Many soft food materials, including vegetable shortening, exhibit complex rheological behaviour with properties that resemble those of a solid and a liquid simultaneously. The fundamental parameters used to describe the rheological response of vegetable shortening were obtained from uniaxial compression tests, including monotonic and cyclic compression, as well as creep and stress relaxation tests. The fundamental parameters obtained from the various compression tests were then used in two mechanical models (viscoelastic and elasto-visco-plastic) to predict the compression and conical indentation response of vegetable shortening. The accuracy of the two models was studied with the help of the commercially available finite element analysis software package Abaqus. It was determined that the viscoelastic model was not suitable for the prediction of the rheological response of shortening. On the other hand, the proposed elasto-visco-plastic model predicted with reasonable accuracy the uniaxial compression and indentation experimental response of vegetable shortening.

Hip resurfacing arthroplasty is touted as an attractive alternative to total hip arthroplasty for treatment of severe joint pain and limited mobility in young patients because it is bone conserving and allows for a greater range of motion. There is concern in the orthopaedic community, however, regarding surgically-induced deformation of hip resurfacing cups. Cup deformation could potentially compromise the tight clearance between the femoral head and cup, resulting in increased wear, acoustic emissions, and joint binding. This phenomenon has been investigated both experimentally and with finite element analysis (FEA). Finite element studies have contributed significantly to our understanding of cup deformation, such as the effect of different cup dimensions on deformation results, but unfortunately such studies were deficient in a number of ways. The first objective of this thesis was to create a three-dimensional finite element model of resurfacing cup deformation that addressed the limitations of previous models pertaining to pelvic geometry, meshing, material properties, and cup insertion, in order to more fully elucidate cup deformation. The second objective was to demonstrate that two-dimensional characterization of cup deformation at the cup rim is insufficient, by more fully characterizing cup deformation in three-dimensions. The geometry was obtained via laser scanning and digital processing of a hemi-pelvis replica, meshing was performed without the use of shell elements, linear elasticity with strain-hardening after the onset of yielding was assigned to the cup and bone, and the most appropriate method for simulation of cup insertion was determined via two-dimensional axisymmetric analyses. Also, cup deformation was characterized in three-dimensions. The key findings of this thesis are that bone yield behaviour has important implications on press-fitting simulation, and the cup deforms irregularly and possibly plastically during press-fitting. A three-dimensional finite element model of resurfacing cup deformation that addressed the limitations of previous models was successfully created. Measurement of deformation at the rim of the resurfacing cup for characterization of cup deformation is insufficient; full characterization of cup deformation in three-dimensions is necessary. Future work should incorporate clinical testing to obtain model inputs such as impact and muscle forces, as well as model validation.

Head injuries are very common in daily life and in war field. Head injuries are classified into open and closed. The mechanical mechanisms involved in closed head injuries are very different from those in open head injuries. Closed head injuries are more often re-ported with the use of protective device such as helmets. Helmets were found effective in reducing open head injuries, but less effective for closed head injuries. Finite element modeling is an effective and efficient tool for investigating head injuries. In this thesis, a two-dimensional finite element model was constructed based on a Mag-netic Resonance Image (MRI) scan data from a patient. MATLAB programming was used to extract the information from the MRI scan data. The finite element model was then used to investigate factors affecting closed head injuries. As a new contribution to closed head injury study, the fluid component in the human head, CSF, was studied by a group of comparative simulations. The other three factors, elasticity modulus of the cra-nium, contact area of impact, and impact duration were also investigated. Their effects on reducing the strain values in the brain were measured. Investigation results show that, increasing elasticity modulus of the cranium, contact area of impact and impact duration are very helpful to reduce the strain values in the brain. Helmet is helpful to protect people from closed head injuries because it can change all these three factors by using different shell stiffness and different padding material. The cerebrospinal fluid is effective in protecting the brain from impacts, as a fluid is able to reduce normal strains and filter nearly all shear strains transferred to the brain. It indicates that if a layer of fluid could be added as a layer in a protective helmet, the helmet would be more effective in protecting the brain. Conclusions obtained from the investigations are helpful for preventing closed head injuries and for improving design of protective devices such as helmets.

Elevated intracranial pressure (ICP) in closed head injury may lead to a vegetative state and even death. Current methods available for measuring ICP may cause infection, haemorrhage or not reliable. A patient-specific correlation between ICP and an external vibration response was used for ICP evaluation, which based on finite element (FE) modeling. In FE modeling, a two dimensional FE model of human head was built in ANSYS. Geometry information was obtained from a magnetic resonance image of the human head, while the material properties were acquired from literatures. Vibration responses, e.g., displacement, velocity, acceleration and equivalent strain, were obtained for applied ICPs in FE analyses. Correlations between ICP and vibration responses were established. Effects of impact magnitude and impact duration were studied. Response sensitivity was defined to find a vibration response that is sensitive to ICP change. A procedure based on response sensitivity was proposed for ICP evaluation.

