The focus of this thesis is on using mechanical strain to tailor the electronic properties of graphene. The first half covers the electro-mechanical coupling for graphene in different configurations, namely a hexagonal Y-junction, various shaped bubbles on different substrates, and with kirigami cuts. For all of these cases, a novel combination of tight-binding electronic structure calculations and molecular dynamics is utilized to demonstrate how mechanical loading and deformation impacts the resulting electronic structure and transport. For the Y-junction, a quasi-uniform pseudo magnetic field induced by strain restricts transport to Landau-level and edge-state-assisted resonant tunneling. For the bubbles, the shape and the nature of the substrate emerge as decisive factors determining the effectiveness of the nanoscale pseudo magnetic field tailoring in graphene. Finally, for the kirigami, it is shown that the yield and fracture strains of graphene, a well-known brittle material, can be enhanced by a factor of more than three using the kirigami structure, while also leading to significant enhancements in the localized pseudo magnetic fields. The second part of the thesis focuses on dissipation mechanisms in graphene nanomechanical resonators. Thermalization in nonlinear systems is a central concept in statistical mechanics and has been extensively studied theoretically since the seminal work of Fermi, Pasta, and Ulam (FPU). Using molecular dynamics and continuum modeling of a ring-down setup, it is shown that thermalization due to nonlinear mode coupling intrinsically limits the quality factor of nanomechanical graphene drums and turns them into potential test beds for FPU physics. The relationship between thermalization rate, radius, temperature and prestrain is explored and investigated.

Recent advances in non-local continuum models, notably peridynamics, have spurred a paradigm shift in solid mechanics simulation by allowing accurate mathematical representation of singularities and discontinuities. This doctoral work attempts to extend the use of this theory to a community more familiar with local continuum models. In this communication, a coupling strategy - the morphing method -, which bridges local and non-local models, is presented. This thesis employs the morphing method to ease use of the non-local model to represent problems with failure-induced discontinuities. First, we give a quick review of strategies for the simulation of discrete degradation, and suggest a hybrid local/non-local alternative. Second, we present the technical concepts involved in the morphing method and evaluate the quality of the coupling. Third, we develop a numerical tool for the simulation of the hybrid model for fracture and damage and demonstrate its capabilities on numerical model examples

This project concerns the computational solution of inverse problems formulated as partial differential equation (PDE)-constrained optimization problems with interior data. The areas addressed are twofold. First, we present a novel software architecture designed to solve inverse problems constrained by an elliptic system of PDEs. These generally require the solution of forward and adjoint problems, evaluation of the objective function, and computation of its gradient, all of which are approximated numerically using finite elements. The creation of specialized "layered"' elements to perform these tasks leads to a modular software structure that improves code maintainability and promotes functional interoperability between different software components. Second, we address issues related to forward model definition in the presence of boundary condition (BC) uncertainty. We propose two variational formulations to accommodate that uncertainty: (a) a Bayesian formulation that assumes Gaussian measurement noise and a minimum strain energy prior, and (b) a Lagrangian formulation that is completely free of displacement and traction BCs. This work is motivated by applications in the field of biomechanical imaging, where the mechanical properties within soft tissues are inferred from observations of tissue motion. In this context, the constraint PDE is well accepted, but considerable uncertainty exists in the BCs. The approaches developed here are demonstrated on a variety of applications, including simulated and experimental data. We present modulus reconstructions of individual cells, tissue-mimicking phantoms, and breast tumors.

Cell modulus and prestress are important determinants of cell behavior. This study creates new software tools to compute the modulus and prestress distribution within a living cell. As input, we have a sequence of images of a cell plated on a substrate with fluorescently labeled fibronectin dots. The cell generates focal adhesions with the dots and thus deforms the substrate. A sequence of images of the cell and the fibronectin dots shows their deformation. We tested three different ways to track the movement of the fluorescent fibronectin dots. We demonstrated the accuracy and the adaptability of each method on a sequence of test images with a rigid movement. We found the best method for dot tracking is a combination of successive dot identification and digital image correlation. The dot deformation provides a measure of traction forces acting on the cell. From traction forces thus inferred, we use FEM to compute the stress distribution within a cell. We consider two approaches. The first is based on the assumption that the cell has homogeneous elastic properties. This is straightforward and requires only the cell being meshed and the linear elasticity problem solved on that mesh. Second, we relaxed the homogeneity assumption. We used previously published correlations between prestress and modulus to iteratively update the modulus and prestress distributions within the cell. A novel feature of this work is the implicit reconstruction of the modulus distribution without a measured displacement field, and the reconstruction of the prestress distribution accounting for intracellular inhomogeneity.

