Fraturas são descontinuidades físicas, presentes em diversos materiais utilizados na engenharia, e são responsáveis pela redução da resistência e da rigidez global dos materiais. Tratando-se de fraturas de pequena dimensão, é possível definir a existência de duas escalas: a escala microscópica, onde as fraturas são visíveis, e a escala macroscópica, onde o material fraturado é homogêneo. Maghous et al. (2010) utilizaram a micromecânica para expor o tensor de rigidez homogeneizado para materiais elásticos fraturados, fazendo a ressalva de que fraturas transmitem esforços por suas faces. Utilizando os conceitos formulados por Maghous, Lorenci (2013) ampliou sua aplicação, estendendo à distribuição aleatória das fraturas. Utilizando o mesmo procedimento realizado por Lorenci, determinou-se os tensores de rigidez homogeneizados para materiais elásticos fraturados, os quais foram empregados para formular as condições de propagação de fraturas para materiais elásticos. Conceitualmente, a condição de propagação de fraturas em meios elásticos é formulada com base em conceitos clássicos da termodinâmica, baseados na dissipação de energia. Tratando-se de meios viscoelásticos, a dissipação de energia adquire um novo termo denominado de dissipação viscosa. Nguyen (2010) estabeleceu uma condição de propagação de fissuras em meios viscoelásticos, entretanto, as fissuras admitidas por Nguyen não são responsáveis pela transferência de esforços. Para estender a análise de Nguyen ao caso de fraturas, foi necessário determinar os tensores de relaxação do material viscoelástico fraturado, estes tensores foram obtidos combinando-se os tensores elásticos homogeneizados com os conceitos da transformada de Carson-Laplace, admitindo que as fraturas não se propagam ao longo do tempo. Com base no tensor de relaxação isótropo homogeneizado, determinou-se um modelo reológico equivalente que represente o material viscoelástico fraturado assumindo diferentes modelos reológicos para a matriz e para fraturas. Por fim, analisou-se as condições de propagação de fraturas em meios viscoelásticos de duas formas: de forma aproximada (apurando os estudos realizados por Nguyen) e de forma homogeneizada (admitindo que a propagação de fraturas se dá na escala macroscópica). / responsible for reducing the overall strength and stiffness of the material. In the case of small fractures, is possible set two scales: a microscopic scale, where fractures are visible, and the macroscopic scale, where the fractured material is homogeneous. Maghous et al. (2010) used the micromechanics to expose the homogenized stiffness tensor for fractured elastic materials, making the observation that fractures transmit efforts by their faces. Using the concepts formulated by Maghous, Lorenci (2013) expanded its application, extending to a random distribution of fractures. Using the same procedure performed by Lorenci, the homogenized stiffness tensor was determined for fractured elastic materials, which were employed to formulate the fracture propagation conditions for elastic materials. Conceptually, the fracture propagation conditions for elastic means is made based on classical concepts of thermodynamics, based on the energy dissipation. In the case of viscoelastic means, the energy dissipation acquires a new term called viscous dissipation. Nguyen (2010) established a condition of crack propagation in viscoelastic means, however, the Nguyen’s cracks are not responsible for the transfer of efforts. To extend Nguyen analysis to the case of fractures, was necessary to determine the relaxation tensor for viscoelastic fractured materials, these tensors are obtained by combining the homogenized elastic tensor to the concepts of the Carson- Laplace transform, assuming that the fractures are not propagate over time. Based on the isotropic homogenized relaxation tensors, was determined an equivalent rheological model representing the fractured viscoelastic material assuming different rheological models for matrix and fractures. Finally, was analyzed the fracture propagation conditions in viscoelastic means in two ways: in an approximate way (improving the studies conducted by Nguyen) and homogenized form (assuming that the propagation of fractures occurs at the macroscopic scale).

