.

(2) Damaged fault zones are usually found around natural faults, but their effects on earthquake ruptures have been largely unknown. We simulate earthquake ruptures in damaged fault zones with material properties constrained by seismic and geological observations. We show that reflected waves in fault zones are effective at generating pulse-like ruptures and head waves tend to accelerate and decelerate rupture speeds. These mechanisms are robust in natural fault zones with large attenuation and off-fault plasticity. Moreover, earthquakes in damaged fault zones can propagate at super-Rayleigh speeds that are unstable in homogeneous media. Supershear transitions in fault zones do not require large fault stresses. In the end, we present observations in the Big Bear region, where variability of rupture speeds of small earthquakes correlates with the laterally variable materials in a damaged fault zone.

Methods for melting temperature calculation

Melting temperature calculation has important applications in the theoretical study of phase diagrams and computational materials screenings. In this thesis, we present two new methods, i.e., the improved Widom's particle insertion method and the small-cell coexistence method, which we developed in order to capture melting temperatures both accurately and quickly.

We propose a scheme that drastically improves the efficiency of Widom's particle insertion method by efficiently sampling cavities while calculating the integrals providing the chemical potentials of a physical system. This idea enables us to calculate chemical potentials of liquids directly from first-principles without the help of any reference system, which is necessary in the commonly used thermodynamic integration method. As an example, we apply our scheme, combined with the density functional formalism, to the calculation of the chemical potential of liquid copper. The calculated chemical potential is further used to locate the melting temperature. The calculated results closely agree with experiments.

We propose the small-cell coexistence method based on the statistical analysis of small-size coexistence MD simulations. It eliminates the risk of a metastable superheated solid in the fast-heating method, while also significantly reducing the computer cost relative to the traditional large-scale coexistence method. Using empirical potentials, we validate the method and systematically study the finite-size effect on the calculated melting points. The method converges to the exact result in the limit of a large system size. An accuracy within 100 K in melting temperature is usually achieved when the simulation contains more than 100 atoms. DFT examples of Tantalum, high-pressure Sodium, and ionic material NaCl are shown to demonstrate the accuracy and flexibility of the method in its practical applications. The method serves as a promising approach for large-scale automated material screening in which the melting temperature is a design criterion.

We present in detail two examples of refractory materials. First, we demonstrate how key material properties that provide guidance in the design of refractory materials can be accurately determined via ab initio thermodynamic calculations in conjunction with experimental techniques based on synchrotron X-ray diffraction and thermal analysis under laser-heated aerodynamic levitation. The properties considered include melting point, heat of fusion, heat capacity, thermal expansion coefficients, thermal stability, and sublattice disordering, as illustrated in a motivating example of lanthanum zirconate (La₂Zr₂O₇). The close agreement with experiment in the known but structurally complex compound La₂Zr₂O₇ provides good indication that the computation methods described can be used within a computational screening framework to identify novel refractory materials. Second, we report an extensive investigation into the melting temperatures of the Hf-C and Hf-Ta-C systems using ab initio calculations. With melting points above 4000 K, hafnium carbide (HfC) and tantalum carbide (TaC) are among the most refractory binary compounds known to date. Their mixture, with a general formula Ta_xHf_1-xC_y, is known to have a melting point of 4215 K at the composition Ta₄HfC₅, which has long been considered as the highest melting temperature for any solid. Very few measurements of melting point in tantalum and hafnium carbides have been documented, because of the obvious experimental difficulties at extreme temperatures. The investigation lets us identify three major chemical factors that contribute to the high melting temperatures. Based on these three factors, we propose and explore a new class of materials, which, according to our ab initio calculations, may possess even higher melting temperatures than Ta-Hf-C. This example also demonstrates the feasibility of materials screening and discovery via ab initio calculations for the optimization of "higher-level" properties whose determination requires extensive sampling of atomic configuration space.

