Elastic Propagation in random media: applications to the imaging of volcano structures

High-frequency seismograms contain features that reflect the random inhomogeneities of the earth. In this work I use an imaging method to locate the high contrast small- scale heterogeneity respect to the background earth medium. This method was first introduced by Nishigami (1991) and than applied to different volcanic and tectonically active areas (Nishigami, 1997, Nishigami, 2000, Nishigami, 2006). The scattering imaging method is applied to two volcanic areas: Campi Flegrei and Mt. Vesuvius. Volcanic and seismological active areas are often characterized by complex velocity structures, due to the presence of rocks with different elastic properties. I introduce some modifications to the original method in order to make it suitable for small and highly complex media. In particular, for very complex media the single scattering approximation assumed by Nishigami (1991) is not applicable as the mean free path becomes short. The multiple scattering or diffusive approximation become closer to the reality. In this thesis, differently from the ordinary Nishigami’s method (Nishigami, 1991), I use the mean of the recorded coda envelope as reference curve and calculate the variations from this average envelope. In this way I implicitly do not assume any particular scattering regime for the "average" scattered radiation, whereas I consider the variations as due to waves that are singularly scattered from the strongest heterogeneities. The imaging method is applied to a relatively small area (20 x 20 km), this choice being justified by the small length of the analyzed codas of the low magnitude earthquakes. I apply the unmodified Nishigami’s method to the volcanic area of Campi Flegrei and compare the results with the other tomographies done in the same area. The scattering images, obtained with frequency waves around 18 Hz, show the presence of high scatterers in correspondence with the submerged caldera rim in the southern part of the Pozzuoli bay. Strong scattering is also found below the Solfatara crater, characterized by the presence of densely fractured, fluid-filled rocks and by a strong thermal anomaly. The modified Nishigami’s technique is applied to the Mt. Vesuvius area. Results show a low scattering area just below the central cone and a high scattering area around it. The high scattering zone seems to be due to the contrast between the high rigidity body located beneath the crater and the low rigidity materials located around it. The central low scattering area overlaps the hydrothermal reservoirs located below the central cone. An interpretation of the results in terms of geological properties of the medium is also supplied, aiming to find a correspondence of the scattering properties and the geological nature of the material. A complementary result reported in this thesis is that the strong heterogeneity of the volcanic medium create a phenomenon called "coda localization". It has been verified that the shape of the seismograms recorded from the stations located at the top of the volcanic edifice of Mt. Vesuvius is different from the shape of the seismograms recorded at the bottom. This behavior is justified by the consideration that the coda energy is not uniformly distributed within a region surrounding the source for great lapse time.

Structural and elastic properties of DNA and chromatin

We investigate a chain consisting of two coupled worm-like chains withconstant distance between the strands. The effects due todouble-strandedness of the chain are studied. In a previous analyticalstudy of this system an intrinsic twist-stretch coupling and atendency of kinking is predicted. Even though a local twist structureis observed the predicted features are not recovered. A new model for DNA at the base-pair level is presented. Thebase-pairs are treated as flat rigid ellipsoids and thesugar-phosphate backbones are represented as stiff harmonic springs.The base-pair stacking interaction is modeled by a variant of theGay-Berne potential. It is shown by systematic coarse-graininghow the elastic constants of a worm-like chain are related to thelocal fluctuations of the base-pair step parameters. Even though a lotof microscopic details of the base-pair geometry is neglected themodel can be optimized to obtain a B-DNA conformation as ground stateand reasonable elastic properties. Moreover the model allows tosimulate much larger length scales than it is possible with atomisticsimulations due to the simplification of the force-field and inparticular due to the possibility of non-local Monte-Carlo moves. Asa first application the behavior under stretching is investigated. Inagreement with micromanipulation experiments on single DNA moleculesone observes a force-plateau in the force-extension curvescorresponding to an overstretching transition from B-DNA to aso-called S-DNA state. The model suggests a structure for S-DNA withhighly inclined base-pairs in order to enable at least partialbase-pair stacking. Finally a simple model for chromatin is introduced to study itsstructural and elastic properties. The underlying geometry of themodeled fiber is based on a crossed-linker model. The chromatosomesare treated as disk-like objects. Excluded volume and short rangenucleosomal interaction are taken into account by a variant of theGay-Berne potential. It is found that the bending rigidity and thestretching modulus of the fiber increase with more compact fibers. Fora reasonable parameterization of the fiber for physiologicalconditions and sufficiently high attraction between the nucleosomes aforce-extension curve is found similar to stretching experiments onsingle chromatin fibers. For very small stretching forces a kinkedfiber forming a loop is observed. If larger forces are applied theloop formation is stretched out and a decondensation of the fibertakes place.