Progressive bone loss and weakening bone strength associated with aging predispose the elderly population to osteoporosis and millions of costly fragility fractures. Micro finite element (µFE) analysis based on clinical high-resolution skeletal imaging provides an accurate computational solution to assessing the mechanical properties of bone, which can be used as the dominant factors for fracture risk. However, the current µFE analysis technique is impractical for clinical use due to its prohibitive computational costs, which result from the “voxel-to-element” approach of modeling human bone regardless of its microstructural pattern. I developed a novel plate-rod microstructural modeling technique for highly efficient patient-specific µFE analysis and translated it to clinical research for the assessment of bone strength in osteoporosis and fragility fractures. Trabecular microstructure is composed of interconnected plate-like and rod-like trabeculae. Instead of converting every image voxel directly into an element, the plate-rod modeling approach created mechanical characterization for every individual trabecular plate and rod. The validation studies demonstrated that the PR model was able to reproduce the morphology and mechanical behavior of the original trabecular microstructure, while reducing the size of the µFE model and improving the efficiency of µFE simulations. First, the PR models of trabecular bone were developed based on high-resolution micro computed tomography (µCT), and evaluated in comparison with computational gold standard-voxel µFE models and experimental gold standard-mechanical testing for estimating Young’s modulus and yield strength of human trabecular bone. Results suggested that PR model predictions of the trabecular bone mechanical properties were strongly correlated with voxel models and mechanical testing results. Moreover, the PR models were indistinguishable from the corresponding voxel models constructed from the same images in the prediction of trabecular bone Young’s modulus and yield strength. In addition, PR model nonlinear µFE analyses resulted in over 200-fold reduction in computation time compared with voxel model µFE analyses. In the effort of studying the heterogeneous bone mineralization in trabecular plates and rods, I developed an individual trabecula mineralization (ITM) analysis technique that allows quantification of the tissue mineral density of each individual trabecular plate and rod. By examining the variation of mineral density with trabecular types and orientations, it was found that trabecular plates were higher mineralized than trabecular rods. Furthermore, trabecular plate mineral density varied with trabecular orientation, increasing from the longitudinal direction to the transverse direction. ITM provided measurement of mineral density of each trabecular plate and rod, which was converted to trabecula-specific tissue modulus and used in the PR models to incorporate mineral heterogeneity in µFE simulations. Results suggested that heterogeneous PR models did not differ from the homogeneous PR models or specimen-specific PR models in their predictions of apparent Young’s modulus and yield strength of the human trabecular bone specimens from non-diseased donors. Based on the trabecular bone PR model, a whole bone PR model was developed for assessing whole bone mechanical strength at the distal radius and the distal tibia from high-resolution peripheral quantitative computed tomography (HR-pQCT). The accuracy of the whole bone PR model was evaluated on human cadaver radius and tibia specimens which were imaged using HR-pQCT and µCT, respectively, and tested to failure. The whole bone stiffness and yield load of the radius and tibia segments predicted by HR-pQCT PR models were strongly correlated with those predicted by corresponding HR-pQCT voxel models, µCT voxel models, and mechanical testing measurements. The PR models µFE results were indistinguishable from the voxel models constructed from the same HR-pQCT images. Moreover, the PR models significantly reduced the computational time for nonlinear µFE assessment of whole bone strength. After evaluating the accuracy and efficiency of the newly developed whole bone PR model, it was employed in a clinical study aimed at characterizing the abnormalities of trabecular plate and rod microstructure, cortical bone, and whole bone mechanical properties in postmenopausal women with vertebral fractures. Women with vertebral fractures had thinner cortical bone, and larger trabecular area compared to their non-fractured peers. ITS analyses suggested vertebral fracture subjects had deteriorated trabecular microstructure, evidenced by fewer trabecular plates, less axially aligned trabeculae and less trabecular connectivity at both radius and tibia. These microstructural deficits translated into reduced whole bone stiffness and yield load at radius and tibia as predicted by PR model nonlinear µFE simulation. More importantly, logistic regression indicated that whole bone yield load was effective in discriminating the vertebral fracture subjects from the non-fractured controls.

Thesis (B.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1978. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / B.S.

M.Med., Orthopaedic Surgery, Faculty of Health Sciences, University of the Witwatersrand, 2010

No description available.