MEMS for Diabetic Retinopathy

As the worldwide prevalence of diabetes mellitus continues to increase, diabetic retinopathy remains the leading cause of visual impairment and blindness in many developed countries. Between 32 to 40 percent of about 246 million people with diabetes develop diabetic retinopathy. Approximately 4.1 million American adults 40 years and older are affected by diabetic retinopathy. This glucose-induced microvascular disease progressively damages the tiny blood vessels that nourish the retina, the light-sensitive tissue at the back of the eye, leading to retinal ischemia (i.e., inadequate blood flow), retinal hypoxia (i.e., oxygen deprivation), and retinal nerve cell degeneration or death. It is a most serious sight-threatening complication of diabetes, resulting in significant irreversible vision loss, and even total blindness.

Unfortunately, although current treatments of diabetic retinopathy (i.e., laser therapy, vitrectomy surgery and anti-VEGF therapy) can reduce vision loss, they only slow down but cannot stop the degradation of the retina. Patients require repeated treatment to protect their sight. The current treatments also have significant drawbacks. Laser therapy is focused on preserving the macula, the area of the retina that is responsible for sharp, clear, central vision, by sacrificing the peripheral retina since there is only limited oxygen supply. Therefore, laser therapy results in a constricted peripheral visual field, reduced color vision, delayed dark adaptation, and weakened night vision. Vitrectomy surgery increases the risk of neovascular glaucoma, another devastating ocular disease, characterized by the proliferation of fibrovascular tissue in the anterior chamber angle. Anti-VEGF agents have potential adverse effects, and currently there is insufficient evidence to recommend their routine use.

In this work, for the first time, a paradigm shift in the treatment of diabetic retinopathy is proposed: providing localized, supplemental oxygen to the ischemic tissue via an implantable MEMS device. The retinal architecture (e.g., thickness, cell densities, layered structure, etc.) of the rabbit eye exposed to ischemic hypoxic injuries was well preserved after targeted oxygen delivery to the hypoxic tissue, showing that the use of an external source of oxygen could improve the retinal oxygenation and prevent the progression of the ischemic cascade.

The proposed MEMS device transports oxygen from an oxygen-rich space to the oxygen-deficient vitreous, the gel-like fluid that fills the inside of the eye, and then to the ischemic retina. This oxygen transport process is purely passive and completely driven by the gradient of oxygen partial pressure (pO₂). Two types of devices were designed. For the first type, the oxygen-rich space is underneath the conjunctiva, a membrane covering the sclera (white part of the eye), beneath the eyelids and highly permeable to oxygen in the atmosphere when the eye is open. Therefore, sub-conjunctival pO₂ is very high during the daytime. For the second type, the oxygen-rich space is inside the device since pure oxygen is needle-injected into the device on a regular basis.

To prevent too fast or too slow permeation of oxygen through the device that is made of parylene and silicone (two widely used biocompatible polymers in medical devices), the material properties of the hybrid parylene/silicone were investigated, including mechanical behaviors, permeation rates, and adhesive forces. Then the thicknesses of parylene and silicone became important design parameters that were fine-tuned to reach the optimal oxygen permeation rate.

The passive MEMS oxygen transporter devices were designed, built, and tested in both bench-top artificial eye models and in-vitro porcine cadaver eyes. The 3D unsteady saccade-induced laminar flow of water inside the eye model was modeled by computational fluid dynamics to study the convective transport of oxygen inside the eye induced by saccade (rapid eye movement). The saccade-enhanced transport effect was also demonstrated experimentally. Acute in-vivo animal experiments were performed in rabbits and dogs to verify the surgical procedure and the device functionality. Various hypotheses were confirmed both experimentally and computationally, suggesting that both the two types of devices are very promising to cure diabetic retinopathy. The chronic implantation of devices in ischemic dog eyes is still underway.

The proposed MEMS oxygen transporter devices can be also applied to treat other ocular and systemic diseases accompanied by retinal ischemia, such as central retinal artery occlusion, carotid artery disease, and some form of glaucoma.