<p>In this dissertation, the spectral element method is developed to simulate electromagnetic field in nano-structure consisting of dielectric, metal or semiconductor. The spectral element method is a special kind of high order finite element method, which has spectral accuracy. When the order of the basis function increases, the accuracy increases exponentially. The goal of this dissertation is to implement the spectral element method to calculate the electromagnetic properties of various semiconductor nano-structures, including photonic crystal, photonic crystal slab, finite size photonic crystal block, nano dielectric sphere. The linear electromagnetic characteristics, such as band structure and scattering properties, can be calculated by this method with high accuracy. In addition, I have explored the application of the spectral element method in nonlinear and quantum optics. The effort will focus on second harmonic generation and quantum dot nonlinear dynamics. </p><p>The electromagnetic field can be simulated in both frequency domain and time domain. Each method has different application for research and engineering. In this dissertation, the first half of the dissertation discusses the frequency domain solver, and the second half of the dissertation discusses the time domain solver.</p><p>For frequency domain simulation, the basic equation is the second order vector Helmholtz equation of the electric field. This method is implemented to calculate the band structure of photonic crystals consisting of dielectric material as well as metallic materials. Because the photonic crystal is periodic, only one unit cell need to be simulated in the computational domain, and a periodic boundary condition is applied. The spectral accuracy is inspected. Adding the radiation boundary condition at top and bottom of the computational region, the scattering properties of photonic crystal slab can be calculated. For multiple layers photonic crystal slab, the block-Thomas algorithm is used to increase the efficiency of the calculation. When the simulated photonic crystals are finite size, unlike an infinitely periodic system, the periodic boundary condition does not apply. In order to increase the efficiency of the simulation, the domain decomposition method is implemented. </p><p>The second harmonic generation, which is a kind of nonlinear optical effect, is simulated by the spectral element method. The vector Helmholtz equations of multiple frequencies are solved in parallel and the consistence solution with nonlinear effect is obtained by iterative solver. The sensitivity of the second harmonic generation to the thickness of each layer can be calculated by taking the analytical differential of the equation to the thickness of each element. </p><p>The quantum dot dynamics in semiconductor are described by the Maxwell-Bloch equations. The frequency domain Maxwell-Bloch equations are deduced. The spectral element method is used to solve these equations to inspect the steady state quantum dot dynamic behaviors under the continuous wave electromagnetic excitation.</p><p>For time domain simulation, the first order curl equations in Maxwell equations are the basic equations. A spectral element method based on brick element is implemented to simulate a nano-structure consisting of woodpile photonic crystal. The resonance of a micro-cavity consisting of a point defect in the woodpile photonic crystal block is simulated. In addition, the time domain Maxwell-Bloch equations are implemented in the solver. The spontaneous emission process of quantum dot in the micro-cavity is inspected. </p><p>Another effort is to implement the Maxwell-Bloch equations in a previously implemented domain decomposition spectral element/finite element time domain solver. The solver can handle unstructured mesh, which can simulate complicated structure. The time dependent dynamics of a quantum dot in the middle of a nano-sphere are investigated by this implementation. The population inversion under continuous and pulse excitation is investigated. </p><p>In conclusion, the spectral element method is implemented for frequency domain and time domain solvers. High efficient and accurate solutions for multiple layers nano-structures are obtained. The solvers can be applied to design nano-structures, such as photonic crystal slab resonators, and nano-scale semiconductor lasers.</p> / Dissertation

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The thesis proposes a new procedure to describe bone anisotropy in the finite element model using computed tomography (CT) images. First, bone density was correlated to CT numbers using the empirical function established in previous studies; pointwise bone density gradient was then calculated from interpolation functions of bone densities. Second, principal anisotropic directions were defined using the bone density gradient. Third, the magnitude of bone density gradient was incorporated to an existing bone elasticity-density correlation established by experiments. A method was also introduced to assign the anisotropic material properties to finite element models in Abaqus. The effect on the predicted von Misses stresses and principal strains in the bone by adopting the anisotropic or isotropic material model was investigated by finite element simulations using Abaqus.

This dissertation reports investigations on shear in cracked reinforced concrete (RC) elements including the development and implementation of a material subroutine for the commercial finite element (FE) program ABAQUS. The material subroutine UMAT is intended to substantially improve the shear behaviour of the standard concrete options of ABAQUS. At first the important shear theories are reviewed in detail and their advantages and drawbacks are summarised. The modified compression field theory (MCFT) is identified as a suitable shear theory worth being coded for its application in FE analysis. A comprehensive check on the MCFT confirms its suitability in a slightly modified form for the investigation of a variety of cracked structural RC elements. This check is conducted on a section analysis level by means of a developed program called LAYER which is coded according to the MCFT. The main part of the work is the implementation and testing of the material subroutine UMAT which is added to the source code of ABAQUS via an interface provided by the commercial FE program. Finally, the UMAT is utilised for examining the ductility of RC walls. It is concluded that shear deflections can influence the displacement and curvature ductility of squat structures in a substantial way, even though a flexural type of failure might prevail.

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