Thesis (Ph.D.)--University of the Witwatersrand, Faculty of Engineering, 1988. / Mining induced fracturing and associated deformations can commonly be observed around deep gold mining excavations. As the rockmass behaviour and the stability of the excavations are directly influenced by these processes, a proper understanding of this influence would certainly improve current mining practices with respect to blasting, rock breaking, support design and mining lay-outs. The main subject of this thesis is the physics of failure and post failure behaviour of rock and similar materials. Failure is denned here as a state at which the material has been subjected to fracture and/or damage processes. The applicability of commonly used constitutive models in representing such failure and post failure processes has been investigated mainly by means of numerical simulations. Mechanisms which control fundamental fracture and damage processes have been analysed by comparing the results from relevant laboratory experiments with numerical models. Linear elastic fracture mechanics has been applied to explain and simulate the formation of large scale extension fractures which form in response to excessive tensile stresses. Using the flaw concept it is demonstrated that these fractures not only initiate and propagate from the surface of an opening in compressed rock, but that so called secondary fracturing can be initiated from within the solid rock as well. The effect of geological discontinuities such as bedding planes, faults and joints on the formation of (extension) fractures has also been investigated and it has been shown how the presence of such discontinuities can cause the formation o f additional fractures. Micro mechanical models have been, used to investigate the interaction and coalescence processes of micro fractures. It was found that the formation of large scale extension fracturing can be explained from such processes, but so called shear fractures could not directly be reproduced, although such a possibility has been claimed by previous researchers. The formation of shear fractures is of particular- interest as violent failure of rock, which is subjected to compressive stresses only, is often associated with such fractures. In an all compressive stress environment, only shear deformations would allow for the relief of excess stress and thus energy. The formation of shear fractures is associated with complex mechanisms and shear fractures can therefore not directly be represented by tingle cracks. In contrast to the propagation of tensile fractures, which can readily be explained by traditional fracture mechanics in terms of stress concentrations around the crack tip, the propagation of shear fractures requires a different explanation. In this thesis an attempt has nevertheless been made to reproduce shear fractures by direct application of fracture mechanics. This his been done by representing a shear fracture as a single crack and by assuming fracture growth criteria which are either based on critical excess shear stresses, or on a maximum energy release. Both criteria are completely empirical and require a value for the critical shear resistance in the same way as a critical tensile resistance is required to represent the formation of tensile fracture; , The determination of a critical tensile resistance ( Kk ) is relatively straight forward, as the formation of tensile fractures from a pre-existing flaw can be reproduced and observed in standard laboratory tests. The determination of a critical shear resistance is, however, not a common practice, as the formation of a shear fracture from a pre-existing flaw is very infrequently observed. The application of shear fracture growth criteria nevertheless resulted in plausible fracture patterns, which suggests that such criteria are realistic. It is argued here however that the formation of shear fractures cannot be associated with primary fracture growth, but rather with the localisation of failure and damage in an area which is subjected to plastic deformation. The application of fracture mechanics is therefore not correct from a fundamental point of view as these processes are not represented. For this reason plasticity theory has also been applied in order to simulate failure in general, and shear failure localisation in particular. It was in principle possible to reproduce the shear fractures with the use of this theory, but numerical restraints affected the results to such an extent that most of the simulations were not realistic. Plasticity theory can also be extended to include brittle behaviour by the use of so called strain softening models. The physical processes which lead to brittle failure are however not directly represented by such models and they may therefore not result in realistic failure patterns. It was in fact found that strain softening models could only produce realistic results if localisation of failure could be prevented. The effect of numerical restraints becomes even more obvious with a strain softening model in the case of failure localisation. While the plasticity models appear inappropriate in representing brittle failure, they demonstrated that plastic deformations can be associated with stress changes which may lead to subsequent brittle fracturing. Although only indirect attempts have been made to reproduce this effect, as appropriate numerical tools are not available, it is clear that many observations of extension fracturing could be explained by plastic deformations preceding the brittle fracturing processes. Many rocks are classified as brittle, but plastic deformation processes often occur during the damage processes as