The research presented in this thesis focuses on understanding the biomechanical effects of various cranial features that are often ignored in finite element models (FEMs) because their size, position, and complex shapes make them difficult to model. Specifically, this work examines the effects of the alveoli (tooth sockets), periodontal ligament, and squamosal suture on the stress and strain distributions in a cranium under masticatory and dynamic tooth loads. Results from this research will help determine if these features have a significant effect on stress and strain patterns and will yield guidelines as to if or under what conditions they need to be modeled in future FE skull model analyses. As part of this research, three sets of FEMs were developed to address a hypothesis focusing on each cranial feature. The first set of models examined the effect of the tooth sockets on the stress and strain distributions in a cranium under static biting conditions to determine if improperly modeled sockets produce strong global effects in craniofacial regions. The second set of models were used to assess the effect of the PDL's material behavior on the stresses and strains in a cranium under static biting and dynamic tooth loading conditions to determine if the PDL plays an important role in reducing stresses and strains in a model. The final set of models were used to determine the effect of the squamosal suture size on the stresses and strain energies in a cranium under static biting conditions to see if an increase in suture size decreases the risk of separation of the temporal bone from the parietal bone. Results for all analyses indicate the effects of the cranial features are local (i.e. within the vicinity of the feature), with no meaningful global effects. This suggests the sockets, PDL, and squamosal suture do not play an important role in global stress and strain distributions in a cranium under masticatory and dynamic tooth loads. Therefore, it may be safe to ignore the sockets, PDLs, and squamosal sutures during the FE modeling process if the objective of the analysis is to understand global stress and strain patterns.

Improvement of high temperature applications relies on the further development of ultra-high temperature materials (UHTMs). Higher performance and efficiency is driving the need for improvements in energy conversion and propulsion systems. Rocket nozzles, gas turbine engines and hypersonic aircraft depend on a better understanding of a material's performance at high temperatures. More specifically, the characterization of creep properties of high temperature materials is required. Conventional creep testing methods are limited to about 1700 degrees Celsius. Non-contact methods have been developed, which rotate spherical samples up to 33,000 rotations per second. A load is supplied by centripetal acceleration causing deformation of the sample. Non-contact methods have been performed above 2000 degrees Celsius. The induction drive developed in the previous work has decoupled temperature from rotation, greatly expanding the experimental testing range. Creep mechanisms may involve dislocation motion or the diffusional flow of atoms. Creep may be dominated by dislocation glide, dislocation climb, or diffusional-flow mechanisms. Multiple creep mechanisms can be active in a sample, but one is often dominant in a given regime which depends on stress, temperature and grain size. This work studies the creep behavior of samples in regions of transition between dominating creep mechanisms, and the effect on the precision of the measurement. Two finite element models have been developed in the current work. A two-dimensional Norton creep model replaces the more computationally expensive three-dimensional Norton creep model developed in the previous work. Furthermore, a two-dimensional Double Power Law model has been developed to simulate creep behavior of high temperature materials in regimes of mixed dominance. The two-dimensional Norton and Double Power Law models are used to identify and characterize creep in the regions of transition between dominating creep mechanisms. Simulations are analyzed to determine the effect of regimes of mixed dominance on the creep measurements of rotating samples of high temperature materials.

Friction stir welding (FSW) is a solid-state joining process that offers advantages over traditional fusion welding. The amount of heat generated during a FSW process greatly influences the final properties of the weld. The heat is generated through two main mechanisms: friction and plastic deformation, with friction being the larger contributor in a FSW process. There is a need to develop better predictive models of the heat generation and heat transfer in FSW. Almost all models seen in the literature validate temperature predictions on only one side of the tool/workpiece interface, thus ignoring possible inaccuracy that comes from incorrect partitioning of heat generated by friction. This work seeks to model and validate both sides of the interface by matching experimental results for both the plunge and steady state phases of FSW for AA 6061-T6. Proper model validation allowed for a study of the sensitivity of the model predictions to changes in the friction coefficient and heat transfer coefficient at the tool/workpiece interface. Most models in the literature use the Coulomb friction law with a fixed friction coefficient, even though the Norton law better incorporates local material behavior. As such, for the plunge phase of FSW, a method for achieving a time dependent friction coefficient was developed and employed to match experimental temperatures, using Norton's viscoplastic friction law. A friction coefficient of 0.65 was used at the start of the plunge phase, decreasing to 0.08 during the steady state phase. This decrease in magnitude from plunge to steady state is similar to the decrease of the Coulomb friction coefficient calculated by Meyghani et al in a 2017 study. Tuning the models resulted in temperature predictions that differed from experimental measurements by no more than 1.5 percent for the non-steady state plunge and by no more than 9 percent for the steady state simulation. For both models, changes in the heat transfer coefficient had a large effect on tool temperature and very little effect on workpiece temperatures. Increasing the friction coefficient led to a proportional increase in temperature for both the tool and workpiece.

