Modeling and analysis of hysteretic structural behavior

For damaging response, the force-displacement relationship of a structure is highly nonlinear and history-dependent. For satisfactory analysis of such behavior, it is important to be able to characterize and to model the phenomenon of hysteresis accurately. A number of models have been proposed for response studies of hysteretic structures, some of which are examined in detail in this thesis. There are two popular classes of models used in the analysis of curvilinear hysteretic systems. The first is of the distributed element or assemblage type, which models the physical behavior of the system by using well-known building blocks. The second class of models is of the differential equation type, which is based on the introduction of an extra variable to describe the history dependence of the system.

Owing to their mathematical simplicity, the latter models have been used extensively for various applications in structural dynamics, most notably in the estimation of the response statistics of hysteretic systems subjected to stochastic excitation. But the fundamental characteristics of these models are still not clearly understood. A response analysis of systems using both the Distributed Element model and the differential equation model when subjected to a variety of quasi-static and dynamic loading conditions leads to the following conclusion: Caution must be exercised when employing the models belonging to the second class in structural response studies as they can produce misleading results.

The Massing's hypothesis, originally proposed for steady-state loading, can be extended to general transient loading as well, leading to considerable simplification in the analysis of the Distributed Element models. A simple, nonparametric identification technique is also outlined, by means of which an optimal model representation involving one additional state variable is determined for hysteretic systems.

On the behavior of pliable plate dynamics in wind : application to vertical axis wind turbines

Numerous studies have shown that flexible materials improve resilience and durability of a structure. Several studies have investigated the behavior of elastic plates under the influence of a free stream, such as studies of the fluttering flag and others of shape reconfiguration, due to a free stream.

The principle engineering contribution of this thesis is the design and development of a vertical axis wind turbine that features pliable blades which undergo various modes of behavior, ultimately leading to rotational propulsion of the turbine. The wind turbine design was tested in a wind tunnel and at the Caltech Laboratory for Optimized Wind Energy. Ultimately, the flexible blade vertical axis wind turbine proved to be an effective way of harnessing the power of the wind.

In addition, this body of work builds on the current knowledge of elastic cantilever plates in a free stream flow by investigating the inverted flag. While previous studies have focused on the fluid structure interaction of a free stream on elastic cantilever plates, none had studied the plate configuration where the trailing edge was clamped, leaving the leading edge free to move. Furthermore, the studies presented in this thesis establish the geometric boundaries of where the large-amplitude flapping occurs.

Effect of pressure on mechanical behavior of filled elastomers

The Young's modulus, stress-strain curves, and failure properties of glass bead-filled EPDM vulcanizates were studied under superposed hydrostatic pressure. The glass bead-filled EPDM was employed as a representation of composite systems, and the hydrostatic pressure controls the filler-elastomer separation under deformation. This separation shows up as a volume change of the system, and its infuence is reflected in the mechanical behavior as a reinforcing effect of variable degree.

The strain energy stored in the composite system in simple tension was calculated by introducing a model which is described as a cylindrical block of elastomer with two half spheres of filler on each end with their centers on the axis of the cylinder. In the derivation of the strain energy, assumptions were made to obtain the strain distribution in the model, and strain energy-strain relation for the elastomer was also assumed. The derivation was carried out for the case of no filler-elastomer separation and was modified to include the case of filler-elastomer separation.

The resulting strain energy, as a function of stretch ratio and volume of the system, was used to obtain stress-strain curves and volume change-strain curves of composite systems under superposed hydrostatic pressure.

Changes in the force and the lateral dimension of a ring specimen were measured as it was stretched axially under a superposed hydrostatic pressure in order to calculate the mechanical properties mentioned above. A tensile tester was used which is capable of sealing the whole system to carry out a measurement under pressure. A thickness measuring device, based on the Hall effect, was built for the measurement of changes in the lateral dimension of a specimen.

The theoretical and experimental results of Young's modulus and stress-strain curves were compared and showed fairly good agreement.

The failure data were discussed in terms of failure surfaces, and it was concluded that a failure surface of the glass-bead-filled EPDM consists of two cones.