well. The sliding crack for instance, which is thought to represent many micro mechanical deformation processes in rock, directly induces plastic deformations when activated. A pure brittle rock, which may be defined as a rock in which absolutely no plastic deformation processes take place, may therefore only be of academic interest as it is inconceivable that such a rock materiel exists. Only in such an academic case would (linear) elastic fracture mechanics be directly applicable. As plastic deformation processes do play a role in real rock materials it is important to investigate their influence on subsequent brittle failure processes. The elastic stress distribution, which is often used to explain the onset of brittle fracturing, may be misleading as plastic deformations can substantially affect the stress distribution . -recediny fracture initiation. In an attempt to combine both plastic and brittle failure, use has been made of tessellation models, which in effect define potential fracture paths in a random mesh. The advantage of these models is that various failure criteria, with or without strain softening potential, can be used without the numerical restraints which are normally associated with the conventional continuum models. The results of these models are also not free from numerical artefacts, but they appear to be more realistic in general. One o f the m;ij, r conclusions based on these results is that shear failure does not occur in a localised fashion, but is associated with the uniform distribution and extension of damage. Shear failure, which can be related directly to plastic failure, can however induce brittle, tensile, failure due to stress redistribution. While the theories of fracture mechanics and plasticity are well established, their application to rock mechanical problems often leads to unrealistic results. Commonly observed firacture patterns in rock, loaded in compression, are most often not properly reproduced by numerical models for a combination of reasons. Either a model concentrates on the discrete fracturing processes, in which case the plastic deformation processes are ignored, or plasticity is represented, but brittle failure is pooxiy catered for. While theoretically a combination of these models might lead to better representations and simulations, numerical problems do affect all models to a certain extent and a practical solution is not immediately available. The results of numerical models can therefore only be analysed with caution and the underlying assumptions and numerical problems associated with a particular technique need to be appreciated before such results can be interpreted with any sense. Many of the problems are identified here and this may assist researchers in the interpretation of results from numerical simulations. Laboratory experiments, which have been chosen for analyses, involve specimens which have been subjected to compressive stresses and which contain openings from which failure and fracturing is initiated. Such specimens are less subjective to boundary influences and are far more representative of conditions around mining excavations than typical uni- and tri-axial tests. The uniform stress conditions in these latter tests allow boundary effects to dominate the stress concentrations, and thus failure initiation, in the specimens. The large stress gradients, which can be expected to occur around underground excavations, are not reproduced in such specimens. As a consequence failure is not u atained within a particular area, but spreads throughout the complete specimen in the uni- and tri-axial tests. Specimens containing openings are therefore far more likely to reproduce the fracture patterns which can be observed around deep level mining excavations. Numerical simulations of brittle, tensile fracturing around mining excavations resulted in consistent fracture patterns. Fracture patterns could however be strongly influenced by the presence of geological (pre-existing) discontinuities such as bedding planes. Although tensile stresses are often assumed to be absent around deej: <y vel excavations because typical hanging- and foot-walls are subjected to compressive horizontal strain and thus stress, the numerical models identified alternative locations o f Ix 'sile stress and also mechanisms which could induce secondary tensile stresses, A failure criterion has therefore been identified as the most likely cause of large scale fracturing while shear fracturing may only occur in the absence of such tensile stresses .and only as a consequence of failure localisation in damaged rock rather than fracture propagation (in solid rock). Geological discontinuities can easily induce tensile stresses vVher mobilised and may even replace the mining induced fractures by offering a more efficient meat s for energy release. The latter possibility is a true three dimensional issue which has not be en addressed any further in this study, but may be very relevant to jointed rock. Although dynamic failure has not directly been addressed, one of the micliamsms lor brittle, and thus stress relieving, failure under compressive strass conditi ons has been investigated in detail, namely shear fracturing. Shear fractures are effect vely the only discontinuities which allow for stress relief under such conditi ons', in the ibaence of preexisting, geological discontinuities, and are therefore quite rele vant to dynamic rock failure, such as rock bursts, in deep level mining conditions. Potential mechanisms for shear fracture formation and the numerical simulation of these features have been investigated and this may especially assist further research into rock bursts.

