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1
Luo, Sai, and 罗赛. "Fabric evolution of two-dimensional idealized particle assemblage during shear." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2012. http://hub.hku.hk/bib/B49799721.
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Microstructure or fabric definitely affects macroscopic mechanical behavior of granular material. It is also well-observed that fabric evolves with shearing or plastic deformation. In this study, a series of two-dimensional numerical direct shear tests are carried out with the discrete element method, to study the initial fabric effect on global material responses and their micro-macroscopic relations. Idealized particle assemblages are made up of mono-size elongated particles and are prepared by a “deposition” method. Elongated particle is modeled by the built-in clump logic, in which constitutive balls are joined together without further breakage. In the deposition method, there are three controlling parameters, including, deposited direction, inter-particle friction coefficient and particle number, to prepare specimens with similar initial density but different initial packing or fabric. Three types of fabric of particle assemblages are examined quantitatively and are monitored during shearing, including, particle orientations (PO), contact normal forces (NF), and void spaces (VS). These fabric distributions are described by two parameters―anisotropic degree ( ) and orientation angle ( ), with clear physical implications. An additional parameter ( ) describing the average size of voids, is used to quantify void perimeter. It is found that this parameter has a relation with the assemblage’s volumetric response. C
With the systematic and meticulous quantification method, the linkage between the macroscopic and microscopic responses of particle assemblages is discussed quantitatively. The results show that the initial packing affects the shear zone thickness, initial stiffness, peak strength, and dilation rate. In the shear zone, particle orientations do not exhibit a unique state at the final stage of direct shearing. At that state, strong normal forces and strong voids are parallel to the major principal stress direction. It seems that the initial packing does not affect their final distributions. At the end of reverse shearing, strong voids and strong normal forces in the shear zone give an essentially unique state, and their preferential directions are related to the changed loading direction. However, apparent stable particle orientations are still affected by the initial fabric.published_or_final_version
Civil Engineering
Master
Master of Philosophy
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PRUETT, CHARLES DAVID. "NUMERICAL SIMULATION OF NONLINEAR WAVES IN FREE SHEAR LAYERS (MIXING, COMPUTATIONAL, FLUID DYNAMICS, HYDRODYNAMIC STABILITY, SPATIAL, FLUID FLOW MODEL)." Diss., The University of Arizona, 1986. http://hdl.handle.net/10150/183869.
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A numerical model has been developed which simulates the three-dimensional stability and transition of a periodically forced free shear layer in an incompressible fluid. Unlike previous simulations of temporally evolving shear layers, the current simulations examine spatial stability. The spatial model accommodates features of free shear flow, observed in experiments, which in the temporal model are precluded by the assumption of streamwise periodicity; e.g., divergence of the mean flow and wave dispersion. The Navier-Stokes equations in vorticity-velocity form are integrated using a combination of numerical methods tailored to the physical problem. A spectral method is adopted in the spanwise dimension in which the flow variables, assumed to be periodic, are approximated by finite Fourier series. In complex Fourier space, the governing equations are spatially two-dimensional. Standard central finite differences are exploited in the remaining two spatial dimensions. For computational efficiency, time evolution is accomplished by a combination of implicit and explicit methods. Linear diffusion terms are advanced by an Alternating Direction Implicit/Crank-Nicolson scheme whereas the Adams-Bashforth method is applied to convection terms. Nonlinear terms are evaluated at each new time level by the pseudospectral (collocation) method. Solutions to the velocity equations, which are elliptic, are obtained iteratively by approximate factorization. The spatial model requires that inflow-outflow boundary conditions be prescribed. Inflow conditions are derived from a similarity solution for the mean inflow profile onto which periodic forcing is superimposed. Forcing functions are derived from inviscid linear stability theory. A numerical test case is selected which closely parallels a well-known physical experiment. Many of the aspects of forced shear layer behavior observed in the physical experiment are captured by the spatial simulation. These include initial linear growth of the fundamental, vorticity roll-up, fundamental saturation, eventual domination of the subharmonic, vortex pairing, emergence of streamwise vorticity, and temporary stabilization of the secondary instability. Moreover, the spatial simulation predicts the experimentally observed superlinear growth of harmonics at rates 1.5 times that of the fundamental. Superlinear growth rates suggest nonlinear resonances between fundamental and harmonic modes which are not captured by temporal simulations.
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Amany, Aya Nicole Marie. "Characterization of shear and bending stiffness for optimizing shape and material of lightweight beams." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=112553.
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Optimized slender and short-thick beams are used in building, aircraft and machine structures to increase performance at a lower material cost. A previous work proposes an optimum shape, material and size selection model to design lightweight slender beams under pure bending. In short-thick beams, the transverse shear effects are no longer negligible and impact the choice of the optimum shape. This work extends such an optimum selection model to consider both slender and short-thick beams, by formulating the total beam stiffness design requirement as a combination of shear and bending stiffness. Selection charts are developed to show the impact of design variables, such as shape, size, material and slenderness, on the total beam stiffness. The model of total beam stiffness is validated against computational results from finite element analyses of beam models. A case study demonstrates the use of the selection charts to compare the performance of beams at the conceptual design stage.
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Reimnitz, Marc. "Shear-slip induced seismic activity in underground mines : a case study in Western Australia." University of Western Australia. School of Civil and Resource Engineering, 2004. http://theses.library.uwa.edu.au/adt-WU2004.0062.
