The master’s thesis deals with issues belonging to the field of dental biomechanics, specifically the mechanical interaction of dental implants with the bone tissue of the mandible. The thesis focuses on the stress-strain analysis of the mandible with the implant inserted in different positions, with a different angle relative to the occlusal plane. The solution is performed by computational modeling using the finite element method. The geometry model of mandible was created based on CT images. The aim of the master’s thesis was also to compare the influence of the choice of the material model of cancellous bone tissue on the resulting stress-strain states of the mandible with the dental implant. Three material models of cancellous bone tissue were created - two homogeneous material model and a heterogeneous material model, which was based on CT image data. The work also investigates the effect of rotation (+5° or -5°) of implants in basic positions on the resulting stress-strain states. The stress-strain analysis showed that position and rotation has a greater effect on the stress and strain of bone tissue and implant than the chosen material model of cancellous bone tissue.

A need exists for a more robust method of evaluating musculoskeletal injuries resulting from impact conditions, particularly blasts. Computational modeling is a promising method of achieving this goal. The accuracy of a model depends on high quality mechanical properties for each component. This study examined the mechanical properties of porcine muscle along with structure property relationships. Fresh muscle was tested in compression and tension at strain rates of 0.1 s-1, 0.01 s-1, and 0.001 s-1. Viscoelastic properties were observed including strain rate dependency, stress state dependency, anisotropy, relaxation, and hysteresis. Image analysis was conducted in compression on controls, 30% strain, and 50% strain, relating stress-strain data with structural changes. The effect of rigor was also seen in the tensile response of muscle. Thawed tissue was examined to investigate the effects of freezing. It was found that freezing did not significantly change the mechanical properties, but substantial microstructural changes did occur.

The use of polymeric materials in the manufacturing industry has vastly increased since the 1950’s. Because of the large amounts of material involved in modern processing operations, attempts have been made over the years to numerically simulate the processes, in the hope of optimizing operating parameters. However, in contrast to other, more traditional materials such as steel or glass, there is not a well understood connection between the microscopic structure and the (highly non-linear) macroscopic physical response of polymers. Because of this lack of microscopic cause - macroscopic effect knowledge, many descriptions of the physical response of polymers are largely phenomenological ones; that is, the equations used to model the stress/strain response make no attempt to convey information about the microscopic structure of the material.</p> <p> In the present work, five constitutive equations - Mooney-Rivlin, Ogden, G’Sell Two-term Polynomial and K-BKZ - are used to model the stress/strain response of two different polymers commonly used in thermoforming and blowmolding operations, ABS and HDPE, to uniaxial elongation and equibiaxial extension. The models are compared to experimental stress/strain data obtained from an industrial source, and the applicability of their predictions are investigated with regards to variations in strain, strain rate and temperature. Lastly, since the vast majority of real processes involve biaxial, not uniaxial, deformations, the ability of the models to predict equibiaxial response using parameters fit solely to uniaxial data is considered, in order to investigate the possibility of being able to forego the need for expensive, difficult biaxial tests. / Thesis / Master of Engineering (MEngr)

A comprehensive experimental study was conducted to determine the limitations in processing conditions for superdrawing. Experimental studies were carried out by uniaxial drawing tests at temperatures from 90 to 120°C and at strain rates ranging from 0.008/s to 0.425/s. Crystallinity and orientation of the drawn samples were evaluated using differential scanning calorimetry and birefringence measurements. This study revealed that increasing temperature from 110°C to 120°C leads to more crystallization at low strain rates (0.001/s), and less crystallization at high strain rates (0.1/s). Furthermore, it was shown for the first time that the mechanism of crystallinity development in PET undergoes a transition at draw temperature of 113°C and strain rate of 0.17/s. A new one-dimensional constitutive model was developed to predict the stress-strain behavior of PET fibers as they are drawn to very large draw ratios (up to 10) over a wide range of temperature (90-120°C) and strain rate (0.008-0.425/s). The model was based on the rubber elasticity theory and non-linear viscoelasticity.