Ce travail de thèse est consacré à la manipulation et la déformation optique d'interfaces liquides molles, cela dans deux géométries fondamentales: plane et sphérique. Nous montrons alors que les déformations induites par pression de radiation optique permettent de déduire les propriétés des interfaces, comme la tension interfaciale par exemple. Dans le cadre de la déformation d'une interface liquide plane par pression de radiation, nous généralisons pour la première fois la manifestation électro-hydrodynamique des cônes de Taylor au régime optique, en montrant que des cônes liquides peuvent émerger sous fortes excitation laser. Nous avons alors caractérisé la morphologie de ces « cônes optiques » et nous montrons que l'angle de ces derniers dépend à la fois des paramètres de l'excitation laser mais aussi des caractéristiques des fluides. Une étude analytique ainsi qu'une étude numérique ont alors été menées afin de rendre compte des comportements observés.Afin d'étudier la déformation d'interfaces molles en géométrie sphérique, nous avons développé un double piège optique fibré en dispositif microfluidique dans une configuration inédite en termes de longueur d'onde excitatrice et de puissance laser. Nous avons alors appliqué notre dispositif à la déformation de vésicules en tant qu'objets modèles mous et nous montrons que notre double piège est bien adapté à la caractérisation rhéologique d'objets micrométriques déformables. Grâce à l'utilisation de faisceaux laser de forte puissance, nous mettons ici en évidence expérimentalement l'apparition d'un régime non-linéaire de déformation au sein de notre double piège optique. / This thesis work is devoted to the optical manipulation and deformation of soft liquid interfaces, in two fundamental geometries: plane and spherical. We then show that the deformations induced by optical radiation pressure allow to deduce the properties of interfaces, such as interfacial tension for example. In the framework of the deformation of a plane liquid interface by optical radiation pressure, we generalize for the first time the electro-hydrodynamic manifestation of Taylor cones to the optical regime, showing that liquid cones can emerge under intense laser excitation.We then characterized the morphology of these "optical cones" and we show that their angle depends both on the parameters of the laser excitation and on the characteristics of the fluids. An analytical study as well as a numerical investigation were then conducted to account for the observed behaviors. In order to study the deformation of soft interfaces in spherical geometry, we have developed a fiber-based dual-beam optical trap in a microfluidic device in a novel configuration in terms of excitation wavelength and laser power. We then applied our device to the deformation of vesicles as soft model objects and we show that our dual-beam trap is well adapted to the rheological characterization of deformable micron-sized objects. Thanks to the use of high laser power beams, we experimentally highlight the appearance of a non-linear deformation regime within our double optical trap.

Este trabalho apresenta a teoria de homotopia simples, desenvolvida por J. H. C. Whitehead, com o objetivo de obter um método para classificar espaços com o mesmo tipo de homotopia. Com esta motivação, Whitehead introduz o conceito de equivalência de homotopia simples entre complexos simpliciais, que posteriormente é generalizado para complexos CW, espaços criados pelo próprio Whitehead. Um resultado imediato desta teoria é que quando dois espaços têm o mesmo tipo de homotopia simples, eles têm o mesmo tipo de homotopia. A recíproca desta afirmação é então conjecturada. Mostraremos que trata-se de uma conjectura falsa, contudo a investigação de sua confirmação produz um material que toma rumo próprio. Nosso enfoque são os aspectos algébricos envolvidos nesta investigação / This work presents the simple-homotopy theory, developed by J. H. C. Whitehead, with the goal to get an method to classify spaces with the same homotopy type. So, with this motivation, Whitehead introduced the concept of simple-homotopy equivalence between simplicial complexes, that later was generalized for CW complexes, spaces created by himself. An immediate result of this theory is that, if two spaces have the same simple-homotopy type, they have the same homotopy type. Then, the reciprocal statement is conjectured. We will show that the conjecture is not true, but the research about its truthfulness produces a material that takes its own way. Our approach are the algebraic aspects involved in this research