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Mining induced seismic activity and rockbursting are critical concerns for many underground operations. Seismic activity may arise from the crushing of highly stressed volumes of rock around mine openings or from shear motion on planes of weakness. Shear-slip on major planes of weakness such as faults, shear zones and weak contacts has long been recognized as a dominant mode of failure in underground mines. In certain circumstances, it can generate large seismic events and induce substantial damage to mine openings. The Big Bell Gold mine began experiencing major seismic activity and resultant damage in 1999. Several seismic events were recorded around the second graphitic shear between April 2000 and February 2002. It is likely that the seismic activity occurred as a result of the low strength of the shear structure combined with the high level of mining induced stresses. The stability of the second graphitic shear was examined in order to gain a better understanding of the causes and mechanisms of the seismic activity recorded in the vicinity of the shear structure as mining advanced. The data were derived from the observation of the structure exposures, numerical modelling and seismic monitoring. The numerical modelling predictions and the interpreted seismic monitoring data were subsequently compared in order to identify potential relationships between the two. This thesis proposes the Incremental Work Density (IWD) as a measure to evaluate the relative likelihood of shear-slip induced seismic activity upon major planes of weakness. IWD is readily evaluated using numerical modelling and is calculated as the product of the average driving shear stress and change in inelastic shear deformation during a given mining increment or step. IWD is expected to correlate with shear-slip induced seismic activity in both space and time. In this thesis, IWD was applied to the case study of the second graphitic shear at the Big Bell mine. Exposures of the second graphitic shear yielded information about the physical characteristics of the structure and location within the mine. Numerical modelling was used to examine the influence of mining induced stresses on the overall behaviour of the shear structure. A multi-step model of the mine was created using the three- dimensional boundary element code of Map3D. The shear structure was physically incorporated into the model in order to simulate inelastic shear deformation. An elasto-plastic Mohr-Coulomb material model was used to describe the structure behaviour. The structure plane was divided into several elements in order to allow for the comparison of the numerical modelling predictions and the interpreted seismic data. Stress components, deformation components and IWD values were calculated for each element of the shear structure and each mining step. The seismic activity recorded in the vicinity of the second graphitic shear was back analysed. The seismic data were also gridded and smoothed. Gridding and smoothing of individual seismic moment and seismic energy values resulted in the definition of indicators of seismic activity for each element and mining step. The numerical model predicted inelastic shear deformation upon the second graphitic shear as mining advanced. The distribution of modelled IWD suggested that shear deformation was most likely seismic upon a zone below the stopes and most likely aseismic upon the upper zone of the shear structure. The distribution of seismic activity recorded in the vicinity of the shear structure verified the above predictions. The seismic events predominantly clustered upon the zone below the stopes. The results indicated that the seismic activity recorded in the vicinity of the second graphitic shear was most likely related to both the change in inelastic shear deformation and the level of driving shear stress during mechanical shearing. Time distribution of the seismic events also indicated that shear deformation and accompanying seismic activity were strongly influenced by mining and were time-dependant. Seismic activity in the vicinity of the second graphitic shear occurred as a result of the overall inelastic shear deformation of the shear structure under mining induced stresses. A satisfactory relationship was found between the spatial distribution of modelled IWD upon the shear structure and the spatial distribution of interpreted seismic activity (measured as either smoothed seismic moment or smoothed seismic energy). Seismic activity predominantly clustered around a zone of higher IWD upon the second graphitic shear as mining advanced. However, no significant statistical relationship was found between the modelled IWD and the interpreted seismic activity. The lack of statistical relationship between the modelled and seismic data may be attributed to several factors including the limitations of the techniques employed (e.g. Map3D modelling, seismic monitoring) and the complexity of the process involved.
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Stephens, Max Taylor. "Numerical and Experimental Analysis of Composite Sandwich Links for the LCF System." PDXScholar, 2011. https://pdxscholar.library.pdx.edu/open_access_etds/579.
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Shear links are used as fuse elements in lateral load resisting systems to provide ductility and dissipate seismic energy. These links have traditionally been employed in eccentrically braced frames, but have more recently been suggested for use in the innovative linked column frame system (LCF). Current design specifications for shear links require intermediate web stiffeners to provide out-of-plane web stability so ductility requirements can be achieved. This research focused on moving from discrete transverse web stiffening to continuously stiffened webs in built up shear links. Built up links were designed to yield in shear when subjected to severe cyclic loading, however the webs of the links were designed using two metal sheets joined by an elastic core. These composite "sandwich" webs allowed for an increase in web thickness (and inherent flexural rigidity) without increasing the shear strength of the links. Numerical and experimental investigations were conducted to assess the performance of composite sandwich links subjected to severe loading. Numerical results showed improved web behavior in sandwich links in which the core material was assigned an elastic modulus greater than 5000psi. Due to fabrication limitations, experimental specimens were fabricated with a core material elastic modulus of 1000psi. These specimens did not perform as well as unstiffened base case links in terms global hysteretic behavior or ductility.
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To, Chiu-yin, and 杜昭彥. "A unified elasto-plastic model for saturated loosely compacted completely decomposed granite." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B40203554.
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Wayman, Brian H. "Arterial Response to Local Mechanical Variables: The Effects of Circumferential and Shear Stress." Diss., Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/22611.
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Arteries respond to changes in global mechanical parameters (pressure, flow rate, and longitudinal stretching) by remodeling to restore local parameters (circumferential stress, shear stress, and axial strain) to baseline levels. Because a change in a single global parameter results in changes of multiple local parameters, the effects of individual local parameters on remodeling remain unknown. This study uses a novel approach to study remodeling in organ culture based on independent control of local mechanical parameters. The approach is illustrated by studying the effects of circumferential and shear stress on remodeling-related biological markers. Porcine carotid arteries were cultured for three days at a circumferential stress of 50 kPa or 150 kPa or, in separate experiments, a shear stress of 0.75 Pa or 2.25 Pa. At high circumferential stress, matrix synthesis, smooth muscle cell proliferation, and cell death are significantly greater, but matrix metalloproteinase-2 (MMP-2) and pro-MMP-2 activity are significantly less. In contrast, biological markers measured were unaffected by shear stress. Applications of the proposed approach for improved understanding of remodeling, optimizing mechanical conditioning of tissue engineered arteries, and selection of experimentally motivated growth laws are discussed.
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Evans, T. Matthew. "Microscale Physical and Numerical Investigations of Shear Banding in Granular Soils." Diss., Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/7576.
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Under loading conditions found in many geotechnical structures, it is common to observe failure in zones of high localized strain called shear bands. Existing models predict these localizations, but provide little insight into the micromechanics within the shear bands. This research captures the variation in microstructure inside and outside of shear bands that were formed in laboratory plane strain and two-dimensional discrete element method (DEM) biaxial compression experiments.