Deformational properties of soil, in terms of modulus and damping, exert a great influence on seismic response of soil sites. However, these properties for sands containing some portion of fines particles have not been systematically addressed. In addition, simultaneous modelling of the modulus and damping behaviour of soils during cyclic loading is desirable. This study presents an experimental and computational investigation into the deformational properties of sands containing fines content in the context of site response analysis. The experimental investigation is carried on sandy soils sourced from Christchurch, New Zealand using a dynamic triaxial apparatus while the computational aspect is based on the framework of total-stress one-dimensional (1D) cyclic behaviour of soil. The experimental investigation focused on a systematic study on the deformational behaviour of sand with different amounts of fines content (particle diameter ≤ 75µm) under drained conditions. The silty sands were prepared by mixing clean sand with three different percentages of fines content. A series of bender element tests at small-strain range and stress-controlled dynamic triaxial tests at medium to high-strain ranges were conducted on samples of clean sand and silty sand. This allowed measurements of linear and nonlinear deformational properties of the same specimen for a wide strain range. The testing program was designed to quantify the effects of void ratio and fines content on the low-strain stiffness of the silty sand as well as on the nonlinear stress-strain relationship and corresponding shear modulus and damping properties as a function of cyclic shear strains. Shear wave velocity, Vs, and maximum shear modulus, Gmax, of silty sand was shown to be significantly smaller than the respective values for clean sands measured at the same void ratio, e, or same relative density, Dr. However, the test results showed that the difference in the level of nonlinearity between clean sand and silty sands was small. For loose samples prepared at an identical relative density, the behaviour of clean sand was slightly less nonlinear as compared to sandy soils with higher fines content. This difference in the nonlinear behaviour of clean sand and sandy soils was negligible for dense soils. Furthermore, no systematic influence of fines content on the material damping curve was observed for sands with fines content FC = 0 to 30%. In order to normalize the effects of fines on moduli of sands, equivalent granular void ratio, e*, was employed. This was done through quantifying the participation of fines content in the force transfer chain of the sand matrix. As such, a unified framework for modelling of the variability of shear wave velocity, Vs, (or shear modulus, Gmax) with void ratio was achieved for clean sands and sands with fines, irrespective of their fines content. Furthermore, modelling of the cyclic stress-strain behaviour based on this experimental program was investigated. The modelling effort focused on developing a simple constitutive model which simultaneously models the soil modulus and damping relationships with shear strains observed in laboratory tests. The backbone curve of the cyclic model was adopted based on a modified version of Kondner and Zelasko (MKZ) hyperbolic function, with a curvature coefficient, a. In order to simulate the hysteretic cycles, the conventional Masing rules (Pyke 1979) were revised. The parameter n, in the Masing’s criteria was assumed to be a function of material damping, h, measured in the laboratory. As such the modulus and damping produced by the numerical model could match the stress-strain behaviour observed in the laboratory over the course of this study. It was shown that the Masing parameter n, is strain-dependent and generally takes values of n ≤ 2. The model was then verified through element test simulations under different cyclic loadings. It was shown that the model could accurately simulate the modulus and the damping simultaneously. The model was then incorporated within the OpenSees computational platform and was used to scrutinize the effects of damping on one-dimensional seismic site response analysis. For this purpose, several strong motion stations which recorded the Canterbury earthquake sequence were selected. The soil profiles were modelled as semi-infinite horizontally layered deposits overlying a uniform half-space subjected to vertically propagating shear waves. The advantages and limitations of the nonlinear model in terms of simulating soil nonlinearity and associated material damping were further scrutinized. It was shown that generally, the conventional Masing criteria unconservatively may underestimate some response parameters such as spectral accelerations. This was shown to be due to larger hysteretic damping modelled by using conventional Masing criteria. In addition, maximum shear strains within the soil profiles were also computed smaller in comparison to the values calculated by the proposed model. Further analyses were performed to study the simulation of backbone curve beyond the strain ranges addressed in the experimental phase of this study. A key issue that was identified was that relying only on the modulus reduction curves to simulate the stress-strain behaviour of soil may not capture the actual soil strength at larger strains. Hence, strength properties of the soil layer should also be incorporated to accurately simulate the backbone curve.