Kinematics of the Sicily and Calabria Subduction System from Elastic Block Modeling of GPS Data

We use data from about 700 GPS stations in the EuroMediterranen region to investigate the present-day behavior of the the Calabrian subduction zone within the Mediterranean-scale plates kinematics and to perform local scale studies about the strain accumulation on active structures. We focus attenction on the Messina Straits and Crati Valley faults where GPS data show extentional velocity gradients of ∼3 mm/yr and ∼2 mm/yr, respectively. We use dislocation model and a non-linear constrained optimization algorithm to invert for fault geometric parameters and slip-rates and evaluate the associated uncertainties adopting a bootstrap approach. Our analysis suggest the presence of two partially locked normal faults. To investigate the impact of elastic strain contributes from other nearby active faults onto the observed velocity gradient we use a block modeling approach. Our models show that the inferred slip-rates on the two analyzed structures are strongly impacted by the assumed locking width of the Calabrian subduction thrust. In order to frame the observed local deformation features within the present- day central Mediterranean kinematics we realyze a statistical analysis testing the indipendent motion (w.r.t. the African and Eurasias plates) of the Adriatic, Cal- abrian and Sicilian blocks. Our preferred model confirms a microplate like behaviour for all the investigated blocks. Within these kinematic boundary conditions we fur- ther investigate the Calabrian Slab interface geometry using a combined approach of block modeling and χ2ν statistic. Almost no information is obtained using only the horizontal GPS velocities that prove to be a not sufficient dataset for a multi-parametric inversion approach. Trying to stronger constrain the slab geometry we estimate the predicted vertical velocities performing suites of forward models of elastic dislocations varying the fault locking depth. Comparison with the observed field suggest a maximum resolved locking depth of 25 km.

Hypersonic elastic excitations in soft mesoscopic structures

This dissertation is devoted to the experimental exploration of the propagation of elastic waves in soft mesoscopic structures with submicrometer dimensions. A strong motivation of this work is the large technological relevance and the fundamental importance of the subject. Elastic waves are accompanied by time-dependent fluctuations of local stress and strain fields in the medium. As such, the propagation phase velocities are intimately related to the elastic moduli. Knowledge of the elastic wave propagation directly provides information about the mechanical properties of the probed mesoscopic structures, which are not readily accessible experimentally. On the other hand, elastic waves, when propagating in an inhomogeneous medium with spatial inhomogeneities comparable to their wavelength, exhibit rather rich behavior, including the appearance of novel physical phenomena, such as phononic bandgap formation. So far, the experimental work has been restricted to macroscopic structures, which limit wave propagation below the KHz range. It was anticipated that an experimental approach capable of probing the interplay of the wave propagation with the controlled mesoscopic structures would contribute to deeper insights into the fundamental problem of elastic wave propagation in inhomogeneous systems. The mesoscopic nature of the structures to be studied precludes the use of traditional methods, such as sound transmission, for the study of elastic wave propagation. In this work, an optical method utilizing the inelastic scattering of photons by GHz frequency thermally excited elastic waves, known as Brillouin light scattering spectroscopy (BLS), was employed. Two important classes of soft structures were investigated: thin films and colloidal crystals. For the former, the main interest was the effect of the one-dimensional (1D) confinement on the wave propagation due to the presence of the free-surface or interface of the layer and the utilization of these waves to extract relevant material parameters. For the second system, the primary interest was the interaction of the elastic wave and the strong scattering medium with local resonance units in a three-dimensional (3D) periodic arrangement.