Plane strain compression tests were conducted on dry specimens of Ottawa 20-30 sand to calibrate the device, assess global response repeatability, and develop a procedure to quantitatively define the onset of localization. A new methodology was employed to quantify and correct for the additional stresses imparted by the confining membrane in the vicinity of the shear band. Unsheared and sheared specimens of varying dilatancy were solidified using a two-stage resin impregnation procedure. DEM tests were performed using an innovative servo-controlled flexible lateral confinement algorithm to provide additional insights into laboratory results.
The solidified specimens were sectioned and the resulting surfaces prepared for microstructure observation using bright field microscopy and morphological analysis. Local void ratio distributions and their statistical properties were determined and compared. Microstructural parameters for subregions in a grid pattern and along predefined inclined zones were also calculated. Virtual surfaces parallel to the shear band were identified and their roughnesses assessed. Similar calculations were performed on the DEM simulations at varying strain levels to characterize the evolution of microstructure with increasing strain.
The various observations showed that the mean, standard deviation, and entropy of the local void ratio distributions all increased with increasing strain levels, particularly within regions of high local strains. These results indicate that disorder increases within a shear band and that the soil within the shear band does not adhere to the classical concept of critical state, but reaches a terminal void ratio that is largely a function of initial void ratio. Furthermore, there appears to be a transition zone between the far field and the fully formed shear block, as opposed to an abrupt delineation as traditionally inferred.
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Pinilla, Camilo Ernesto. "Numerical simulation of shear instability in shallow shear flows." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=115697.
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The instabilities of shallow shear flows are analyzed to study exchanges processes across shear flows in inland and coastal waters, coastal and ocean currents, and winds across the thermal-and-moisture fronts. These shear flows observed in nature are driven by gravity and governed by the shallow water equations (SWE). A highly accurate, and robust, computational scheme has been developed to solve these SWE. Time integration of the SWE was carried out using the fourth-order Runge-Kutta scheme. A third-order upwind bias finite difference approximation known as QUICK (Quadratic Upstream Interpolation of Convective Kinematics) was employed for the spatial discretization. The numerical oscillations were controlled using flux limiters for Total Variation Diminishing (TVD). Direct numerical simulations (DNS) were conducted for the base flow with the TANH velocity profile, and the base flow in the form of a jet with the SECH velocity profile. The depth across the base flows was selected for the' balance of the driving forces. In the rotating flow simulation, the Coriolis force in the lateral direction was perfectly in balance with the pressure gradient across the shear flow during the simulation. The development of instabilities in the shear flows was considered for a range of convective Froude number, friction number, and Rossby number. The DNS of the SWE has produced linear results that are consistent with classical stability analyses based on the normal mode approach, and new results that had not been determined by the classical method. The formation of eddies, and the generation of shocklets subsequent to the linear instabilities were computed as part of the DNS. Without modelling the small scales, the simulation was able to produce the correct turbulent spreading rate in agreement with the experimental observations. The simulations have identified radiation damping, in addition to friction damping, as a primary factor of influence on the instability of the shear flows admissible to waves. A convective Froude number correlated the energy lost due to radiation damping. The friction number determined the energy lost due to friction. A significant fraction of available energy produced by the shear flow is lost due the radiation of waves at high convective Froude number. This radiation of gravity waves in shallow gravity-stratified shear flow, and its dependence on the convective Froude number, is shown to be analogous to the Mach-number effect in compressible flow. Furthermore, and most significantly, is the discovery from the simulation the crucial role of the radiation damping in the development of shear flows in the rotating earth. Rings and eddies were produced by the rotating-flow simulations in a range of Rossby numbers, as they were observed in the Gulf Stream of the Atlantic, Jet Stream in the atmosphere, and various fronts across currents in coastal waters.
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Guvenen, Haldun. "Aerodynamics of bodies in shear flow." Diss., The University of Arizona, 1989. http://hdl.handle.net/10150/184917.
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This dissertation investigates spanwise periodic shear flow past two-dimensional bodies. The flow is assumed to be inviscid and incompressible. Using singular perturbation techniques, the solution is developed for ε = L/ℓ ≪ 1, where L represents body cross-sectional size, and ℓ the period of the oncoming flow U(z). The singular perturbation analysis involves three regions: the inner, wake and outer regions. The leading order solutions are developed in all regions, and in the inner region higher order terms are obtained. In the inner region near the body, the primary flow (U₀, V₀, P₀) corresponds to potential flow past the body with a local free stream value of U(z). The spanwise variation in U(z) produces a weak O(ε) secondary flow W₁ in the spanwise direction. As the vortex lines of the upstream flow are convected downstream, they wrap around the body, producing significant streamwise vorticity in a wake region of thickness O(L) directly behind the body. This streamwise vorticity induces a net volume flux into the wake. In the outer region far from the body, a nonlifting body appears as a distribution of three-dimensional dipoles, and the wake appears as a sheet of mass sinks. Both singularity structures must be included in describing the leading outer flow. For lifting bodies, the body appears as a lifting line, and the wake appears as a sheet of shed vorticity. The trailing vorticity is found to be equal to the spanwise derivative of the product of the circulation and the oncoming flow. For lifting bodies the first higher order correction to the inner flow is the response of the body to the downwash produced by the trailing vorticity. At large distances from the body, the flow takes on remarkably simple form.
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McKellar, Dougan Kelk. "A dislocation model of plasticity with particular application to fatigue crack closure." Thesis, University of Oxford, 2001. http://ora.ox.ac.uk/objects/uuid:45183b90-017f-4ac1-9550-94772a0ca88b.