Magnetic behavior of basic iron(III) compounds. I. Magnetic behavior of the basic iron sulphates and basic iron chromate. II. Magnetic behavior of delta ferric oxide hydroxide

I. The thermomagnetic behavior and infrared spectroscopic features of KFe₃(SO₄)₂(OH)₆ (jarosite), (H₃O)Fe₃(SO₄)₂ (OH)₆ (hydronium jarosite), KFe₃(CrO₄)₂ (OH)₆, Fe(OH)SO₄ (basic iron sulfate), and Fe(OH)CrO₄ (basic iron chromate) are reported. Fe(OH)CrO₄ and KFe₃(CrO₄)₂ (OH)₆ are shown to be weak ferro magnets with Curie temperatures of 73 and 71 °K, respectively. This unusual magnetic behavior is rationalized in terms of the ionic spin configurations of the phases. Exchange coupling through chromate bridging groups is shown to be weak.

II. The magnetic behavior and the influence of preparative history on the magnetic behavior of δFeO(OH) is reported. δFeO(OH) is shown to be a fine-particulate, uniaxial, magnetic species. Magnetization data for this species are shown to be consistent with the existence of magnetically inactive layers surrounding magnetic particles.

High pressure states in condensed matter: I. High pressure behavior of the iron-sulphur system with applications to the earth's core. II. Empirical equation of state for organic compounds at high pressures

Part I:

The earth's core is generally accepted to be composed primarily of iron, with an admixture of other elements. Because the outer core is observed not to transmit shear waves at seismic frequencies, it is known to be liquid or primarily liquid. A new equation of state is presented for liquid iron, in the form of parameters for the 4th order Birch-Murnaghan and Mie-Grüneisen equations of state. The parameters were constrained by a set of values for numerous properties compiled from the literature. A detailed theoretical model is used to constrain the P-T behavior of the heat capacity, based on recent advances in the understanding of the interatomic potentials for transition metals. At the reference pressure of 10⁵ Pa and temperature of 1811 K (the normal melting point of Fe), the parameters are: ρ = 7037 kg/m³, K_S0 = 110 GPa, K_S' = 4.53, K_S" = -.0337 GPa-1, and γ = 2.8, with γ α ρ^-1.17. Comparison of the properties predicted by this model with the earth model PREM indicates that the outer core is 8 to 10 % less dense than pure liquid Fe at the same conditions. The inner core is also found to be 3 to 5% less dense than pure liquid Fe, supporting the idea of a partially molten inner core. The density deficit of the outer core implies that the elements dissolved in the liquid Fe are predominantly of lower atomic weight than Fe. Of the candidate light elements favored by researchers, only sulfur readily dissolves into Fe at low pressure, which means that this element was almost certainly concentrated in the core at early times. New melting data are presented for FeS and FeS₂ which indicate that the FeS₂ is the S-hearing liquidus solid phase at inner core pressures. Consideration of the requirement that the inner core boundary be observable by seismological means and the freezing behavior of solutions leads to the possibility that the outer core may contain a significant fraction of solid material. It is found that convection in the outer core is not hindered if the solid particles are entrained in the fluid flow. This model for a core of Fe and S admits temperatures in the range 3450K to 4200K at the top of the core. An all liquid Fe-S outer core would require a temperature of about 4900 K at the top of the core.

Part II.

The abundance of uses for organic compounds in the modern world results in many applications in which these materials are subjected to high pressures. This leads to the desire to be able to describe the behavior of these materials under such conditions. Unfortunately, the number of compounds is much greater than the number of experimental data available for many of the important properties. In the past, one approach that has worked well is the calculation of appropriate properties by summing the contributions from the organic functional groups making up molecules of the compounds in question. A new set of group contributions for the molar volume, volume thermal expansivity, heat capacity, and the Rao function is presented for functional groups containing C, H, and O. This set is, in most cases, limited in application to low molecular liquids. A new technique for the calculation of the pressure derivative of the bulk modulus is also presented. Comparison with data indicates that the presented technique works very well for most low molecular hydrocarbon liquids and somewhat less well for oxygen-bearing compounds. A similar comparison of previous results for polymers indicates that the existing tabulations of group contributions for this class of materials is in need of revision. There is also evidence that the Rao function contributions for polymers and low molecular compounds are somewhat different.