Fabrication, Characterization, And Deformation of 3D Structural Meta-Materials

Current technological advances in fabrication methods have provided pathways to creating architected structural meta-materials similar to those found in natural organisms that are structurally robust and lightweight, such as diatoms. Structural meta-materials are materials with mechanical properties that are determined by material properties at various length scales, which range from the material microstructure (nm) to the macro-scale architecture (μm – mm). It is now possible to exploit material size effect, which emerge at the nanometer length scale, as well as structural effects to tune the material properties and failure mechanisms of small-scale cellular solids, such as nanolattices. This work demonstrates the fabrication and mechanical properties of 3-dimensional hollow nanolattices in both tension and compression. Hollow gold nanolattices loaded in uniaxial compression demonstrate that strength and stiffness vary as a function of geometry and tube wall thickness. Structural effects were explored by increasing the unit cell angle from 30° to 60° while keeping all other parameters constant; material size effects were probed by varying the tube wall thickness, t, from 200nm to 635nm, at a constant relative density and grain size. In-situ uniaxial compression experiments reveal an order-of-magnitude increase in yield stress and modulus in nanolattices with greater lattice angles, and a 150% increase in the yield strength without a concomitant change in modulus in thicker-walled nanolattices for fixed lattice angles. These results imply that independent control of structural and material size effects enables tunability of mechanical properties of 3-dimensional architected meta-materials and highlight the importance of material, geometric, and microstructural effects in small-scale mechanics. This work also explores the flaw tolerance of 3D hollow-tube alumina kagome nanolattices with and without pre-fabricated notches, both in experiment and simulation. Experiments demonstrate that the hollow kagome nanolattices in uniaxial tension always fail at the same load when the ratio of notch length (a) to sample width (w) is no greater than 1/3, with no correlation between failure occurring at or away from the notch. For notches with (a/w) > 1/3, the samples fail at lower peak loads and this is attributed to the increased compliance as fewer unit cells span the un-notched region. Finite element simulations of the kagome tension samples show that the failure is governed by tensile loading for (a/w) < 1/3 but as (a/w) increases, bending begins to play a significant role in the failure. This work explores the flaw sensitivity of hollow alumina kagome nanolattices in tension, using experiments and simulations, and demonstrates that the discrete-continuum duality of architected structural meta-materials gives rise to their flaw insensitivity even when made entirely of intrinsically brittle materials.

Cryogenic Silicon Optical Reference Cavities

Thermodynamical fluctuations in temperature and position exist in every physical system, and show up as a fundamental noise limit whenever we choose to measure some quantity in a laboratory environment. Thermodynamical fluctuations in the position of the atoms in the dielectric coatings on the mirrors for optical cavities at the forefront of precision metrology (e.g., LIGO, the cavities which probe atomic transitions to define the second) are a current limiting noise source for these experiments, and anything which involves locking a laser to an optical cavity. These thermodynamic noise sources scale physical geometry of experiment, material properties (such as mechanical loss in our dielectric coatings), and temperature. The temperature scaling provides a natural motivation to move to lower temperatures, with a potential huge benefit for redesigning a room temperature experiment which is limited by thermal noise for cryogenic operation.

We design, build, and characterize a pair of linear Fabry-Perot cavities to explore limitations to ultra low noise laser stabilization experiments at cryogenic temperatures. We use silicon as the primary material for the cavity and mirrors, due to a zero crossing in its linear coefficient of thermal expansion (CTE) at 123 K, and other desirable material properties. We use silica tantala coatings, which are currently the best for making high finesse low noise cavities at room temperature. The material properties of these coating materials (which set the thermal noise levels) are relatively unknown at cryogenic temperatures, which motivates us to study them at these temperatures. We were not able to measure any thermal noise source with our experiment due to excess noise. In this work we analyze the design and performance of the cavities, and recommend a design shift from mid length cavities to short cavities in order to facilitate a direct measurement of cryogenic coating noise.