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The purpose of this project is to quantify the effects of increasing spinal ligament fidelity on the mechanics of the human lumbar spine using finite element analysis (FEA). In support of this goal, a material characterization study was completed to provide anisotropic, nonlinear material parameters for the human anterior longitudinal ligament. (ALL). Cadaveric samples of the human ALL were tested using a punch test technique. Multi- axial force-deformation data were gathered and fit to a commonly used transversely isotropic material model using an FEA system identification routine. The resulting material parameters produced a curve that correlated well with the experimental curve (R2≥0.98). Recently published material data on several major spinal ligaments have been incorporated into an existing finite element model of the human lumbar spine. This data includes the results from the above mentioned material characterization, similar material characterizations of the supraspinous (SSL) and interspinous (ISL) ligaments, localized material properties of the SSL and pre-strain data for the ISL, SSL and ALL. These results have been incorporated both separately and compositely into the finite element model and each configuration has been simulated in spinal flexion, extension, axial rotation and lateral bending. Results suggest that the effects of increased ligament model fidelity on bone strain energy were moderate and the effects on disc pressure were slight, and do not justify a change in modeling strategy for most clinical applications. There were significant effects on the ligament stresses of the ligaments that were directly modified, suggesting that these phenomenon should be included in FE models where ligament stresses are the desired metric.

