The mechanical response tissue analyzer (MRTA) tests long bone quality through low frequency, low amplitude vibration in vivo. The MRTA measures complex stiffness over a range of low frequencies, offering a wealth of information on bone composition. Previous MRTA interpretation used lumped parameter algorithms focused on reliably estimating the bone's bending stiffness (EI). To interpret the stiffness response, the first finite element (FE) simulation of the MRTA test of a human tibia was developed to identify dominant parameters that will possibly make linear prediction algorithms more suitable for estimating bone quality. Five FE models were developed in stages by adding complexity. Starting with a solid mesh of the diaphysis, each model was created from its predecessor by sequentially adding: a medullary canal, linear elastic (LE) cancellous epiphyses, linear viscoelastic (LVE) cancellous and cortical bone, and a LVE skin layer. The models were simulated in vibration using a direct steady-state dynamics procedure in ABAQUS to calculate the complex stiffness response. Natural frequency analysis (ABAQUS) verified that the FE models accurately reproduced previous experimental and computational resonances for human tibiae. A solid, LE cortex roughly matched the dominant frequency from experimental MRTA raw data. Adding the medullary canal and LVE properties to bone did not greatly spread the peak or shift the resonant frequency. Adding the skin layer broadened the peak response to better match the MRTA experimental response. These results demonstrate a simulation of the MRTA response based upon published geometries and material data that captures the essence of the instrument. / Master of Science

Micro-motion devices may share a common architecture such that they have a main body of compliant material and some direct actuation elements (e.g., piezoelectric element). The shape of such a compliant material is designed with notches and holes on it, and in this way one portion of the material deforms significantly with respect to other portions of the material a motion in the conventional sense of the rigid body mechanism. The devices of this kind are called compliant mechanisms. Computer tools for the kinematical and dynamic motion analysis of the compliant mechanism are not well-developed. In this thesis a study is presented towards a finite element approach to the motion analysis of compliant mechanisms. This approach makes it possible to compute the kinematical motion of the compliant mechanism within which the piezoelectric actuation element is embedded, as opposed to those existing approaches where the piezoelectric actuation element is either ignored or overly simplified. Further, the developed approach allows computing the global stiffness and the natural frequency of the compliant mechanism. This thesis also presents a prototype compliant mechanism and a test bed for measuring various behaviors of the prototype mechanism. It is shown that the developed approach can improve the prediction of motions of the compliant mechanism with respect to the existing approaches based on a comparison of the measured result (on the prototype) and the simulated result. The approach to computation of the global stiffness and the natural frequency of the compliant mechanism is validated by comparing it with other known approaches for some simple mechanisms.

Asphalt pavement rutting is one of the most commonly observed pavement distresses and is a major safety concern to transportation agencies. Millions of dollars are reportedly spent annually to repair rutted asphalt pavements. Research into improvements of hot-mix asphalt materials, mix designs and methods of pavement evaluation and design, including laboratory and field testing, can provide extended pavement life and significant cost savings in pavement maintenance and rehabilitation. This research describes a method of predicting the behaviour of various asphalt mixes and linking these behaviours to an accelerated performance testing tool and pavement in-situ performance. The elastic, plastic, viscoelastic and viscoplastic components of asphalt mix deformation are also examined for their relevance to asphalt rutting prediction. The finite element method (FEM) allows for analysis of nonlinear viscoplastic behaviour of asphalt mixes. This research determines the critical characteristics of asphalt mixes which control rutting potential and investigates the methods of laboratory testing which can be used to determine these characteristics. The Hamburg Wheel Rut Tester (HWRT) is used in this research for asphalt laboratory accelerated rutting resistance testing and for calibration of material parameters developed in triaxial repeated load creep and creep recovery testing. The rutting resistance criteria used in the HWRT are developed for various traffic loading levels. The results and mix ranking associated with the laboratory testing are compared with the results and mix ranking associated with FEM modeling and new mechanistic-empirical method of pavement design analyses. A good relationship is observed between laboratory measured and analytically predicted performance of asphalt mixes. The result of this research is a practical framework for developing material parameters in laboratory testing which can be used in FEM modeling of accelerated performance testing and pavement in-situ performance.