Development of a hydrocarbon reservoir requires information about the type of fluid that saturates the pore space, and the permeability distribution that determines how the fluid can be extracted. The presence of fractures in a reservoir can be useful for obtaining this information. The main objectives of this thesis are to investigate how fracturing can be detected remotely using exploration seismology. Fracturing will effect seismic data in a number of ways. Firstly, if the fractures are aligned preferentially in some direction, the medium will exhibit long wavelength anisotropy. In turn, if wave propagation is not aligned with one of the symmetry axes of the effective medium then shear wave splitting will depend upon the properties of the fracture filling fluid. Secondly, elastic waves will experience attenuation and dispersion due to scattering and wave-induced fluid flow between the fractures and matrix porosity. This occurs because the fractures are more compliant than the background medium and therefore there will be a pressure gradient formed during passage of the wave, causing fluid to flow between fractures and background. If the direction of shear-wave propagation is not perpendicular or parallel to the plane of fracturing, the wave polarized in the plane perpendicular to the fractures is a quasi-shear mode, and therefore the shear-wave splitting will be sensitive to the fluid bulk modulus. / The magnitude of this sensitivity depends upon the extent to which fluid pressure can equilibrate between pores and fractures during the period of the deformation. In this thesis I use the anisotropic Gassmann equations and existing formulations for the excess compliance due to fracturing to estimate the splitting of vertically propagating shear-waves as a function of the fluid modulus for a porous medium with a single set of dipping fractures and with two conjugate fracture sets dipping with opposite dips to the vertical. This is achieved using two alternative approaches. In the first approach it is assumed that the deformation taking place is quasi-static. That is, the frequency of the elastic disturbance is low enough to allow enough time for fluid to flow between both the fractures and the pore space throughout the medium. In the second approach I assume that the frequency is low enough to allow fluid flow between a fracture set and the surrounding pore space, but high enough so that there is not enough time during the period of the elastic disturbance for fluid flow between different fracture sets to occur. It is found that the second approach yields a much stronger dependency of shear-wave splitting on the fluid modulus than the first one. This is a consequence of the fact that at higher wave frequencies there is not enough time for fluid pressure to equilibrate and therefore the elastic properties of the fluid have a greater effect on the magnitude of the shear-wave splitting. I conclude that the dependency of the shear-wave splitting on the fluid bulk modulus will be at its minimum for quasi-static deformations, and will increase with increasing wave frequency. / In order to treat the problem of dispersion and attenuation due to wave-induced fluid flow I consider interaction of a normally incident time-harmonic longitudinal plane wave with a circular crack imbedded in a porous medium governed by Biot’s equations of dynamic poroelasticity. The problem is formulated in cylindrical coordinates as a system of dual integral equations for the Hankel transform of the wave field, which is then reduced to a single Fredholm integral equation of the second kind. It is found that the scattering that takes place is predominantly due to wave induced fluid flow between the pores and the crack. The scattering magnitude depends on the size of the crack relative to the slow wave wavelength and has its maximum value when they are of the same order. I conclude that this poroelastic effect should not be neglected, at least at seismic frequencies. Using the solution of the scattering problem for a single crack and multiple-scattering theory I estimate the attenuation and dispersion of elastic waves taking place in a porous medium containing a sparse distribution of such cracks. I obtain from this analysis an effective velocity which at low frequencies reduces to the known static Gassmann result and a characteristic attenuation peak at the frequency such that the crack size and the slow wave wavelength are of the same order. / When comparing with a similar model in which multiple scattering effects are neglected I and that there is agreement at high frequencies and discrepancies at low frequencies. I conclude that the interaction between cracks should not be neglected at low frequencies, even in the limit of weak crack density. Since the models only agree with each other at high frequencies, when the time available for fluid diffusion is small, I conclude that the interaction between cracks that takes place as a result of fluid diffusion is negligible at high frequencies. I also compare my results with a model for spherical inclusions and find that the attenuation for spherical inclusions has exactly the same dependence upon frequency, but a difference in magnitude that depends upon frequency. Since the attenuation curves are very close at low frequencies I conclude that the effective medium properties are not sensitive to the shape of an inclusion at wavelengths that are large compared to the inclusion size. However at frequencies such that the wavelength is comparable to or smaller than the inclusion size the effective properties are sensitive to the greater compliance of the flat cracks, and more attenuation occurs at a given frequency as a result.