In addition, we measure the cavities (frequency dependent) photo-thermal response. This can help characterize thermooptic noise in the coatings, which is poorly understood at cryogenic temperatures. We also explore the feasibility of using the cavity to do macroscopic quantum optomechanics such as ground state cooling.

Using Earth Deformation Caused by Surface Mass Loading to Constrain the Elastic Structure of the Crust and Mantle

Surface mass loads come in many different varieties, including the oceans, atmosphere, rivers, lakes, glaciers, ice caps, and snow fields. The loads migrate over Earth's surface on time scales that range from less than a day to many thousand years. The weights of the shifting loads exert normal forces on Earth's surface. Since the Earth is not perfectly rigid, the applied pressure deforms the shape of the solid Earth in a manner controlled by the material properties of Earth's interior. One of the most prominent types of surface mass loading, ocean tidal loading (OTL), comes from the periodic rise and fall in sea-surface height due to the gravitational influence of celestial objects, such as the moon and sun. Depending on geographic location, the surface displacements induced by OTL typically range from millimeters to several centimeters in amplitude, which may be inferred from Global Navigation and Satellite System (GNSS) measurements with sub-millimeter precision. Spatiotemporal characteristics of observed OTL-induced surface displacements may therefore be exploited to probe Earth structure. In this thesis, I present descriptions of contemporary observational and modeling techniques used to explore Earth's deformation response to OTL and other varieties of surface mass loading. With the aim to extract information about Earth's density and elastic structure from observations of the response to OTL, I investigate the sensitivity of OTL-induced surface displacements to perturbations in the material structure. As a case study, I compute and compare the observed and predicted OTL-induced surface displacements for a network of GNSS receivers across South America. The residuals in three distinct and dominant tidal bands are sub-millimeter in amplitude, indicating that modern ocean-tide and elastic-Earth models well predict the observed displacement response in that region. Nevertheless, the sub-millimeter residuals exhibit regional spatial coherency that cannot be explained entirely by random observational uncertainties and that suggests deficiencies in the forward-model assumptions. In particular, the discrepancies may reveal sensitivities to deviations from spherically symmetric, non-rotating, elastic, and isotropic (SNREI) Earth structure due to the presence of the South American craton.

Dynamics of Granular Crystals with Elastic-Plastic Contacts

We study the behavior of granular crystals subjected to impact loading that creates plastic deformation at the contacts between constituent particles. Granular crystals are highly periodic arrangements of spherical particles, arranged into densely packed structures resembling crystals. This special class of granular materials has been shown to have unique dynamics with suggested applications in impact protection. However, previous work has focused on very low amplitude impacts where every contact point can be described using the Hertzian contact law, valid only for purely elastic deformation. In this thesis, we extend previous investigation of the dynamics of granular crystals to significantly higher impact energies more suitable for the majority of applications. Additionally, we demonstrate new properties specific to elastic-plastic granular crystals and discuss their potential applications as well. We first develop a new contact law to describe the interaction between particles for large amplitude compression of elastic-plastic spherical particles including a formulation for strain-rate dependent plasticity. We numerically and experimentally demonstrate the applicability of this contact law to a variety of materials typically used in granular crystals. We then extend our investigation to one-dimensional chains of elastic-plastic particles, including chains of alternating dissimilar materials. We show that, using the new elastic-plastic contact law, we can predict the speed at which impact waves with plastic dissipation propagate based on the material properties of the constituent particles. Finally, we experimentally and numerically investigate the dynamics of two-dimensional and three-dimensional granular crystals with elastic-plastic contacts. We first show that the predicted wave speeds for 1D granular crystals can be extended to 2D and 3D materials. We then investigate the behavior of waves propagating across oblique interfaces of dissimilar particles. We show that the character of the refracted wave can be predicted using an analog to Snell's law for elastic-plastic granular crystals and ultimately show how it can be used to design impact guiding "lenses" for mitigation applications.