O principal objetivo deste trabalho é realizar a análise estrutural de edifícios de andares múltiplos que apresentam núcleos resistentes, considerando a deformação pelo esforço cortante nos mesmos, bem como nos pilares. Para atingir esse objetivo, será preciso que o comportamento à flexão dos elementos verticais de contraventamento passe a ser regido pela teoria de barras de Timoshenko e não mais pela de Euler-Bernoulli. Foram então desenvolvidos algoritmos que, utilizando o Método dos Elementos Finitos (MEF), permitem calcular os fatores de forma de quaisquer seções transversais abertas de paredes delgadas pertencentes a núcleos estruturais, bem como a distribuição da tensão de cisalhamento na seção transversa em função do esforço cortante atuante. As alterações acima descritas foram feitas em um programa de análise de edifícios denominado CEASO 01, de autoria de MATIAS JR (1997). Embora esse programa realize análise não-linear geométrica, a consideração da deformação por cortante só foi implementada na análise linear. Apresentam-se, ao final, exemplos numéricos que permitem avaliar a influência da deformação pelo esforço cortante sobre os deslocamentos e esforços de núcleos resistentes e pilares. / The main aim of this work is to perform structural analysis of multistory buildings with resistant cores, taking into account shear deformation in those elements, as well as in columns. To achieve this objective, the flexural behaviour of vertical elements must be governed by Timoshenko beam theory, rather than the Euler-Bernoulli theory. Procedures using the finite element method (FEM) were developped, which enable to evaluate shear correction factors of generic thin-walled open sections and shear stress distribution as a function of the shear resultant. Changes described above were made in a structural analysis program named CEASO 01, whose author is MATIAS JR (1997). Even though this program is able to perform nonlinear analysis, only in linear analysis the effect of shear deformation is taken into account. Numerical examples are provided, which enable to evaluate the influence of taking into account shear deformation on displacements and stress resultants of resistant cores and columns.

Wong Ngai-ning. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 65-67). / Abstracts in English and Chinese. / Abstract --- p.ii / Content --- p.iv / List of Table --- p.v / List of Figures --- p.v / Acknowledgement --- p.vii / Dedication --- p.viii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Related work --- p.2 / Chapter 1.2 --- Background --- p.6 / Chapter 1.3 --- Contribution --- p.23 / Chapter 1.4 --- Thesis roadmap --- p.24 / Chapter 2 --- The Capacitance method --- p.25 / Chapter 2.1 --- Theoretical Comparison --- p.29 / Chapter 3 --- Collision detection --- p.32 / Chapter 3.1 --- Searching the hierarchy --- p.33 / Chapter 3.2 --- Neighborhood algorithm --- p.35 / Chapter 3.3 --- Regional sphere tree update --- p.38 / Chapter 4 --- Implementation --- p.41 / Chapter 4.1 --- System Architecture --- p.41 / Chapter 4.2 --- Multi-contact latency --- p.45 / Chapter 5 --- Result and Analysis --- p.46 / Chapter 5.1 --- Pre-computation --- p.46 / Chapter 5.2 --- Relation matrix Establishment --- p.47 / Chapter 5.3 --- Sphere tree construction --- p.49 / Chapter 5.4 --- Regional sphere tree update --- p.50 / Chapter 5.5 --- Graphic result --- p.52 / Chapter 6 --- Conclusion and Future work --- p.62 / Chapter 6.1 --- Conclusion --- p.62 / Chapter 6.2 --- Future work --- p.64 / Reference --- p.65 / Appendix A --- p.68 / Appendix B --- p.70