Bone is a largely bipartite viscoelastic composite. Its mechanical behavior is determined by strain rate and the relative proportions of its principal constituent elements, hydroxyapatite and collagen, but is also largely dictated by their geometry and topology. Collagen fibrils include many segments of tropocollagen in staggered, parallel sequences. The physical staggering of this tropocollagen allows for gaps known as hole-zones, which serve as nucleation points for apatite mineral. The distance between adjacent repeat units of tropocollagen is known as D-Spacing and can be measured by Atomic Force Microscopy (AFM). This D-Spacing can vary in length slightly within a bundle, but by an additional order of magnitude within the same specimen, and can significantly alter the proportion of hydroxyapatite. Previous researchers have built and refined a Finite Element Analysis “Complex Model” to capture the consequences of adjusting D-Spacing and the viscoelastic parameters. This will ultimately serve to elucidate and perhaps predict the mechanical consequences of biological events that alter these parameters. This study aims to further refine the model’s precision by accounting for crosslinking between fibrils, the presence of which serves to add mechanical strength. This study also looks to refine the currently used rheological models by way of frequency dependent parameters in the hopes of improving model accuracy over a wider frequency range. Hormonal factors such as estrogen can significantly determine the composition of bone. Menopause marks a significant reduction in circulating estrogen and has been shown to factor heavily in the development of conditions like osteoporosis. Because sheep feature a hormonal cycle and skeletal structure similar to humans, three of six mature Columbia-Rambouillet ewes were randomly selected to undergo an ovariectomy, the remainder serving as sham-operated controls. Twelve months later twenty-five beam samples were harvested from their radius bones for mechanical analysis and other testing, including atomic force microscopy (AFM) and dynamic mechanical analysis (DMA). The data gleaned from these tests provide an experimental basis of comparison with The Complex Model. A 2-D Finite Element Analysis model in Abaqus was first created by Miguel Mendoza, which enforced viscoelasticity and a realistic proportion and placement of hydroxyapatite and collagen. The viscoelasticity was modeled using a Standard Linear Solid involving springs and a dashpot element. Crosslinks of varying number and location were arranged within the former model configuration as node to surface tie-constraints to explore the treatment of the FEA Model as a more realistic assembly of parts. Frequencies utilized for this model included 1, 3, 9 and 12 Hz. This approach is referred to in this research as the Intermolecular Forces (IMF) Scheme. The model was subsequently refined by Christopher Ha and Austin Cummings. The model was characterized by 2x100 unit half-cells, the lengths of which were randomly generated by a Python script. This script ingested the mean and standard deviation D-Spacing length to generate a model geometrically similar to a real specimen bearing those dimensions. A frequency dependent value for the dashpot element in the rheological model used for tropocollagen was developed using this latter FEA model, named the Complex Model. Dashpot values explored for this variable dashpot included 0.0125, 0.125, 0.3125, 0.45, 0.5875, 0.725, 0.8625 and 1.25 GPa-s, some values chosen for their high performance in past studies and others to further narrow the search for the best performing dashpot. All dashpot values were investigated over the previously stated frequencies in addition to 2, 5, 7 and 12 Hz. The best fit dashpot values were plotted against the frequencies in which they best performed and a polynomial trend line was fitted to establish an equation, and that equation was used to modify an existing user material subroutine for tropocollagen to provide an automatic frequency dependent dashpot value to Abaqus. This approach is referred to in this research as the Variable Dashpot (VD) Scheme. Results for the IMF scheme generally performed poorly, with the fully tie-constrained model performing best with 0.77 and 0.024 for R2 and RMSE respectively. Of the randomized crosslink models, that with the lowest number (N=20) of randomly placed non-enzymatic crosslinks performed best with 0.81 and 0.051 for R2 and RMSE respectively. Increasing the number of randomized crosslinks reduced model fit, and the remaining three variants exhibited mean R2 and RMSE values of 0.66-0.67 and 0.052 respectively. For the VD scheme, models running custom modified variable dashpot UMATs yielded R2 and RMSE values of 0.87 and 0.012 for C2207, and 0.89 and 0.008 for C1809. This is a notable fit considering all other material property parameters are held constant throughout each frequency. In the rheological model, this research also found a striking difference between the frequency dependent viscous element values that made each model perform best. This indicates that differences in D-Spacing standard deviations between OVX and control may be associated with distinct strain-rate dependent mechanical responses.

Atherosclerosis causes hundreds of thousands of deaths in the US alone every year. Fibrous cap rupture is one of the leading causes of these fatalities. Thin cap atheromas are commonly regarded as vulnerable plaque, however the effect of calcium upon a thin fibrous cap with lipid pool is poorly understood. Some studies have shown that calcium adds to stability of the lesion, while others have proven otherwise. An article by Li et al. 2007 suggests location is the key factor. By varying the percentage of calcium and lipid within a defined region, the stress on the cap was estimated using an idealized finite element arterial model. Also the thickness of the fibrous cap was varied to determine whether the stress was solely a function of lipid percentage or a combination. Plaque, arterial wall, lipid, and calcium were modeled using linear elastic, isotropic, and incompressible material properties. The first test varied the thin cap thickness from 65 to 500 microns and tested the calcified lipid model at varying lipid/calcium percentages. The lipid/Calcium pool increased/decreased 10% each test. As the cap thickness becomes thinner than 100 microns, the stress level increases rapidly. The second test compared a model with lipid pool and calcium behind the lipid with a thin cap of 65 microns to a model with lipid pool of the same size and thin cap of 65 microns but only fibrous tissue surrounding (no calcium). The lipid pool increased from 10 to 90% lipid. The result of this test found that at higher lipid percentages, the calcium increased the stress on the cap. By understanding the material properties of plaque and the structure of the lesion, future developments may be able to evaluate rupture risk. This idealized study illustrates the ability of computation models to provide insight into clinical situations.

Finite element models for the analysis of solid slabs and precast hollow core slabs composite girders are presented. For both models, 8-node three-dimensional solid elements are used in the analysis. The material non-linearity of all components of the composite girders is taken into consideration. The non-linear load-slip characteristics of the headed shear stud connectors are included in the models. The models predict load – deflection behaviour and stress distribution along the length of the beam. Good agreement is obtained between the models and results previously published.