Micro-motion devices may share a common architecture such that they have a main body of compliant material and some direct actuation elements (e.g., piezoelectric element). The shape of such a compliant material is designed with notches and holes on it, and in this way one portion of the material deforms significantly with respect to other portions of the material a motion in the conventional sense of the rigid body mechanism. The devices of this kind are called compliant mechanisms. Computer tools for the kinematical and dynamic motion analysis of the compliant mechanism are not well-developed. In this thesis a study is presented towards a finite element approach to the motion analysis of compliant mechanisms. This approach makes it possible to compute the kinematical motion of the compliant mechanism within which the piezoelectric actuation element is embedded, as opposed to those existing approaches where the piezoelectric actuation element is either ignored or overly simplified. Further, the developed approach allows computing the global stiffness and the natural frequency of the compliant mechanism. This thesis also presents a prototype compliant mechanism and a test bed for measuring various behaviors of the prototype mechanism. It is shown that the developed approach can improve the prediction of motions of the compliant mechanism with respect to the existing approaches based on a comparison of the measured result (on the prototype) and the simulated result. The approach to computation of the global stiffness and the natural frequency of the compliant mechanism is validated by comparing it with other known approaches for some simple mechanisms.

Biological materials are complex hierarchical systems subjected to external stimuli like mechanical forces, chemical potentials and electrical signals. A deeper understanding of the behavior of these materials is required for the response characterization of healthy and diseased conditions. The primary aim of this dissertation is to study the mechanics of biological materials like cells and tissues from a computational perspective and relate its behavior with experimental works, so as to provide a framework for the identification and treatment of pathological conditions like cancer and vascular diseases. The first step towards understanding the behavior of a biological cell is to comprehend its response to external mechanical stimuli. Experimentally derived material properties of cells have found to vary by orders of magnitude even for the same cell type. The primary cause of such disparity is attributed to the stimulation process, and the theoretical models used to interpret the experimental data. The variations in mechanical properties obtained from the experimental and theoretical studies can be overcome only through the development of a sound mathematical framework correlating the derived mechanical property with the cellular structure. Such a formulation accounting for the inhomogeneity of the cytoplasm due to stress fibers and actin cortex is developed in this work using Mori-Tanaka method of homogenization. Mechanical modeling of single cells would be extremely useful in understanding its behavior in an experimental setup. Characterization of in-vivo response of cells requires mathematical modeling of the embedding environment like fibers and fluids, which forms the extra cellular matrix. Studies on fluid-tissue interactions in biomechanics have primarily relied on either an iterative solution of the individual solid or tissue phases or a sequential solution of the entire domain using a coupled algorithm. In this dissertation, a new computational methodology for the analysis of fluid-tissue interaction problem is presented. The modeling procedure is based on a biphasic representation of fluid and tissue domain, consisting of fluid and solid phases. The biphasic-fluid interaction model is also implemented to study the transfer of low-density lipoprotein from the blood to the arterial wall, and also the nutrient transfer in the tissue scaffolds of a bioreactor.

After Total Knee Arthroplasty, contact stresses at the surface and stresses at the implant-cement-bone interface are directly related to the joint contact forces. These stresses are a major factor in wear and fatigue, aseptic loosening, stress shielding and osteoporosis. Implant contact stresses influence the wear and fatigue damage of the Ultra High Molecular Weight Polyethylene (UHMWPE) articulating surface, decreasing the longevity of the implant. The contact stresses are influenced by the kinematics, the bearing congruency of the articulating surfaces and insert thickness. Thus, various studies have focused on the prediction and optimization of kinematics at the joint interface, contact areas, and stresses in different knee implant designs. As a result, the successful total knee replacement designs depend on joint kinematics and the contact stresses. The objective of this study was to perform contact stress analysis on a newly designed surface guided knee implant, in order to evaluate the design with respect to the potential of polyethylene wear. In order to test the performance of this design, Finite Element Modeling (FEM) was used as a good medium to analyze the design’s specifications, and to evaluate the results of the stress analysis of the design. For validation and also comparison with previous studies, results of this study were compared with those of related work with similar loading and constraints. Based on the gathered data from FE analysis of the design, it can be concluded that the new surface guided knee implant shows lower peak contact pressure than other previously evaluated implants. / October 2015