Current methodologies for characterization of tympanic membranes (TMs) have some limitations. They: are qualitative rather than quantitative, consist of single point mobility measurements, or only include one-dimensional deformation measurements. Furthermore, none of the current clinical tools for diagnosis of hearing losses have the capability to measure the shape of TM, which is very useful for anatomical or pathological investigations. The multi-wavelength lensless digital holography system (MLDHS) reported in this work consists of laser delivery (LD), optical head (OH), and computing platform (CP) subsystems, with capabilities of real-time, non-contact, full-field of view measurements. One version of the LD houses two tunable near-infrared external-cavity diode lasers with central wavelengths of 780.24nm and 779.74nm respectively, an acousto-optic modulator, and a laser-to-fiber mechanism. The output of the LD is delivered to an ultra-fast MEMS-based fiber optic switch and the light beam is directed to the OH, which is arranged to perform imaging and measurements by phase-shifting holography. The second LD version subsystem contains one tunable near-infrared diode laser in the range from 770nm to 789nm, an anamorphic prism pair, an acousto-optic modulator, a half-wave plate, and a fiber coupler assembly. The output of the LD is delivered to the OH directly. The OH is designed by 3D optical ray tracing simulations in which components are rotated at specific angles to overcome reflection issues. A high-resolution digital camera with pixel size of 6.7μm by 6.7μm in the OH is used for image recording at high-rates while the CP acquires and processes images in either time-averaged or double-exposure modes. The choice of working version depends on the requirements of the measurement and the sample under test. MLDHS can obtain shape and one-dimensional deformations along one optical axis (z-axis). In order to recover 3D deformations, assumptions based on elasticity theory are prerequisites for the calculations: (a) the TM is analyzed as a thin shell; (b) shape before and after deformation is considered nearly the same since acoustic pressure typically introduces nanometer scale deformations; and (c) normal vectors remain perpendicular to the deformed mid-plane of the TM. Another part of this Thesis is the design and prototyping of the MLDHS, which translates this holographic platform into a simple and compact holographic instrument for measurements of the visible tympanic-membrane motions in live patients. Therefore, the OH subsystem needs to be light and portable, as it can be mounted on a robotic arm be near the ear canal, while the LD subsystem needs to be stable and safely protected. Preliminary results of acoustically induced 3D deformations and shape measurements by a single instrument that demonstrate the capabilities of the devices developed in this Thesis are presented.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Includes bibliographical references. / by I-Wei Chen. / Ph.D.

There are many mathematical and engineering methods, problems and experiments which make use of the finite element method. For any given use of the finite element method we get an approximate solution and we usually wish to have some indication of the accuracy in the approximation. In the case when the calculation is done to estimate a quantity of interest the indication of the accuracy is concerned with estimating the difference between the unknown exact value and the finite element approximation. With a means of estimating the error, this can sometimes be used to determine how to improve the accuracy by repeating the computation with a finer mesh. A large part of this thesis is concerned with a set-up of this type with the physical problem described in a weak form and with the error in the estimate of the quantity of interest given in terms of a function which solves a related dual problem. We consider this in the case of modelling the large deformation of thin incompressible isotropic hyperelastic sheets under pressure loading. We assume throughout that the thin sheet can be modelled as a membrane, which gives us a two dimensional description of a three dimensional deformation and this simplifies further to a one space dimensional description in the axisymmetric case when we use cylindrical polar coordinates. In the general case we consider the deformation under quasi-static conditions and in the axisymmetric case we consider both quasi-static conditions and dynamic conditions, which involves the full equations of motion, which gives three different problems. In all the three problems we describe how to get the finite element solution, we describe associated dual problems, we describe how to solve these dual problems and we consider using the dual solutions in error estimation. There is hence a common framework. The details however vary considerably and much of the thesis is in describing each case.