The most-discussed pairing symmetry in Sr₂RuO₄ is chiral p-wave, pₓ ± p[sub]y, whose degeneracy is protected by the lattice symmetry. When the lattice symmetry is lowered by the application of a symmetry-breaking field, the degeneracy can be lifted, potentially leading to a splitting of the superconducting transition. To lift the degeneracy, the symmetry breaking field used in this study is uniaxial stress. Uniaxial stress generated by a piezo-electric actuator can continuously tune the electronic structure and in situ lower the tetragonal symmetry in Sr₂RuO₄. Previous studies of magnetic susceptibility and resistivity under uniaxial stress have revealed that there is a strong peak in T[sub]c when the stress is applied along the a-axis of Sr₂RuO₄. In addition, it has been proposed that the peak in T[sub]c coincides with a van Hove singularity in the band structure, and measurements of Hc₂ at the maximum T[sub]c indicate the possibility of an even parity condensate for Sr₂RuO₄ at the peak in Tc. In this thesis, the heat capacity approach is used to study the thermodynamic behavior of Sr₂RuO₄ under uniaxial stress applied along the crystallographic a-axis of Sr₂RuO₄. The first thermodynamic evidence for the peak in T[sub]c is obtained, proving that is a bulk property. However, the experimental data show no clear evidence for splitting of the superconducting transition; only one phase transition can be identified within the experimental resolution. The results impose strong constraints on the existence of a second phase transition, i.e. the size of the second heat capacity jump would be small or the second T[sub]c would have to be very close to the first transition. In addition to these results, I will present heat capacity data from the normal state of Sr₂RuO₄. The experimental results indicate that there is an enhancement of specific heat at the peak in T[sub]c, consistent with the existence of the van Hove singularity. The possibility of even parity superconductivity at the maximum T[sub]c has also been investigated. However, the heat capacity measurements are shown to be relatively insensitive to such a change, so it has not been possible to obtain strong and unambiguous evidence for whether it takes place or not.

Mounting evidence suggests that the normal biomechanical state of arteries may include a nearly equibiaxial intramural stress, and that arteries tend to undergo rapid and dramatic remodeling when perturbed from this normal state. Technical developments in the early 1980s and late 1990s enabled in vitro and ex vivo studies, respectively, of isolated perfused microvessels, and it is clear that they share many similarities in behavior with arteries. To date, however, there has been no systematic study of the effects of biaxial loading on the biomechanical behavior of arterioles. In this project, we describe a modification to a prior in vitro arteriole test system that allowed us to investigate the role of altered axial stretch on the passive, myogenic, and fully contracted biaxial behavior of isolated rat cremaster arterioles. We show that axial stretches from 85% to 110% of normal values induce modest changes in the measured circumferential and axial stress-stretch behavior and similarly in traditional measures of distensibility and myogenic index. Nevertheless, altered axial stretch has a dramatic affect on the biaxial state of stress and it appears that near equibiaxial stress occur at axial stretches larger than those used previously. Whereas this finding will not affect prior estimates of material and functional behavior, it may have important implications for the design of long-term ex vivo and in vivo studies wherein vessel growth and remodeling are critical.