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The ability to predict fatigue crack growth rates is essential in safety critical systems. The discovery of fatigue crack closure in 1970 caused a flourish of research in attempts to simulate this behaviour, which crucially affects crack growth rates. Historically, crack tip plasticity models have been based on one-dimensional rays of plasticity emanating from the crack tip, either co-linear with the crack (for the case of plane stress), or at a chosen angle in the plane of analysis (for plane strain). In this thesis, one such model for plane stress, developed to predict fatigue crack closure, has been refined. It is applied to a study of the relationship between the apparent stress intensity range (easily calculated using linear elastic fracture mechanics), and the true stress intensity range, which includes the effects of plasticity induced fatigue crack closure. Results are presented for all load cases for a finite crack in an infinite plane, and a method is demonstrated which allows the calculation of the true stress intensity range for a growing crack, based only on the apparent stress intensity range for a static crack. Although the yield criterion is satisfied along the plastic ray, these one-dimensional plasticity models violate the yield criterion in the area immediately surrounding the plasticity ray. An area plasticity model is therefore required in order to model the plasticity more accurately. This thesis develops such a model by distributing dislocations over an area. Use of the model reveals that current methods for incremental plasticity algorithms using distributed dislocations produce an over-constrained system, due to misleading assumptions concerning the normality condition. A method is presented which allows the system an extra degree of freedom; this requires the introduction of a parameter, derived using the Prandtl-Reuss flow rule, which relates the magnitude of slip on complementary shear planes. The method is applied to two problems, confirming its validity.
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Song, Charlotte Kathryn Cody. "Hydrodynamic stability of confined shear-driven flows." Diss., Georgia Institute of Technology, 2003. http://hdl.handle.net/1853/17662.
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Mercer, Geoffry Norman. "On standing waves and models of shear dispersion /." Title page, contents and summary only, 1992. http://web4.library.adelaide.edu.au/theses/09PH/09phm5541.pdf.
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Corteen, Jacob. "Shear banding in metallic glasses : a mathematical perspective inspired by soil mechanics." Thesis, University of Sheffield, 2014. http://etheses.whiterose.ac.uk/6473/.
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There have been many approaches to engineering toughness in metallic glasses. Some have worked in composites, such as the transformation-toughened examples developed recently. Others have delved into the fundamental nature of deformation in these systems. Here, a number of mathematical models from other fields are applied in order to shed light on some of these advances. A model of transformation toughening more typically used in ceramics is adapted to consider the question of whether martensitic transformation in CuZr austenitic nanocrystals can in fact toughen the surrounding glass by the same mechanism as is typically invoked for crystalline materials. The results draw that explanation into question - the volume change associated with transformation in that system is just too small to significantly modify the shear band tip stress state, and the shape strain terms are constrained by variant self-accommodation and matters of orientation. A model developed to describe dilatant shear banding in granular media is then adapted to draw new insight on the same problem in metallic glasses. By modelling the glassy system as made up of clusters that behave like particles in sand or gravel, arranged into load-bearing force chains that fail by buckling, the behaviour of the system is shown to depend on a series of spring constants that represent the local packing and bonding in the glass. These spring constants emerge as a new order parameter, promising the possibility of a direct quantitative link between the state of structural order and the degree of dilatation associated with deformation. The new order parameters represent a first step to bridging the gap between nanoscale bonding and structure, and larger-scale properties.
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Warren, Paul A. "Mathematical models of 3-D ocular mechanics and control." Thesis, University of Sheffield, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.312221.
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Hipp, Hans Christoph 1959. "Numerical investigation of mode interaction in free shear layers." Thesis, The University of Arizona, 1988. http://hdl.handle.net/10150/276871.
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Numerical simulations of incompressible, two-dimensional, monochromatically and bichromatically forced laminar free shear layers are performed on the basis of a vorticity-velocity formulation of the complete Navier-Stokes equations employing central finite differences. Spatially periodic shear layers developing in time (temporal model) are compared with shear layers developing in the stream-wise direction (spatial model). The regimes of linear growth and saturation of the fundamental are quantitatively scrutinized, the saturation of the subharmonic and vortex merging are investigated, and the effects of a forcing phase-shift between fundamental and subharmonic. For the spatial model the appearance of an unforced subharmonic was also examined. It was found that contrary to temporal shear layers a significant control of vortex merging by means of a forcing phase-shift and vortex shredding are not possible in spatial shear layers due to strong dispersion.
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Lee, M. E. M. "Mathematical models of the carding process." Thesis, University of Oxford, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249543.
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Carding is an essential pre-spinning process whereby masses of dirty tufted fibres are cleaned, disentangled and refined into a smooth coherent web. Research and development in this `low-technology' industry have hitherto depended on empirical evidence. In collaboration with the School of Textile Industries at the University of Leeds, a mathematical theory has been developed that describes the passage of fibres through the carding machine. The fibre dynamics in the carding machine are posed, modelled and simulated by three distinct physical problems: the journey of a single fibre, the extraction of fibres from a tuft or tufts and many interconnecting, entangled fibres. A description of the life of a single fibre is given as it is transported through the carding machine. Many fibres are sparsely distributed across machine surfaces, therefore interactions with other neighbouring fibres, either hydrodynamically or by frictional contact points, can be neglected. The aerodynamic forces overwhelm the fibre's ability to retain its crimp or natural curvature, and so the fibre is treated as an inextensible string. Two machine topologies are studied in detail, thin annular regions with hooked surfaces and the nip region between two rotating drums. The theoretical simulations suggest that fibres do not transfer between carding surfaces in annular machine geometries. In contrast to current carding theories, which are speculative, a novel explanation is developed for fibre transfer between the rotating drums. The mathematical simulations describe two distinct mechanisms: strong transferral forces between the taker-in and cylinder and a weaker mechanism between cylinder and doffer. Most fibres enter the carding machine connected to and entangled with other fibres. Fibres are teased from their neighbours and in the case where their neighbours form a tuft, which is a cohesive and resistive fibre structure, a model has been developed to understand how a tuft is opened and broken down during the carding process. Hook-fibre-tuft competitions are modelled in detail: a single fibre extracted from a tuft by a hook and diverging hook-entrained tufts with many interconnecting fibres. Consequently, for each scenario once fibres have been completely or partially extracted, estimates can be made as to the degree to which a tuft has been opened-up. Finally, a continuum approach is used to simulate many interconnected, entangled fibre-tuft populations, focusing in particular on their deformations. A novel approach describes this medium by density, velocity, directionality, alignment and entanglement. The materials responds to stress as an isotropic or transversely isotropic medium dependent on the degree of alignment. Additionally, the material's response to stress is a function of the degree of entanglement which we describe by using braid theory. Analytical solutions are found for elongational and shearing flows, and these compare very well with experiments for certain parameter regimes.