Influence of microstructure variability on short crack growth behavior

Fatigue life in metals is predicted utilizing regression analysis of large sets of experimental data, thus representing the material’s macroscopic response. Furthermore, a high variability in the short crack growth (SCG) rate has been observed in polycrystalline materials, in which the evolution and distributionof local plasticity is strongly influenced by the microstructure features. The present work serves to (a) identify the relationship between the crack driving force based on the local microstructure in the proximity of the crack-tip and (b) defines the correlation between scatter observed in the SCG rates to variability in the microstructure. A crystal plasticity model based on the fast Fourier transform formulation of the elasto-viscoplastic problem (CP-EVP-FFT) is used, since the ability to account for the both elastic and plastic regime is critical in fatigue. Fatigue is governed by slip irreversibility, resulting in crack growth, which starts to occur during local elasto-plastic transition. To investigate the effects of microstructure variability on the SCG rate, sets of different microstructure realizations are constructed, in which cracks of different length are introduced to mimic quasi-static SCG in engineering alloys. From these results, the behavior of the characteristic variables of different length scale are analyzed: (i) Von Mises stress fields (ii) resolved shear stress/strain in the pertinent slip systems, and (iii) slip accumulation/irreversibilities. Through fatigue indicator parameters (FIP), scatter within the SCG rates is related to variability in the microstructural features; the results demonstrate that this relationship between microstructure variability and uncertainty in fatigue behavior is critical for accurate fatigue life prediction.

Robust Nonlinear Output Regulation by Identification Tools

The present thesis focuses on the problem of robust output regulation for minimum phase nonlinear systems by means of identification techniques. Given a controlled plant and an exosystem (an autonomous system that generates eventual references or disturbances), the control goal is to design a proper regulator able to process the only measure available, i.e the error/output variable, in order to make it asymptotically vanishing. In this context, such a regulator can be designed following the well known “internal model principle” that states how it is possible to achieve the regulation objective by embedding a replica of the exosystem model in the controller structure. The main problem shows up when the exosystem model is affected by parametric or structural uncertainties, in this case, it is not possible to reproduce the exact behavior of the exogenous system in the regulator and then, it is not possible to achieve the control goal. In this work, the idea is to find a solution to the problem trying to develop a general framework in which coexist both a standard regulator and an estimator able to guarantee (when possible) the best estimate of all uncertainties present in the exosystem in order to give “robustness” to the overall control loop.

Modeling and simulation of fibrinogen and its adsorption behavior

In this thesis different approaches for the modeling and simulation of the blood protein fibrinogen are presented. The approaches are meant to systematically connect the multiple time and length scales involved in the dynamics of fibrinogen in solution and at inorganic surfaces. The first part of the thesis will cover simulations of fibrinogen on an all atom level. Simulations of the fibrinogen protomer and dimer are performed in explicit solvent to characterize the dynamics of fibrinogen in solution. These simulations reveal an unexpectedly large and fast bending motion that is facilitated by molecular hinges located in the coiled-coil region of fibrinogen. This behavior is characterized by a bending and a dihedral angle and the distribution of these angles is measured. As a consequence of the atomistic detail of the simulations it is possible to illuminate small scale behavior in the binding pockets of fibrinogen that hints at a previously unknown allosteric effect. In a second step atomistic simulations of the fibrinogen protomer are performed at graphite and mica surfaces to investigate initial adsorption stages. These simulations highlight the different adsorption mechanisms at the hydrophobic graphite surface and the charged, hydrophilic mica surface. It is found that the initial adsorption happens in a preferred orientation on mica. Many effects of practical interest involve aggregates of many fibrinogen molecules. To investigate such systems, time and length scales need to be simulated that are not attainable in atomistic simulations. It is therefore necessary to develop lower resolution models of fibrinogen. This is done in the second part of the thesis. First a systematically coarse grained model is derived and parametrized based on the atomistic simulations of the first part. In this model the fibrinogen molecule is represented by 45 beads instead of nearly 31,000 atoms. The intra-molecular interactions of the beads are modeled as a heterogeneous elastic network while inter-molecular interactions are assumed to be a combination of electrostatic and van der Waals interaction. A method is presented that determines the charges assigned to beads by matching the electrostatic potential in the atomistic simulation. Lastly a phenomenological model is developed that represents fibrinogen by five beads connected by rigid rods with two hinges. This model only captures the large scale dynamics in the atomistic simulations but can shed light on experimental observations of fibrinogen conformations at inorganic surfaces.