Collective behavior of asperities as a model for friction and adhesion

Understanding friction and adhesion in static and sliding contact of surfaces is important in numerous physical phenomena and technological applications. Most surfaces are rough at the microscale, and thus the real area of contact is only a fraction of the nominal area. The macroscopic frictional and adhesive response is determined by the collective behavior of the population of evolving and interacting microscopic contacts. This collective behavior can be very different from the behavior of individual contacts. It is thus important to understand how the macroscopic response emerges from the microscopic one. In this thesis, we develop a theoretical and computational framework to study the collective behavior. Our philosophy is to assume a simple behavior of a single asperity and study the collective response of an ensemble. Our work bridges the existing well-developed studies of single asperities with phenomenological laws that describe macroscopic rate-and-state behavior of frictional interfaces. We find that many aspects of the macroscopic behavior are robust with respect to the microscopic response. This explains why qualitatively similar frictional features are seen for a diverse range of materials. We first show that the collective response of an ensemble of one-dimensional independent viscoelastic elements interacting through a mean field reproduces many qualitative features of static and sliding friction evolution. The resulting macroscopic behavior is different from the microscopic one: for example, even if each contact is velocity-strengthening, the macroscopic behavior can be velocity-weakening. The framework is then extended to incorporate three-dimensional rough surfaces, long- range elastic interactions between contacts, and time-dependent material behaviors such as viscoelasticity and viscoplasticity. Interestingly, the mean field behavior dominates and the elastic interactions, though important from a quantitative perspective, do not change the qualitative macroscopic response. Finally, we examine the effect of adhesion on the frictional response as well as develop a force threshold model for adhesion and mode I interfacial cracks.

Establishing the C. elegans uterine seam cell (utse) as a novel model for studying cell behavior

The molecular inputs necessary for cell behavior are vital to our understanding of development and disease. Proper cell behavior is necessary for processes ranging from creating one’s face (neural crest migration) to spreading cancer from one tissue to another (invasive metastatic cancers). Identifying the genes and tissues involved in cell behavior not only increases our understanding of biology but also has the potential to create targeted therapies in diseases hallmarked by aberrant cell behavior.

A well-characterized model system is key to determining the molecular and spatial inputs necessary for cell behavior. In this work I present the C. elegans uterine seam cell (utse) as an ideal model for studying cell outgrowth and shape change. The utse is an H-shaped cell within the hermaphrodite uterus that functions in attaching the uterus to the body wall. Over L4 larval stage, the utse grows bidirectionally along the anterior-posterior axis, changing from an ellipsoidal shape to an elongated H-shape. Spatially, the utse requires the presence of the uterine toroid cells, sex muscles, and the anchor cell nucleus in order to properly grow outward. Several gene families are involved in utse development, including Trio, Nav, Rab GTPases, Arp2/3, as well as 54 other genes found from a candidate RNAi screen. The utse can be used as a model system for studying metastatic cancer. Meprin proteases are involved in promoting invasiveness of metastatic cancers and the meprin-likw genes nas-21, nas-22, and toh-1 act similarly within the utse. Studying nas-21 activity has also led to the discovery of novel upstream inhibitors and activators as well as targets of nas-21, some of which have been characterized to affect meprin activity. This illustrates that the utse can be used as an in vivo model for learning more about meprins, as well as various other proteins involved in metastasis.

Force chains, friction, and flow: Behavior of granular media across length scales

We study the behavior of granular materials at three length scales. At the smallest length scale, the grain-scale, we study inter-particle forces and "force chains". Inter-particle forces are the natural building blocks of constitutive laws for granular materials. Force chains are a key signature of the heterogeneity of granular systems. Despite their fundamental importance for calibrating grain-scale numerical models and elucidating constitutive laws, inter-particle forces have not been fully quantified in natural granular materials. We present a numerical force inference technique for determining inter-particle forces from experimental data and apply the technique to two-dimensional and three-dimensional systems under quasi-static and dynamic load. These experiments validate the technique and provide insight into the quasi-static and dynamic behavior of granular materials.