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Moore, Matthew Richard. "New mathematical models for splash dynamics." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:c94ff7f2-296a-4f13-b04b-e9696eda9047.
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In this thesis, we derive, extend and generalise various aspects of impact theory and splash dynamics. Our methods throughout will involve isolating small parameters in our models, which we can utilise using the language of matched asymptotics. In Chapter 1 we briefly motivate the field of impact theory and outline the structure of the thesis. In Chapter 2, we give a detailed review of classical small-deadrise water entry, Wagner theory, in both two and three dimensions, highlighting the key results that we will use in our extensions of the theory. We study oblique water entry in Chapter 3, in which we use a novel transformation to relate an oblique impact with its normal-impact counterpart. This allows us to derive a wide range of solutions to both two- and three-dimensional oblique impacts, as well as discuss the limitations and breakdown of Wagner theory. We return to vertical water-entry in Chapter 4, but introduce the air layer trapped between the impacting body and the liquid it is entering. We extend the classical theory to include this air layer and in the limit in which the density ratio between the air and liquid is sufficiently small, we derive the first-order correction to the Wagner solution due to the presence of the surrounding air. The model is presented in both two dimensions and axisymmetric geometries. In Chapter 5 we move away from Wagner theory and systematically derive a series of splash jet models in order to find possible mechanisms for phenomena seen in droplet impact and droplet spreading experiments. Our canonical model is a thin jet of liquid shot over a substrate with a thin air layer trapped between the jet and the substrate. We consider a variety of parameter regimes and investigate the stability of the jet in each regime. We then use this model as part of a growing-jet problem, in which we attempt to include effects due to the jet tip. In the final chapter we summarise the main results of the thesis and outline directions for future work.
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Huang, Xin, and 黃昕. "Exploring critical-state behaviour using DEM." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2014. http://hdl.handle.net/10722/206742.
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The critical state soil mechanics (CSSM) framework originally proposed by Schofield & Wroth (1968) has been shown to capture the mechanical behaviour of soils effectively. The particulate implementation of the discrete element method (DEM) can replicate many of the complex mechanical characteristics associated with sand. This research firstly shows that the CSSM framework is useful to assess whether a DEM simulation gives a response that is representative of a real soil. The research then explores the capacity of DEM to extend understanding of soil behaviour within the CSSM framework.
The influence of sample size on the critical-state response observed in DEM simulations that use rigid-wall boundaries was examined. The observed sensitivity was shown to be caused by higher void ratios and lower contact densities adjacent to the boundaries. When the void ratio (e) and mean stress (p’) of the homogeneous interior regions were considered, the influence of sample size on the position of the critical state line (CSL) in e-log(p’) space diminished.
A parametric study on the influence of the interparticle friction (μ) on the load-deformation response was carried out. The macro-scale stress-deformation characteristics were nonlinearly related to μ and the particle-scale measures (fabric, contact force distribution, etc.) varied systematically with μ. The limited effect of increases in μ on the overall strength at high μ values (μ>0.5) is attributable to transition from sliding-dominant to rolling-dominant contact behaviour. A μ value higher than 0.5 leads to a CSL in e-log(p’) space that does not capture real soil response.
True-triaxial simulations with different intermediate stress ratios (b) were performed. The dependency of strength on b agreed with empirical failure criteria for sands and was related to a change of buckling modes of the strong force chains as b increased. DEM simulations showed that the position of the CSL in e-log(p’) space depends on the intermediate stress ratio b. This sensitivity seems to be related to the dependency of the directional fabric anisotropy on b. The link between the state parameter and both soil strength and dilatancy proposed by Jefferies & Been (2006) was reproduced in DEM simulations.
A new rotational resistance model was proposed and it was shown that the new model can qualitatively capture the influence of particle shape on the mechanical behaviour of sand. However, it was shown that the effect of rotational resistance is limited and to quantitatively compare the DEM simulation results with laboratory testing data, e.g., the critical-state loci, it is necessary to use non-spherical particles.published_or_final_version
Civil Engineering
Doctoral
Doctor of Philosophy
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Beckham, Jon Regan. "Analysis of mathematical models of electrostatically deformed elastic bodies." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 169 p, 2008. http://proquest.umi.com/pqdweb?did=1475178561&sid=27&Fmt=2&clientId=8331&RQT=309&VName=PQD.
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Morland, Lawrence Christopher. "Mathematical models for a fluid flow arising in turbine blade cooling passages." Thesis, University of Oxford, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.330029.
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Beylin, Andrey V. "Supersymmetric Landau Models." Scholarly Repository, 2011. http://scholarlyrepository.miami.edu/oa_dissertations/624.
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This work is focused on the different supersymmetric extensions of the Landau model. We aim to fully solve each model and describe its energy levels, wavefunctions, Hilbert space and define a norm on it, as well as find symmetry generators and transformations with respect to them. Several possible generalizations were considered before. It was found for Landau model on the so called Superflag manifold as well as planar Superflag and Superplane Landau models that standard norm on the Hilbert space is not positive definite. Later for planar cases it was found that it is possible to fix this by introducing a new norm which will be invariant and positive definite. Surprisingly this procedure brings up "hidden" symmetries for the known super Landau models. In the dissertation we apply the same procedure for Landau model on superpshere and Superflag manifolds. It turns out that superpsherical Landau model is equivalent to the Superflag model with one of the parameters fixed. Because the model on superpshere can be recovered from the Superflag we will do calculations of corrected norm only for the Superflag. After this we develop a different generalization of the Superplane Landau model. Starting with Lagrangian in a superfield form we introduce two arbitrary functions of superfields K(Φ) and V(Φ) into the Lagrangian. We follow with the component form of Lagrangian. The quantization of the model is possible, and we will show that there is a reparametrization which turn equation of motion of the first scheme into the second set. Standard metric is again non-positive definite and we apply already known procedure to correct it. It will not be possible to solve Schrodinger equations in general with undefined K and V, so we consider one specific case which give us Landau model on a sphere with N = 2 supersymmetry, which put it apart from the superspherical Landau model, which have a superpshere for a target space but do not possess supersymmetry.