The heterogeneous and anisotropic nature of wood material creates additional design challenges not present with the use of other structural materials such as steel and aluminum. The natural variation in the physical properties of wood members requires that the specified strengths and resistances used for design calculations be based on the quantities measured for the fifth percentile of all wood materials tested. The result is that design may be unnecessarily conservative and subsequently inefficient. The same properties that cause uncertainty surrounding the physical properties of biological materials also create difficulty in applying non-destructive evaluation techniques. Strain measurement is one particular technique that is extremely valuable for materials of known and consistent stress-strain relationships, but whose usefulness is diminished when applied to biological materials. To demonstrate the need for more accurate strain measurement in light-framed structures, the predictive calculations and structural modelling of a post-framed building was compared to its demonstrated performance. The analysis did not adequately reflect the actual performance of the building, and it was determined that additional monitoring of light-framed buildings through systems such as strain measurement was required to gain a better understanding of the performance characteristics in order to optimize evaluation techniques. This project aimed to develop a system that accurately measures strain in dimensional lumber of different types, which in turn will enable researchers to enhance monitoring the performance of light-frame structures and optimize design analysis and structural modelling techniques. The development of a methodology that provides a practical means by which to perform in-situ testing of post-frame buildings and decreases the complexity of post-frame building monitoring will contribute to the advancement of design and analysis techniques. In the calibration phase of the project, metal foil resistance strain gages were mounted onto wooden specimens with dimensions of 5 x 13 x 40 mm, 5 x 40 x 100 mm, and 2 x 20 x 50 mm, and acrylic specimens with dimensions of 3 x 25 x 75 mm. These specimens were then subjected to loading in an ATS universal testing machine in the Physical Properties Lab at the University of Manitoba. Stress-strain curves were developed based upon the observed stress and strain levels. These calibrated gages were then mounted on to a 38 x 89 mm specimen of S-P-F dimensional lumber which represented a typical light-framed building material. This assembly was then subjected to a similar loading procedure as the calibrated gage and stress-strain curves were generated once again. The slopes of the stress-strain curves developed from the two phases of the project were compared to determine if a consistent correlation existed. The three sizes of wood specimens did not demonstrate a consistent correlation. However, the acrylic specimen demonstrated consistent correlation amongst two groups of three with correlation coefficients within a forty percent range in one group and within a nine percent range in the other group. This suggests that further experimental refinements could produce the desired results. / October 2007

Mounting evidence suggests that the normal biomechanical state of arteries may include a nearly equibiaxial intramural stress, and that arteries tend to undergo rapid and dramatic remodeling when perturbed from this normal state. Technical developments in the early 1980s and late 1990s enabled in vitro and ex vivo studies, respectively, of isolated perfused microvessels, and it is clear that they share many similarities in behavior with arteries. To date, however, there has been no systematic study of the effects of biaxial loading on the biomechanical behavior of arterioles. In this project, we describe a modification to a prior in vitro arteriole test system that allowed us to investigate the role of altered axial stretch on the passive, myogenic, and fully contracted biaxial behavior of isolated rat cremaster arterioles. We show that axial stretches from 85% to 110% of normal values induce modest changes in the measured circumferential and axial stress-stretch behavior and similarly in traditional measures of distensibility and myogenic index. Nevertheless, altered axial stretch has a dramatic affect on the biaxial state of stress and it appears that near equibiaxial stress occur at axial stretches larger than those used previously. Whereas this finding will not affect prior estimates of material and functional behavior, it may have important implications for the design of long-term ex vivo and in vivo studies wherein vessel growth and remodeling are critical.

An extensive amount of research has been reported in previous literature on the behaviour of FRP-confined concrete subjected to concentric axial compression. However, data on the behaviour of high strength concrete confined with various types and configurations of FRP systems is still lacking and no consensus exists on the complete response of FRP-confined concrete. In addition, no appropriate design guidelines are currently available. This thesis reports results from an experimental program involving 112 cylindrical concrete specimens, 88 of which were FRP-wrapped and the remaining 24 were control specimens. All the specimens were 152 mm in diameter and 305 mm in length. Test variables included: amount of FRP materials used, strength and stiffness of FRP materials, concrete strength, and the health of concrete at the time of strengthening. Experimental results indicated that a pre-repair load of up to 77% of the unconfined concrete strength had no appreciable effect on the stress-strain response of FRP-confined concrete. With an increase of the unconfined concrete strength, the strength enhancement, energy absorption capacity, ductility factor and work (energy) index at rupture of FRP jackets all decreased remarkably. A positive correlation was found between confined concrete ductility and FRP rupture strain. In addition, a gradual post-peak failure of the specimens, observed previously from FRP-confined concrete columns tested at the University of Toronto, was also observed in some of the current tests -- owing to the high speed data acquisition system. That ductile failure can be attributed to the gradual unzipping failure of FRP jacket, which in turn is related to specimen size. A new constitutive model was developed based on material properties, force equilibrium and strain compatibility. The size effect was taken into account in the model, which is able to accommodate concrete with a wide range of strength (25 MPa to 110 MPa) confined with various types and configurations FRP systems. Design equations from CSA S806-02 and CSA S6-06 provide reasonable and conservative estimates for the FRP-confined concrete strength. To calculate the peak strain for FRP-confined concrete, an equation based on the work by Berthet et al. (2006) is proposed.