The influence of infill walls on seismic behavior of a historical building in Shanghai

Seismic assessment and seismic strengthening are the key issues need to be figured out during the process of protection and reusing of historical buildings. In this thesis the seismic behaviors of the hinged steel structure, a typical structure of historical buildings, i.e. hinged steel frames in Shanghai, China, were studied based on experimental investigations and theoretic analysis. How the non-structural members worked with the steel frames was analyzed thoroughly. Firstly, two 1/4 scale hinged steel frames were constructed based on the structural system of Bund 18, a historical building in Shanghai: M1 model without infill walls, M2 model with infill walls, and tested under the horizontal cyclic loads to investigate their seismic behavior. The Shaking Table Test and its results indicated that the seismic behavior of the hinged steel frames could be improved significantly with the help of non-structural members, i.e., surrounding elements outside the hinged steel frames and infilled walls. To specify, the columns are covered with bricks, they consist of I shape formed steel sections and steel plates, which are clenched together. The steel beams are connected to the steel column by steel angle, thus the structure should be considered as a hinged frame. And the infilled wall acted as a compression diagonal strut to withstand the horizontal load, therefore, the seismic capacity and stiffness of the hinged steel frames with infilled walls could be estimated by using the equivalent compression diagonal strut model. A SAP model has been constructed with the objective to perform a dynamic nonlinear analysis. The obtained results were compared with the results obtained from Shaking Table Test. The Test Results have validated that the influence of infill walls on seismic behavior can be estimated by using the equivalent diagonal strut model.

Cement distribution, volume, and compliance in vertebroplasty: some answers from an anatomy-based nonlinear finite element study

STUDY DESIGN: The biomechanics of vertebral bodies augmented with real distributions of cement were investigated using nonlinear finite element (FE) analysis. OBJECTIVES: To compare stiffness, strength, and stress transfer of augmented versus nonaugmented osteoporotic vertebral bodies under compressive loading. Specifically, to examine how cement distribution, volume, and compliance affect these biomechanical variables. SUMMARY OF BACKGROUND DATA: Previous FE studies suggested that vertebroplasty might alter vertebral stress transfer, leading to adjacent vertebral failure. However, no FE study so far accounted for real cement distributions and bone damage accumulation. METHODS: Twelve vertebral bodies scanned with high-resolution pQCT and tested in compression were augmented with various volumes of cements and scanned again. Nonaugmented and augmented pQCT datasets were converted to FE models, with bone properties modeled with an elastic, plastic and damage constitutive law that was previously calibrated for the nonaugmented models. The cement-bone composite was modeled with a rule of mixture. The nonaugmented and augmented FE models were subjected to compression and their stiffness, strength, and stress map calculated for different cement compliances. RESULTS: Cement distribution dominated the stiffening and strengthening effects of augmentation. Models with cement connecting either the superior or inferior endplate (S/I fillings) were only up to 2 times stiffer than the nonaugmented models with minimal strengthening, whereas those with cement connecting both endplates (S + I fillings) were 1 to 8 times stiffer and 1 to 12 times stronger. Stress increases above and below the cement, which was higher for the S + I cases and was significantly reduced by increasing cement compliance. CONCLUSION: The developed FE approach, which accounts for real cement distributions and bone damage accumulation, provides a refined insight into the mechanics of augmented vertebral bodies. In particular, augmentation with compliant cement bridging both endplates would reduce stress transfer while providing sufficient strengthening.