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Zhao, Qian, and 赵倩. "A thermomechanical approach to constitutive modeling of geomaterials." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B47166836.
Full textAbstract:
Modeling of the mechanical behavior of geomaterials is a fundamental yet very
difficult problem in geotechnical engineering. The difficulty lies in that the
engineering behavior of geomaterials is strongly nonlinear and anisotropic,
depending on confining pressure, void ratio, stress history, and drainage conditions.
A traditional approach to the modeling of geomaterials is to formulate empirical
equations to fit experimental data. Generally, this approach is not able to provide
physical insights into the diverse responses observed in the soil mechanics
laboratories. Another conventional approach is to make use of the classical
plasticity theory, established mainly for metals, to develop constitutive models for
geomaterials. While this approach is capable of shedding light on the mechanisms
involved, it has been recognized that such models may violate the basic laws of
physics.
The objective of this thesis is to apply a new approach to constructing constitutive
models for geomaterials, by making use of thermomechanical principles. The
essence of the new approach is that the constitutive behavior of geomaterials can be
completely determined once two thermomechanical potentials, i.e. the free energy
and dissipation rate functions, are specified. The yield function and flow rule in the
classical plasticity theory can be established from the two potentials, and the
models so derived satisfy the basic laws of physics automatically. In this thesis, the
theoretical framework for constructing thermomechanical models is introduced.
Several concepts in relation to plastic work, dissipated and stored energy are
discussed. Both the isotropic and anisotropic models are formulated and realized in
this framework and the generated predictions are compared with the test data of a
series of triaxial compression tests on sand. To address the important density- and
pressure-dependent behaviors of sand in the framework, a state-dependent
thermomechanical model is developed, by introducing the state parameter into the
dissipation rate function such that a unique set of model parameters is able to
predict the behaviors of sand for a wide variation of densities and pressures. Finally,
a thermomechanical model for predicting the complex unloading and reloading
behaviors of sand is developed by modifying the hardening laws, and the
performance of this model is investigated.published_or_final_version
Civil Engineering
Master
Master of Philosophy
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He, Shu Yu. "Field study on influence of atmospheric parameters and vegetation on variation of soil suction around tree vicinity." Thesis, University of Macau, 2018. http://umaclib3.umac.mo/record=b3868734.
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Gilpin, Richard. "The numerical solution and analysis of mathematical models for bubbly two-phase flow." Thesis, University of Oxford, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.289348.
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Chin, David 1982. "Wall shear patterns of a 50% asymmetric stenosis model using photochromic molecular flow visualization." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=111613.
Full textAbstract:
Photochromic Molecular Flow Visualization is an in vitro, experimental technique that uses high speed image acquisition combined with an ultraviolet laser to capture instantaneous flow profiles. It is particularly adept at measuring near wall velocities which are necessary for accurate wall shear rate measurements. This thesis describes the implementation and validation of the technique at McGill. The system was used to investigate the wall shear rate patterns in an idealized 50% asymmetric stenosis model under steady flow for Reynolds numbers 206, 99 and 50. A large recirculation zone with flow reattachment was seen downstream of the stenosis with maximum shear values occurring slightly upstream of peak stenosis for Reynolds number 206. This information is vital to ongoing dynamic cell culture experiments aimed at understanding the progression of atherosclerosis.
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Gaballa, Mohamed Abdelrhman Ahmed. "Nonlinear multiphasic mechanics of soft tissue using finite element methods." Diss., The University of Arizona, 1989. http://hdl.handle.net/10150/184837.
Full textAbstract:
The purpose of the research was to develop a quantitative method which could be used to obtain a clearer understanding of the time-dependent fluid filteration and load-deformation behavior of soft, porous, fluid filled materials (e.g. biological tissues, soil). The focus of the study was on the development of a finite strain theory for multiphasic media and associated computer models capable of predicting the mechanical stresses and the fluid transport processes in porous structures (e.g. across the large blood vessels walls). The finite element (FE) formulation of the nonlinear governing equations of motion was the method of solution for a poroelastic (PE) media. This theory and the FE formulations included the anisotropic, nonlinear material; geometric nonlinearity; compressibility and incompressibility conditions; static and dynamic analysis; and the effect of chemical potential difference across the boundaries (known as swelling effect in biological tissues). The theory takes into account the presence and motion of free water within the biological tissue as the structure undergoes finite straining. Since it is well known that biological tissues are capable of undergoing large deformations, the linear theories are unsatisfactory in describing the mechanical response of these tissues. However, some linear analyses are done in this work to help understand the more involved nonlinear behavior. The PE view allows a quantitative prediction of the mechanical response and specifically the pore pressure fluid flow which may be related to the transport of the macromolecules and other solutes in the biological tissues. A special mechanical analysis was performed on a representative arterial walls in order to investigate the effects of nonlinearity on the fluid flow across the walls. Based on a finite strain poroelastic theory developed in this work; axisymmetric, plane strain FE models were developed to study the quasi-static behavior of large arteries. The accuracy of the FE models was verified by comparison with analytical solutions wherever is possible. These numerical models were used to evaluate variables and parameters, that are difficult or may be impossible to measure experimentally. For instance, pore pressure distribution within the tissue, relative fluid flow; deformation of the wall; and stress distribution across the wall were obtained using the poroelastic FE models. The effect of hypertension on the mechanical response of the arterial wall was studied using the nonlinear finite element models. This study demonstrated that the finite element models are powerful tools for the study of the mechanics of complicated structures such as biological tissue. It is also shown that the nonlinear multiphasic theory, developed in this thesis, is valid for describing the mechanical response of biological tissue structures under mechanical loadings.