by Ng, Hiu Tung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 121-123). / by Ng, Hiu Tung. / Acknowledgement --- p.i / Abstract --- p.ii / Table of Contents --- p.iv / List of Figures --- p.viii / List of Tables --- p.xi / Chapter Chapter One --- Introduction --- p.1 / Chapter 1.1 --- Non-destructive testing techniques --- p.2 / Chapter 1.1.1 --- Liquid penetration technique --- p.2 / Chapter 1.1.2 --- Electrical methods (Eddy current testing) --- p.3 / Chapter 1.1.3 --- Ultrasonic testing --- p.4 / Chapter 1.1.4 --- Radiography --- p.5 / Chapter 1.1.5 --- Magnetic methods --- p.6 / Chapter 1.2 --- The development of Barkhausen and magnetoacoustic emissions --- p.7 / Chapter 1.2.1 --- Barkhausen emission --- p.7 / Chapter 1.2.2 --- Magnetoacoustic emission --- p.8 / Chapter 1.3 --- The advantages of using Barkhausen and magnetoacoustic emission over the other nondestructive techniques --- p.10 / Chapter Chapter Two --- Fundamental concept in ferromagnetic materials --- p.12 / Chapter 2.1 --- Ferromagnetism --- p.12 / Chapter 2.1.1 --- Curie point --- p.13 / Chapter 2.1.2 --- Hysteresis loop --- p.14 / Chapter 2.2 --- Magnetic domains --- p.17 / Chapter 2.2.1 --- Magneto static energy --- p.17 / Chapter 2.2.2 --- Structure of domain wall --- p.19 / Chapter 2.2.3 --- Domain wall motion --- p.21 / Chapter 2.2.4 --- Domain nucleation --- p.22 / Chapter 2.3 --- Magnetostriction --- p.28 / Chapter 2.3.1 --- Spontaneous magnetostriction --- p.28 / Chapter 2.3.2 --- Saturation magnetostriction --- p.29 / Chapter 2.3.3 --- Field-induced magnetostriction --- p.29 / Chapter 2.3.4 --- Magnetostriction of polycrystalline --- p.30 / Chapter 2.4 --- Effect of stress on magnetic properties --- p.36 / Chapter 2.4.1 --- Stress --- p.36 / Chapter 2.4.2 --- Effect of stress on the magnetization --- p.37 / Chapter 2.4.3 --- Effect of stress on the magnetostriction --- p.38 / Chapter 2.5 --- Eddy current shielding --- p.41 / Chapter Chapter Three --- Barkhausen emission and magnetoacoustic emission --- p.42 / Chapter 3.1 --- Barkhausen emission --- p.42 / Chapter 3.1.1 --- The wall potential energy model of Barkhausen emission --- p.43 / Chapter 3.1.2 --- Typical BE profiles --- p.45 / Chapter 3.2 --- Magnetoacoustic emission --- p.48 / Chapter 3.2.1 --- Magnetoacoustic emission model --- p.48 / Chapter 3.2.2 --- Typical MAE profiles --- p.50 / Chapter Chapter Four --- Instrumentation --- p.52 / Chapter 4.1 --- Introduction --- p.52 / Chapter 4.2 --- Experimental setup for Barkhausen emission --- p.53 / Chapter 4.3 --- Experimental setup for magnetoacoustic emission --- p.56 / Chapter 4.4 --- Specimen treatment --- p.58 / Chapter 4.4.1 --- Furnace --- p.58 / Chapter 4.4.2 --- Instron loading machine --- p.60 / Chapter 4.4.3 --- Optical microscopy --- p.60 / Chapter 4.4.4 --- Vicker's hardness tester --- p.61 / Chapter Chapter Five --- Effect of field frequency and strength on Barkhausen emission in mild steel and nickel --- p.66 / Chapter 5.1 --- Introduction --- p.66 / Chapter 5.2 --- Experiments --- p.67 / Chapter 5.3 --- Results and discussions --- p.68 / Chapter 5.4 --- Conclusions --- p.76 / Chapter Chapter Six --- Effect of residual stress on Barkhausen and magnetoacoustic emissions in steel bar --- p.77 / Chapter 6.1 --- Introduction --- p.77 / Chapter 6.2 --- Experiments --- p.81 / Chapter 6.3 --- Results and discussions --- p.84 / Chapter 6.3.1 --- BE profiles --- p.84 / Chapter 6.3.2 --- MAE profiles --- p.85 / Chapter 6.3.3 --- Optical microscopy and hardness measurements --- p.85 / Chapter 6.4 --- Conclusions --- p.92 / Chapter Chapter Seven --- Effect of residual stress on Barkhausen and magnetoacoustic emissions in a nickel bar --- p.93 / Chapter 7.1 --- Introduction --- p.93 / Chapter 7.2 --- Experiments --- p.96 / Chapter 7.3 --- Results and discussions --- p.97 / Chapter 7.3.1 --- Hardness and optical microscopy measurement --- p.97 / Chapter 7.3.2 --- BE profiles --- p.98 / Chapter 7.3.3 --- MAE profiles --- p.99 / Chapter 7.4 --- Comparison of nickel and mild steel --- p.106 / Chapter 7.5 --- Conclusions --- p.108 / Chapter Chapter Eight --- Effect of dynamic stress on Barkhausen emission in mild steel --- p.109 / Chapter 8.1 --- Introduction --- p.109 / Chapter 8.2 --- Experiments --- p.110 / Chapter 8.3 --- Results and discussions --- p.112 / Chapter 8.4 --- Conclusions --- p.118 / Chapter Chapter Nine --- Conclusions --- p.119 / References --- p.121

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