Concrete is a widely used product and is an important application throughout industry due to its inexpensive cost and wide range of applications. This work focuses on understanding the behavior of high strength concrete in high strain rate ballistic impact loading scenarios. A finite element analysis was created with the implementation of the Concrete Damage and Plasticity Model 2 (CDPM2) to represent the material behavior. The model’s parameters were calibrated to existing literature and the results were analyzed by a comparison of the impact velocity to residual velocity and a qualitative assessment of the impact crater. The model captured the impact dynamics of the contact between the projectile and the concrete target with defined fracture patterns. Impact velocity and target thickness indicated a relatively linear relationship with the final projectile velocity.

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The mechanical behavior of discrete atoms has been studied with molecular dynamics whose computational time is proportional to the square of the number of atoms, O(N²). Recently, a faster algorithm, Atomic-scale Finite Element Method (AFEM) with computational time proportional to the number of atoms, O(N), had been developed. The main idea of AFEM, compared with conventional finite element method is to replace nodes with atoms and elements with electric forces between atoms. When interpreting a non-linear system, it is necessary to use an iteration scheme. A simulation of molecular dynamics based on the Verlet's method was conducted in order to validate AFEM in one dimension. The speed of AFEM was investigated in one and two dimensional atomic systems. The results showed that the computational time of AFEM is approximately proportional to the number of atoms, and the absolute computation time appears to be small. The frameworks of AFEM not only for multi-body potential but also pair potential are presented. Finally, AFEM was applied to analyze and interpret the mechanical behavior of a carbon nanotube and a quartz. The buckling behavior of carbon nanotube showed a good agreement with the results illustrated in the original literature. / Master of Science

The demand for energy from developed and developing economies of the world is driving the search for energy resources to more challenging environments. The exploration and exploitation of hydrocarbons now requires the drillbit to hit pay zones from drillships or platforms that are located on water surfaces below which is, possibly, in excess of ten thousand feet of water above the sea bed. From Brazil, to the Gulf of Mexico and the Gulf of Guinea on the western coast of Africa, hitherto unfamiliar, but now common, concepts in the drilling parlance such as ultra-deep drilling (UDD), ultraextended- reach drilling (uERD) and slimhole drilling, are employed to reach and produce reservoirs which a few decades ago would seem technologically impossible to produce. This is expected to exert tremendous demands on the physical and mechanical properties of the drillstring components. Limiting factors for reaching and producing oil and gas resources hidden very deep in the subsurface are both the capacity of the drilling rig to support the weight of the drillstring, which in some instances can be several kilometres long, and the bending, tensile and impact stresses the string has to withstand in well trajectories that are getting both longer and more tortuous. Associated with this increased well depths and complex well trajectories is the prohibitive cost penalty of a failed drillstring. The in-service failure of drillstrings has always been an issue in the industry long before the wells become this deep and complex. The global oil and gas industry estimates the cost of string failure to be in excess of quarter of a billion dollars annually. Researchers are continuously looking for ways to design against string failure and improve the level of confidence in drillstrings. Defect-tolerant design, tooljoint geometry modification and surface coldworking are just a few of the ideas that have gained mileage in this effort. Others that are now in consideration are the use of nonconventional materials such as aluminium and titanium alloys for drillstring components. More novel, still, is the use of a combination of two materials - one ‘softer’ than the other to form a hybrid string of two materials of unequal moduli of elasticity. This is done to make the string lighter, reduce stress concentration factor at the connections and place fatigue resistant materials in areas of high well bore curvature.In this work a computational technique in the form of two-dimensional finite element analysis is used to develop a robust model of a drillstring connection and to analyse the stresses on the model of a threaded connection of standard drillstring tooljoint made from alloy steel. Further comparative analyses were undertaken on models of drillstrings made from a newly developed drillstring material for ultra-deep drilling, the UD-165, aluminium and titanium alloys and, finally, on hybrid drillstrings made from two different materials of unequal moduli of elasticity. The aim is not only to develop and validate a better method of computational drillstring analysis but also to use the model to investigate and suggest areas of optimisation that will benefit industry especially in the areas hybrid strings.