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Modarres, Najafabadi Seyed Ali. "Dynamics modelling and analysis of impact in multibody systems." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=115886.
Full textAbstract:
In this thesis, we discuss a novel approach to the dynamics modelling and analysis of impact in unilaterally constrained multibody systems. This approach is based on an analysis of energy absorption and restitution during impact, using a decomposition technique, which decouples the kinetic energy associated with the spaces of admissible and constrained motions of unilateral contacts. This is done based on the decomposition of the tangent space of the configuration manifold at the pre-impact instant. The decomposition of the kinetic energy can provide a picture of how the energy absorption and dissipation during impact is related to the variation of the generalized velocities and the configuration of multibody systems.Further, based on the above analysis approach, we introduce a new interpretation of the energetic coefficient of restitution, specially applicable to contact involving multibody systems. This interpretation generalizes the concept of the energetic coefficient of restitution and allows for consideration of simultaneous multiple-point contact scenarios. Moreover, based on the concept of the generalized energetic coefficient of restitution, the contact modes and the post-impact state of planar single-point impact are determined. Further, the problem of simultaneous multiple-point impact is considered, where it is shown that our approach can also be advantageous to characterize the dynamics of interaction in such systems.
The use and applicability of the approach reported are further investigated by conducting an experimental study on a robotic testbed. The open architecture of the testbed allows us to perform various contact experiments, such as single- and multiple-point impact scenarios, with different pre-impact configurations and velocities. The kinematic and dynamic models of the system have been developed and implemented for real-time analysis. It is shown that impact between multibody systems is considerably affected by not only the local dynamics characteristics of the interacting bodies, but also the (global) configuration of the interacting multibody systems. The reported results suggest that the material presented herein offers a useful means to characterize impact in complex systems.
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黃小華 and Siu-wah Wong. "Predicition of fatigue crack propagation using strain energy density method." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1989. http://hub.hku.hk/bib/B31209506.
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馮錦生 and Kam-sang Fung. "Fatigue crack propagation with strain energy density approach." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1989. http://hub.hku.hk/bib/B31209713.
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陳幸福 and Xingfu Chen. "A ductile damage model based on endochronic theory and its applicationto ductile failure analysis." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1993. http://hub.hku.hk/bib/B31233004.
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Murphy, Ryan John. "Mechanochemical and experimental models in mathematical biology." Thesis, Queensland University of Technology, 2022. https://eprints.qut.edu.au/228428/1/Ryan%20John_Murphy_Thesis.pdf.
Full textAbstract:
Experiments that probe epithelial tissue dynamics, cell competition, and tumour growth are fundamental to understand processes in developmental biology, cancer progression and treatment. However, interpreting complex biological experiments is challenging. To address this challenge, we develop and use a range of mathematical models. First, we focus on epithelial tissue dynamics. Second, we use real-time cell cycle imaging to reveal the structure of growing tumour spheroids. We then revisit the seminal Greenspan tumour growth model and use statistical analysis to quantitatively connect it to experimental data for the first time to reveal experimental design choices that lead to reliable biological insight.
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Ching, Wing-han Michael, and 程永鏗. "Modeling of contaminant dispersion by statistical mechanics." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2009. http://hub.hku.hk/bib/B42664500.
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Tang, Baobao. "Development of Mathematical and Computational Models to Design Selectively Reinforced Composite Materials." Thesis, University of Louisiana at Lafayette, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10163313.
Full textAbstract:
Different positions of a material used for structures experience different stresses, sometimes at both extremes, when undergoing processing, manufacturing, and serving. Taking the three-point bending as an example, the plate experiences higher stress in the middle span area and lower stress in both sides of the plate. In order to ensure the performance and reduce the cost of the composite, placement of different composite material with different mechanical properties, i.e. selective reinforcement, is proposed.
Very few study has been conducted on selective reinforcement. Therefore, basic understanding on the relationship between the selective reinforcing variables and the overall properties of composite material is still unclear and there is still no clear methodology to design composite materials under different types of loads.
This study started from the analysis of composite laminate under three point bending test. From the mechanical analysis and simulation result of homogeneously reinforced composite materials, it is found that the stress is not evenly distributed on the plate based on through-thickness direction and longitudinal direction. Based on these results, a map for the stress distribution under three point bending was developed. Next, the composite plate was selectively designed using two types of configurations. Mathematical and finite element analysis (FEA) models were built based on these designs. Experimental data from tests of hybrid composite materials was used to verify the mathematical and FEA models. Analysis of the mathematical model indicates that the increase in stiffness of the material at the top and bottom surfaces and middle-span area is the most effective way to improve the flexural modulus in three point bending test. At the end of this study, a complete methodology to perform the selective design was developed.
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Musa, Zulkarnain 1964. "An accelerated conjugate direction procedure for slope stability analysis." Thesis, The University of Arizona, 1988. http://hdl.handle.net/10150/276912.
Full textAbstract:
CSLIP2 (De Natale, 1987) is the only slope stability program that utilizes a "direction set" optimization routine in its search for the minimum safety factor. However, CSLIP2 which employs Powell's Conjugate Direction Method permits only the horizontal and vertical directions (x and y) to be used as the initial direction set. The efficiency of the existing search routine is improved by replacing the x-y coordinate directions with initial directions that are parallel to and perpendicular to the principal axis of the safety factor contours.
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Sreedhar, Madhu K. "Large eddy simulation of turbulent vortices and mixing layers." Diss., This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-06062008-163324/.
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Zhu, Tulong. "Meshless methods in computational mechanics." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/11795.
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Lacy, Thomas E. Jr. "Distribution effects in damage mechanics." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/15937.
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Miller, Matthew P. "Improved constitutive laws for finite strain inelastic deformation." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/16098.
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Liu, Chi-hong, and 廖志航. "Base friction modelling of discontinuous rock masses." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2002. http://hub.hku.hk/bib/B42577123.
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Li, Lian, and 李煉. "Microscopic study and numerical simulation of the failure process of granite." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B31242005.