At a larger length scale, the mesoscale, we study the emergent frictional behavior of a collection of grains. Properties of granular materials at this intermediate scale are crucial inputs for macro-scale continuum models. We derive friction laws for granular materials at the mesoscale by applying averaging techniques to grain-scale quantities. These laws portray the nature of steady-state frictional strength as a competition between steady-state dilation and grain-scale dissipation rates. The laws also directly link the rate of dilation to the non-steady-state frictional strength.

At the macro-scale, we investigate continuum modeling techniques capable of simulating the distinct solid-like, liquid-like, and gas-like behaviors exhibited by granular materials in a single computational domain. We propose a Smoothed Particle Hydrodynamics (SPH) approach for granular materials with a viscoplastic constitutive law. The constitutive law uses a rate-dependent and dilation-dependent friction law. We provide a theoretical basis for a dilation-dependent friction law using similar analysis to that performed at the mesoscale. We provide several qualitative and quantitative validations of the technique and discuss ongoing work aiming to couple the granular flow with gas and fluid flows.

Behavior of spherical particles at low Reynolds numbers in a fluctuating translational flow

The behavior of spheres in non-steady translational flow has been studied experimentally for values of Reynolds number from 0.2 to 3000. The aim of the work was to improve our qualitative understanding of particle transport in turbulent gaseous media, a process of extreme importance in power plants and energy transfer mechanisms.

Particles, subjected to sinusoidal oscillations parallel to the direction of steady translation, were found to have changes in average drag coefficient depending upon their translational Reynolds number, the density ratio, and the dimensionless frequency and amplitude of the oscillations. When the Reynolds number based on sphere diameter was less than 200, the oscillation had negligible effect on the average particle drag.

For Reynolds numbers exceeding 300, the coefficient of the mean drag was increased significantly in a particular frequency range. For example, at a Reynolds number of 3000, a 25 per cent increase in drag coefficient can be produced with an amplitude of oscillation of only 2 per cent of the sphere diameter, providing the frequency is near the frequency at which vortices would be shed in a steady flow at the mean speed. Flow visualization shows that over a wide range of frequencies, the vortex shedding frequency locks in to the oscillation frequency. Maximum effect at the natural frequency and lock-in show that a non-linear interaction between wake vortex shedding and the oscillation is responsible for the increase in drag.

Thermodynamic and kinetic behavior of an argon plasma jet. Decomposition of nitric oxide between 1300 - 1750 degrees K in an argon plasma

In the first part of the study, an RF coupled, atmospheric pressure, laminar plasma jet of argon was investigated for thermodynamic equilibrium and some rate processes.

Improved values of transition probabilities for 17 lines of argon I were developed from known values for 7 lines. The effect of inhomogeneity of the source was pointed out.

The temperatures, T, and the electron densities, n_e , were determined spectroscopically from the population densities of the higher excited states assuming the Saha-Boltzmann relationship to be valid for these states. The axial velocities, v_z, were measured by tracing the paths of particles of boron nitride using a three-dimentional mapping technique. The above quantities varied in the following ranges: 10¹² ˂ n_e ˂ 10¹⁵ particles/cm³, 3500 ˂ T ˂ 11000 °K, and 200 ˂ v_z ˂ 1200 cm/sec.

The absence of excitation equilibrium for the lower excitation population including the ground state under certain conditions of T and n_e was established and the departure from equilibrium was examined quantitatively. The ground state was shown to be highly underpopulated for the decaying plasma.

Rates of recombination between electrons and ions were obtained by solving the steady-state equation of continuity for electrons. The observed rates were consistent with a dissociative-molecular ion mechanism with a steady-state assumption for the molecular ions.

In the second part of the study, decomposition of NO was studied in the plasma at lower temperatures. The mole fractions of NO denoted by x_NO were determined gas-chromatographically and varied between 0.0012 ˂ x_NO ˂ 0.0055. The temperatures were measured pyrometrically and varied between 1300 ˂ T ˂ 1750°K. The observed rates of decomposition were orders of magnitude greater than those obtained by the previous workers under purely thermal reaction conditions. The overall activation energy was about 9 kcal/g mol which was considerably lower than the value under thermal conditions. The effect of excess nitrogen was to reduce the rate of decomposition of NO and to increase the order of the reaction with respect to NO from 1.33 to 1.85. The observed rates were consistent with a chain mechanism in which atomic nitrogen and oxygen act as chain carriers. The increased rates of decomposition and the reduced activation energy in the presence of the plasma could be explained on the basis of the observed large amount of atomic nitrogen which was probably formed as the result of reactions between excited atoms and ions of argon and the molecular nitrogen.