The Very Low Frequency Electromagnetic (VLF-EM) method, which enables surveying without contact with the ground, is suitable for ground surveys in a wide area and has been used in mapping geology for decades. The technique makes use of signal radiation from military navigation radio transmitters operating in the frequency range of 15-30 kHz. When the electromagnetic wave impinges on the surface it is both reflected back into the air and refracted into the earth. By measuring the shifted reflected magnetic field relative to the primary field, subsurface structures can be constrained. Although the VLF method has been widely used to map geology in the last several decades, few modeling studies have been published. Particularly the effect of topography on VLF measurements is poorly characterized. The objective of my research is to study and simulate the VLF topographic responses, and therefore to distinguish between such responses and actual subsurface resistivity anomalies in VLF-EM data. A few basic models (homogenous half-space, horizontal contact and vertical contact) were first created using the finite-elements modeling software Comsol Multiphysics and verified with theoretical solutions. Subsequently, features such as hills and lakes were incorporated into these basic models and further analyzed. When modeling topographic effects, two relationships between max inphase / max slope and max Quad / max slope versus skin depth / hill width are found, which can be used to predict topographic effects when the slope of a hill and resistivity of the ground are known. Two different sets of field data acquired at Saskatoon’s Diefenbaker Hill and at Cameco’s Cree Extension are compared with the modeling results.

In this thesis the finite element computer code QUEANA simulating the quenching of axisymetric parts and determining the residual stress state was improved by adding pre- and post-processors. The code was further verified by additional numerical experiments and comparison of the results with commercial software &ldquo / MARC&rdquo / . The possible applications of this code are optimization of industrial quenching processes by controlling the evolution of internal stresses and dimensional changes.

abstract: Pb-free solders are used as interconnects in various levels of micro-electronic packaging. Reliability of these interconnects is very critical for the performance of the package. One of the main factors affecting the reliability of solder joints is the presence of porosity which is introduced during processing of the joints. In this thesis, the effect of such porosity on the deformation behavior and eventual failure of the joints is studied using Finite Element (FE) modeling technique. A 3D model obtained by reconstruction of x-ray tomographic image data is used as input for FE analysis to simulate shear deformation and eventual failure of the joint using ductile damage model. The modeling was done in ABAQUS (v 6.10). The FE model predictions are validated with experimental results by comparing the deformation of the pores and the crack path as predicted by the model with the experimentally observed deformation and failure pattern. To understand the influence of size, shape, and distribution of pores on the mechanical behavior of the joint four different solder joints with varying degrees of porosity are modeled using the validated FE model. The validation technique mentioned above enables comparison of the simulated and actual deformation only. A more robust way of validating the FE model would be to compare the strain distribution in the joint as predicted by the model and as observed experimentally. In this study, to enable visualization of the experimental strain for the 3D microstructure obtained from tomography, a three dimensional digital image correlation (3D DIC) code has been implemented in MATLAB (MathWorks Inc). This developed 3D DIC code can be used as another tool to verify the numerical model predictions. The capability of the developed code in measuring local displacement and strain is demonstrated by considering a test case. / Dissertation/Thesis / M.S. Mechanical Engineering 2011

Abstract The main objective of this thesis is to study unique cases for computer-assisted finite element modeling (FEM) of thermal, mechanical and thermo-mechanical problems related to silicon and carbon. Computational modeling contributed to solve scientific problems either by validating the experimental results obtained earlier or by predicting the behavior of a particular system. In the model generation phase, emphasis is placed on simplification of a physical problem without loosing the validity or important details. As a consequence of reasonably reduced variables and also degrees of freedom of the elements in our models, the simulations could be performed using a commercial FEM software package, ANSYS®. To test the capabilities of the method (i) a steady-state finite element thermal analysis has been accomplished and verified by experiments for the case of laser-assisted heating of different materials. (ii) Mechanisms (Dember and Seebeck effects) responsible for the reduction of gold ions and deposition of metallic gold on p-type semiconductors from liquid precursors have been investigated by computing the surface temperature profiles of silicon wafers exposed to laser irradiation. (iii) Temperature field in a multi-component system caused by laser illumination was modeled to determine the heat affected zone in the case of laser soldering of flip-chips on transparent printed circuit board assemblies. (iv) Origin of the experimentally observed residual strain in thermally oxidized porous silicon structures was revealed by computing the strain fields in silicon-silicon oxide porous materials considering both intrinsic and thermal stress components. (v) Finally, we demonstrated that Joule heat generated on a silicon chip can be removed efficiently using micro-fin structures made from aligned carbon nanotubes. Computational fluid dynamics and thermal-electric finite element models were developed to study the steady-state laminar coolant flow and also the temperature distribution for the chips. The presented novel results have potential in silicon and carbon nanotube based technologies, including deeper understanding of the processes and problems in manufacturing electronic devices.