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SOMASUNDARAM, SUJITHAN. "CONSTITUTIVE MODELLING FOR ANISOTROPIC HARDENING BEHAVIOR WITH APPLICATIONS TO COHESIONLESS SOILS (INDUCED, KINEMATIC, NON-ASSOCIATIVENESS)." Diss., The University of Arizona, 1986. http://hdl.handle.net/10150/188165.
Full textAbstract:
A constitutive model based on rate-independent elastoplasticity concepts is developed to simulate the behavior of geologic materials under arbitrary three-dimensional stress paths, stress reversals and cyclic loading. The model accounts for the various factors such as friction, stress path, stress history, induced anisotropy and initial anisotropy that influence the behavior of geologic materials. A hierarchical approach is adapted whereby models of progressively increasing sophistication are developed from a basic isotropic-hardening associative model. The influence of the above factors is captured by modifying the basic model for anisotropic (kinematic) hardening and deviation from normality (nonassociativeness). Both anisotropic hardening and deviation from normality are incorporated by introducing into the formulation a second order tensor whose evolution is governed by the level of induced anisotropy in the material. In the stress-space this formulation may be interpreted as a translating potential surface Q that moves in a fixed field of isotropic yield surfaces. The location of the translating surface in the stress-space, at any stage of the deformation, is given by the 'induced anisotropy' tensor. A measure to represent the level of induced anisotropy in the material is defined. The validity of this representation is investigated based on a series of special stress path tests in the cubical triaxial device on samples of Leighton Buzzard sand. The significant parameters of the models are defined and determined for three sands based on results of conventional laboratory test results. The model is verified with respect to laboratory multiaxial test data under various paths of loading, unloading, reloading and cyclic loading.
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YU, CHUNG-CHYI. "FINITE-ELEMENT ANALYSIS OF TIME-DEPENDENT CONVECTION DIFFUSION EQUATIONS (PETROV-GALERKIN)." Diss., The University of Arizona, 1986. http://hdl.handle.net/10150/183930.
Full textAbstract:
Petrov-Galerkin finite element methods based on time-space elements are developed for the time-dependent multi-dimensional linear convection-diffusion equation. The methods introduce two parameters in conjunction with perturbed weighting functions. These parameters are determined locally using truncation error analysis techniques. In the one-dimensional case, the new algorithms are thoroughly analyzed for convergence and stability properties. Numerical schemes that are second order in time, third order in space and stable when the Courant number is less than or equal to one are produced. Extensions of the algorithm to nonlinear Navier-Stokes equations are investigated. In this case, it is found more efficient to use a Petrov-Galerkin method based on a one parameter perturbation and a semi-discrete Petrov-Galerkin formulation with a generalized Newmark algorithm in time. The algorithm is applied to the two-dimensional simulation of natural convection in a horizontal circular cylinder when the Boussinesq approximation is valid. New results are obtained for this problem which show the development of three flow regimes as the Rayleigh number increases. Detailed calculations for the fluid flow and heat transfer in the cylinder for the different regimes as the Rayleigh number increases are presented.
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Foster, David H. "Fabry-Perot and Whispering Gallery Modes In Realistic Resonator Models." Thesis, view abstract or download file of text, 2006. http://wwwlib.umi.com/cr/uoregon/fullcit?p3211216.
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Thesis (Ph. D.)--University of Oregon, 2006.Typescript. Includes vita and abstract. Includes bibliographical references (leaves 204-213). Also available for download via the World Wide Web; free to University of Oregon users.
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Vohra, Sanjay. "A mechanics framework for modeling fiber deformation on draw rollers and freespans." Diss., Available online, Georgia Institute of Technology, 2006, 2006. http://etd.gatech.edu/theses/available/etd-05172006-141347/.
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Thesis (Ph. D.)--Polymer, Textile & Fiber Engineering, Georgia Institute of Technology, 2007.Karl I. Jacob, Committee Chair ; Youjiang Wang, Committee Member ; Mary Lynn Realff, Committee Member ; Arun Gokhale, Committee Member ; Rami Haj-Ali, Committee Member.
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Ellis, William Joseph. "Application of statistical mechanics to a model neuron /." Title page, contents and abstract only, 1993. http://web4.library.adelaide.edu.au/theses/09PH/09phe479.pdf.
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McTaggart, Kevin Andrew. "Hydrodynamics and risk analysis of iceberg impacts with offshore structures." Thesis, University of British Columbia, 1989. http://hdl.handle.net/2429/30733.
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The evaluation of design iceberg impact loads for offshore structures and the influence
of hydrodynamic effects on impact loads are examined. Important hydrodynamic effects include iceberg added mass, wave-induced oscillatory iceberg motions, and the influence of a large structure on the surrounding flow field and subsequent velocities of approaching icebergs. The significance of these phenomena has been investigated using a two-body numerical diffraction model and through a series of experiments modelling the drift of various sized icebergs driven by waves and currents approaching a large offshore structure. Relevant findings from the hydrodynamic studies have been incorporated into two probabilistic models which can be used to determine design iceberg collision events with a structure based on either iceberg kinetic energy upon impact or global sliding force acting on the structure. Load exceedence probabilities from the kinetic energy and sliding force models are evaluated using the second-order reliability method. Output from the probabilistic models can be used to determine design collision parameters and to assess whether more sophisticated modelling of various impact processes is required. The influence of the structure on velocities of approaching icebergs is shown to be significant
when the structure horizontal dimension is greater than twice the iceberg dimension. As expected, wave-induced oscillatory motions dominate the collision velocity for smaller icebergs but have a negligible effect on velocity for larger icebergs.Applied Science, Faculty of
Civil Engineering, Department of
Graduate
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Ma, Zhiwen. "A combined differential and integral model for high temperature fuel cells." Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/15831.
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Fiechter, Jerome. "Numerical study of platelet transport in flowing blood." Thesis, Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/16770.
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Fischer, Christian E. "Forging process models for use with global optimization of manufacturing prcesses." Ohio : Ohio University, 1999. http://www.ohiolink.edu/etd/view.cgi?ohiou1175269765.
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