Analytical investigation of squeeze film dampers

Squeeze film damping effects naturally occur if structures are subjected to loading situations such that a very thin film of fluid is trapped within structural joints, interfaces, etc. An accurate estimate of squeeze film effects is important to predict the performance of dynamic structures. Starting from linear Reynolds equation which governs the fluid behavior coupled with structure domain which is modeled by Kirchhoff plate equation, the effects of nondimensional parameters on the damped natural frequencies are presented using boundary characteristic orthogonal functions. For this purpose, the nondimensional coupled partial differential equations are obtained using Rayleigh-Ritz method and the weak formulation, are solved using polynomial and sinusoidal boundary characteristic orthogonal functions for structure and fluid domain respectively. In order to implement present approach to the complex geometries, a two dimensional isoparametric coupled finite element is developed based on Reissner-Mindlin plate theory and linearized Reynolds equation. The coupling between fluid and structure is handled by considering the pressure forces and structural surface velocities on the boundaries. The effects of the driving parameters on the frequency response functions are investigated. As the next logical step, an analytical method for solution of squeeze film damping based upon Green’s function to the nonlinear Reynolds equation considering elastic plate is studied. This allows calculating modal damping and stiffness force rapidly for various boundary conditions. The nonlinear Reynolds equation is divided into multiple linear non-homogeneous Helmholtz equations, which then can be solvable using the presented approach. Approximate mode shapes of a rectangular elastic plate are used, enabling calculation of damping ratio and frequency shift as well as complex resistant pressure. Moreover, the theoretical results are correlated and compared with experimental results both in the literature and in-house experimental procedures including comparison against viscoelastic dampers.

Distortion-sensitive insight into the pretransitional behavior of 4- n -octyloxy-4′-cyanobiphenyl (8OCB)

Results of studies of the static and dynamic dielectric properties in rod-like 4-n-octyloxy-4'-cyanobiphenyl (8OCB) with isotropic (I)–nematic (N)–smectic A (SmA)–crystal (Cr) mesomorphism, combined with measurements of the low-frequency nonlinear dielectric effect and heat capacity are presented. The analysis is supported by the derivative-based and distortion-sensitive transformation of experimental data. Evidence for the I–N and N–SmA pretransitional anomalies, indicating the influence of tricritical behavior, is shown. It has also been found that neither the N phase nor the SmA phase are uniform and hallmarks of fluid–fluid crossovers can be detected. The dynamics, tested via the evolution of the primary relaxation time, is clearly non-Arrhenius and described via τ(T) = τc(T−TC)−phgr. In the immediate vicinity of the I–N transition a novel anomaly has been found: Δτ ∝ 1/(T − T*), where T* is the temperature of the virtual continuous transition and Δτ is the excess over the 'background behavior'. Experimental results are confronted with the comprehensive Landau–de Gennes theory based modeling.

Finite Element Based Nonlinear Normalization of Human Lumbar Intervertebral Disc Stiffness to Account for Its Morphology