Massive shales and fractures are the main cause of seismic anisotropy in the upper-most part of the crust, caused either by sedimentary or tectonic processes. Neglecting the effect of seismic anisotropy in seismic processing algorithms may incorrectly image the seismic reflectors. This will also influence the quantitative amplitude analysis such as the acoustic or elastic impedance inversion and amplitude versus offsets analysis. Therefore it is important to obtain anisotropy parameters from seismic data. Conventional layer stripping inversion schemes and reflector based reflectivity inversion methods are solely dependent upon a specific reflector, without considering the effect of the other layers. This, on one hand, does not take the effect of transmission in reflectivity inversion into the account, and on the other hand, ignores the information from the waves travelling toward the lower layers. I provide a framework to integrate the information for each specific layer from all the rays which have travelled across this layer. To estimate anisotropy parameters I have implemented unconstrained minimization algorithms such as nonlinear conjugate gradients and variable metric methods, I also provide a nonlinear least square method, based on the Levenberg-Marquardt algorithm. In a stack of horizontal transversely isotropic layers with vertical axis of symmetry, where the layer properties are laterally invariant, we provide two different inversion schemes; traveltime and waveform inversion. / Both inversion schemes utilize compressional and joint compressional and converted shear waves. A new exact traveltime equation has been formulated for a dipping transversely isotropic system of layers. These traveltimes are also parametrized by the ray parameters for each ray element. I use the Newton method of minimization to estimate the ray parameter using a random prior model from a uniform distribution. Numerical results show that with the assumption of weak anisotropy, Thomsen’s anisotropy parameters can be estimated with a high accuracy. The inversion algorithms have been implemented as a software package in a C++ object oriented environment.

Bibliography: leaves 216-231. / xvii, 231, [99] leaves : / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Examines the sliding capability of external fixators under load and describes the development and testing of an external fixator capable of providing axial cyclic motion to a fracture site while a patient is walking. / Thesis (M.D.)--University of Adelaide, Dept. of Orthopaedics and Trauma, 1999?

This retrospective study investigated the incidence, characteristics, and risk factors of bone fracture among a group of 518 adults with severe mental retardation between 25 and 75 years old. Data were collected from a large state developmental center in the Western United States between April 1, 1991 and March 31, 1996. Ninety-six of 271 males and 133 of 247 females experienced 291 fractures during the study period. Relative risk of fracture for all males was .658 compared to 1.540 for females. Menopausal status did not significantly influence the risk of fractures among females. Risk of fracture by self-feeding ability ranged from 1.675 for individuals who were tube fed to .343 for those requiring no assistance during meals. As a group, individuals with a body mass index (BMI) less than 20 were at the greatest risk of fracture (RR=2.416). Males with BMI values between 20-25 (RR=.560) and greater than 25 (RR=.373) had a decreased risk of fracture. Ambulatory males and females had a significantly decreased risk of fracture (RR=.356 and .559 respectively). Rib, femur, vertebrae, and radial fractures accounted for nearly 60% of all fractures. The etiology of the 41% of fractures was of unknown origin. Transfers by developmental training personnel (10.3%), falls to the ground (15.8%), and accidents (32.6%) were also frequently related to fracture cause. Logistic regression analysis revealed the occurrence of any fracture was significantly associated with ambulation, calcium intake, body weight, self-feeding ability, and body mass index. / Graduation date: 1997

Spontaneous imbibition plays a very important role in the displacement mechanism of non-wetting fluid in naturally fractured reservoirs. We developed a new 2D two-phase finite element numerical model, as available commercial simulators cannot be used to model small-scale experiments with different boundary conditions as well as complex boundary conditions such as fractures and vugs. Starting with the basic equation of fluid flow, we derived the non-linear diffusion saturation equation. This equation cannot be put in weighted-integral weak variational form and hence Rayleigh-Ritz finite element method (FEM) cannot be applied. Traditionally, the way around it is to use higher order interpolation functions and use Galerkin FEM or reduce the differentiability requirement and use Mixed FEM formulation. Other FEM methods can also be used, but iterative nature of those methods makes them unsuitable for solving large-scale field problems. But if we truncate the non-linear terms and decouple the dependent variables, from the spatial as well as the temporal domains of the primary variable to solve them analytically, the non-linear FEM problem reduces to a simple weighted integral form, which can be put into its corresponding weak form. The advantage of using Rayleigh-Ritz method is that it has immediate effect on the computation time required to solve a particular problem apart from incorporating complex boundary conditions. We compared our numerical models with the analytical solution of this diffusion equation. We validated the FDM numerical model using X-Ray Tomography (CT) experimental data from the single-phase spontaneous imbibition experiment, where two simultaneously varying parameters of weight gain and CT water saturation were used and then went ahead and compared the results of FEM model to that of FDM model. A two-phase field size example was taken and results from a commercial simulator were compared to the FEM model to bring out the limitations of this approach.