Chemical and Electrochemical Behavior of Graphene-Covered Silicon Photoanodes

This dissertation describes efforts over the last five years to develop protective layers for semiconductor photoelectrodes based on monolayer or few-layer graphene sheets. Graphene is an attractive candidate for a protective layer because of its known chemical inertness, transparency, ease of deposition, and limited number of electronic states. Monolayer graphene was found to effectively inhibit loss of photocurrent over 1000 seconds at n-Si/aqueous electrolyte interfaces that exhibit total loss over photocurrent over 100 seconds. Further, the presence of graphene was found to effect only partial Fermi level pinning at the Si/graphene interface with respect to a range of nonaqueous electrolytes. Fluorination of graphene was found to extend the stability imparted on n-Si by the monolayer sheet in aqueous Fe(CN)₆^3-/4- electrolyte to over 100,000 seconds. It was demonstrated that the stability of the photocurrent of n-Si/fluorinated graphene/aqueous electrolyte interfaces relative to n-Si/aqueous electrolyte interfaces is likely attributable to the inhibition of oxidation of the silicon surface.

This dissertation also relates efforts to describe and define terminology relevant to the field of photoelectrochemistry and solar fuels production. Terminology describing varying interfaces employed in electrochemical solar fuels devices are defined, and the research challenges associated with each are discussed. Methods for determining the efficiency of varying photoelectrochemical and solar-fuel-producing cells from the current-voltage behavior of the individual components of such a device without requiring the device be constructed are described, and a range of commonly employed performance metrics are explored.

Dynamic response of hysteretic systems with application to a system containing limited slip

A general class of single degree of freedom systems possessing rate-independent hysteresis is defined. The hysteretic behavior in a system belonging to this class is depicted as a sequence of single-valued functions; at any given time, the current function is determined by some set of mathematical rules concerning the entire previous response of the system. Existence and uniqueness of solutions are established and boundedness of solutions is examined.

An asymptotic solution procedure is used to derive an approximation to the response of viscously damped systems with a small hysteretic nonlinearity and trigonometric excitation. Two properties of the hysteresis loops associated with any given system completely determine this approximation to the response: the area enclosed by each loop, and the average of the ascending and descending branches of each loop.

The approximation, supplemented by numerical calculations, is applied to investigate the steady-state response of a system with limited slip. Such features as disconnected response curves and jumps in response exist for a certain range of system parameters for any finite amount of slip.

To further understand the response of this system, solutions of the initial-value problem are examined. The boundedness of solutions is investigated first. Then the relationship between initial conditions and resulting steady-state solution is examined when multiple steady-state solutions exist. Using the approximate analysis and numerical calculations, it is found that significant regions of initial conditions in the initial condition plane lead to the different asymptotically stable steady-state solutions.

A singular perturbation method of calculating the behavior of supercavitating hydrofoils with rounded noses

A simple, direct and accurate method to predict the pressure distribution on supercavitating hydrofoils with rounded noses is presented. The thickness of body and cavity is assumed to be small. The method adopted in the present work is that of singular perturbation theory. Far from the leading edge linearized free streamline theory is applied. Near the leading edge, however, where singularities of the linearized theory occur, a non-linear local solution is employed. The two unknown parameters which characterize this local solution are determined by a matching procedure. A uniformly valid solution is then constructed with the aid of the singular perturbation approach.

The present work is divided into two parts. In Part I isolated supercavitating hydrofoils of arbitrary profile shape with parabolic noses are investigated by the present method and its results are compared with the new computational results made with Wu and Wang's exact "functional iterative" method. The agreement is very good. In Part II this method is applied to a linear cascade of such hydrofoils with elliptic noses. A number of cases are worked out over a range of cascade parameters from which a good idea of the behavior of this type of important flow configuration is obtained.

Some of the computational aspects of Wu and Wang's functional iterative method heretofore not successfully applied to this type of problem are described in an appendix.