Disc degeneration, usually associated with low back pain and changes of intervertebral stiffness, represents a major health issue. As the intervertebral disc (IVD) morphology influences its stiffness, the link between mechanical properties and degenerative grade is partially lost without an efficient normalization of the stiffness with respect to the morphology. Moreover, although the behavior of soft tissues is highly nonlinear, only linear normalization protocols have been defined so far for the disc stiffness. Thus, the aim of this work is to propose a nonlinear normalization based on finite elements (FE) simulations and evaluate its impact on the stiffness of human anatomical specimens of lumbar IVD. First, a parameter study involving simulations of biomechanical tests (compression, flexion/extension, bilateral torsion and bending) on 20 FE models of IVDs with various dimensions was carried out to evaluate the effect of the disc's geometry on its compliance and establish stiffness/morphology relations necessary to the nonlinear normalization. The computed stiffness was then normalized by height (H), cross-sectional area (CSA), polar moment of inertia (J) or moments of inertia (Ixx, Iyy) to quantify the effect of both linear and nonlinear normalizations. In the second part of the study, T1-weighted MRI images were acquired to determine H, CSA, J, Ixx and Iyy of 14 human lumbar IVDs. Based on the measured morphology and pre-established relation with stiffness, linear and nonlinear normalization routines were then applied to the compliance of the specimens for each quasi-static biomechanical test. The variability of the stiffness prior to and after normalization was assessed via coefficient of variation (CV). The FE study confirmed that larger and thinner IVDs were stiffer while the normalization strongly attenuated the effect of the disc geometry on its stiffness. Yet, notwithstanding the results of the FE study, the experimental stiffness showed consistently higher CV after normalization. Assuming that geometry and material properties affect the mechanical response, they can also compensate for one another. Therefore, the larger CV after normalization can be interpreted as a strong variability of the material properties, previously hidden by the geometry's own influence. In conclusion, a new normalization protocol for the intervertebral disc stiffness in compression, flexion, extension, bilateral torsion and bending was proposed, with the possible use of MRI and FE to acquire the discs' anatomy and determine the nonlinear relations between stiffness and morphology. Such protocol may be useful to relate the disc's mechanical properties to its degree of degeneration.

Magma-Driven Multiple Dike Propagation and Fracture Toughness of Crustal Rocks

Dike swarms consisting of tens to thousands of subparallel dikes are commonly observed at Earth's surface, raising the possibility of simultaneous propagation of two or more dikes at various stages of a swarm's development. The behavior of multiple propagating dikes differs from that of a single dike owing to the interacting stress fields associated with each dike. We analyze an array of parallel, periodically spaced dikes that grow simultaneously from an overpressured source into a semi-infinite, linear elastic host rock. To simplify the analysis, we assume steady state (constant velocity) magma flow and dike propagation. We use a perturbation method to analyze the coupled, nonlinear problem of multiple dike propagation and magma transport. The stress intensity factor at the dike tips and the opening displacements of the dike surfaces are calculated. The numerical results show that dike spacing has a profound effect on the behavior of dike propagation. The stress intensity factors at the tips of parallel dikes decrease with a decrease in dike spacing and are significantly smaller than that for a single dike with the same length. The reduced stress intensity factor indicates that, compared to a single dike, propagation of parallel dikes is more likely to be arrested under otherwise the same conditions. It also implies that fracture toughness of the host rock in a high confining pressure environment may not be as high as inferred from the propagation of a single dike. Our numerical results suggest fracture toughness values on the order of 100 MPa root m. The opening displacements for parallel dikes are smaller than that for a single dike, which results in higher magma pressure gradients in parallel dikes and lower flux of magma transport.

Experimental validation of a nonlinear μ FE model based on cohesive-frictional plasticity for trabecular bone

Trabecular bone is a porous mineralized tissue playing a major load bearing role in the human body. Prediction of age-related and disease-related fractures and the behavior of bone implant systems needs a thorough understanding of its structure-mechanical property relationships, which can be obtained using microcomputed tomography-based finite element modeling. In this study, a nonlinear model for trabecular bone as a cohesive-frictional material was implemented in a large-scale computational framework and validated by comparison of μFE simulations with experimental tests in uniaxial tension and compression. A good correspondence of stiffness and yield points between simulations and experiments was found for a wide range of bone volume fraction and degree of anisotropy in both tension and compression using a non-calibrated, average set of material parameters. These results demonstrate the ability of the model to capture the effects leading to failure of bone for three anatomical sites and several donors, which may be used to determine the apparent behavior of trabecular bone and its evolution with age, disease, and treatment in the future.