Multibody System Dynamics has been responsible for revolutionizing Mechanical Engineering Design by using mathematical models to simulate and optimize the dynamic behavior of a wide range of mechanical systems. These mathematical models not only can provide valuable informations about a system that could otherwise be obtained only by experiments with prototypes, but also have been responsible for the development of many model-based control systems. This work represents a contribution for dynamic modeling of multibody mechanical systems by developing a novel recursive modular methodology that unifies the main contributions of several Classical Mechanics formalisms. The reason for proposing such a methodology is to motivate the implementation of computational routines for modeling complex multibody mechanical systems without being dependent on closed source software and, consequently, to contribute for the teaching of Multibody System Dynamics in undergraduate and graduate levels. All the theoretical developments are based on and motivated by a critical literature review, leading to a general matrix form of the dynamic equations of motion of a multibody mechanical system (that can be expressed in terms of any set of variables adopted for the description of motions performed by the system, even if such a set includes redundant variables) and to a general recursive methodology for obtaining mathematical models of complex systems given a set of equations describing the dynamics of each of its uncoupled subsystems and another set describing the constraints among these subsystems in the assembled system. This work also includes some discussions on the description of motion (using any possible set of motion variables and admitting any kind of constraint that can be expressed by an invariant), and on the conditions for solving forward and inverse dynamics problems given a mathematical model of a multibody system. Finally, some examples of computational packages based on the novel methodology, along with some case studies, are presented, highlighting the contributions that can be achieved by using the proposed methodology. / A Dinâmica de Sistemas Multicorpos tem sido responsável por revolucionar projetos de Engenharia Mecânica pela utilização de modelos matemáticos para simulação e otimização do comportamento dinâmico de uma ampla gama de sistemas mecânicos. Estes modelos matemáticos não somente podem fornecer valiosas informações acerca de um sistema que caso contrário poderiam ser obtidas somente através de experimentos com protótipos, como também têm sido responsável pelo desenvolvimento de diversos sistemas de controle baseados em modelo. Este trabalho representa uma contribuição para a modelagem dinâmica de sistemas mecânicos multicorpos por meio do desenvolvimento de uma nova metodologia modular e recursiva que unifica as principais contribuições de diversos formalismos da Mecânica Clássica. A razão para propor tal metodologia é motivar a implementação de rotinas computacionais para a modelagem de sistemas mecânicos multicorpos complexos sem depender de pacotes de software de código fechado e, consequentemente, contribuir para o ensino de Dinâmica de Sistemas Multicorpos nos níveis de graduação e pós-graduação. Todos os desenvolvimentos teóricos são baseados em e motivados por uma revisão crítica da literatura, conduzindo a uma forma matricial geral das equações dinâmicas de movimento de um sistema mecânico multicorpos (que podem ser expressas em termos de qualquer conjunto de variáveis adotado para a descrição dos movimentos realizados pelo sistema, ainda que tal conjunto inclua variáveis redundantes) e a uma metodologia recursiva geral para a obtenção de modelos matemáticos de sistemas complexos, dado um conjunto de equações descrevendo a dinâmica de cada um de seus subsistemas desacoplados e outro descrevendo os vínculos entre estes subsistemas (no sistema) quando acoplado. Este trabalho também inclui algumas discussões acerca da descrição de movimentos (utilizando qualquer conjunto admissível de variáveis de movimento e admitindo qualquer tipo de vínculo que seja passível de descrição por invariantes), e das condições para a solução dos problemas de dinâmica direta e inversa dado um modelo matemático de um sistema multicorpos. Finalmente, alguns exemplos de pacotes computationais baseados na nova metodologia, juntamente com alguns estudos de caso, são apresentados, ressaltando as contribuições que podem ser alcançadas por meio do uso da metodologia proposta.