Fretting fatigue is a type of contact fatigue which causes premature failure in a number of engineering assemblies subjected to vibration or other forms of cyclic loading. It is concerned with the nucleation of cracks due to oscillatory micro slip between contacting bodies. Therefore, a detailed knowledge of the interface conditions and the means of quantifying crack nucleation are very important, and will be the ultimate goal of this thesis. The analysis of an incomplete contact (Herzian contact) is considered first followed by various complete contacts. Fretting fatigue tests employing a Hertzian contact are analysed accurately by introducing several modifications needed to the classical formulation. With the total state of stress in a strip established, the crack tip stress intensity factor for a crack growing inward from the trailing edge of the contact is determined by the distributed dislocation technique. The results are then correlated with local solutions for the contact stress field which enable an estimate of the crack nucleation life, and hence a characteristic material property quantifying initiation, to be found. The interfacial contact pressure distribution beneath a complete sliding contact between elastically similar components, in the presence of friction, has been studied in detail, with particular reference to contacts whose edge angles are 60 degree, 90 degree and 120 degree. The possible types of behaviour at the edge of contacts, namely power order singularity, power order bounded and square root bounded, are discussed. A full understanding of the behaviour requires a detailed study of a characteristic equation, and this shows the kinds of pressure distribution to be anticipated, which can vary very markedly. The transition from power order behaviour to local separation and bounded behaviour is examined, and an appropriate asymptotic form developed. The problem of trapezium shaped punches pressed into a frictional, elastically similar half-plane, and subject to sequential normal and shear loading, under partial slip, is studied. Detailed considerations have again been given to the specific cases of 60 degree, 90 degree and 120 degree punches, and maps have been developed showing the initial mix of stick, slip and separation regions, together with the steady state response when the shearing force is cycled. Conditions for full stick are established.

The aim of the current study is to develop an efficient model which can predict low-energy compatible microstructures in ferroelectric bulks and film devices and their dynamic behaviour. The results are expected to assist in the interpretation of microstructure observations and provide a knowledge of the possible domain arrangements that can be used to design future materials with optimum performance. Several recent models of ferroelectric crystals assume low energy domain configurations. They are mainly based on the idea of fine phase mixtures and average compatibility, and can require intensive computation resulting in complex domain configurations which rarely occur in nature. In this research, criteria for the exact compatibility of domain structure in the form of a periodic multi-rank laminate are developed. Exactly compatible structure is expected to be energetically favourable and does not require the concept of a fine mixture to eliminate incompatibilities. The resulting method is a rapid and systematic procedure for finding exactly compatible microstructures. This is then used to explore minimum rank compatible microstructure in various crystal systems and devices. The results reveal routes in polarization and strain spaces along which microstructure can continuously evolve, including poling paths for ferro- electric single crystals. Also, the method is capable to generate all possible exactly compatible laminate configurations for given boundary conditions. It is found that simple configurations are often energetically favourable in conditions where previous approaches would predict more complex domain patterns. Laminate domain patterns in ferroelectrics are classified and corre- lated with observations of domains in single crystals, showing good agreement. The evolution of microstructures under applied mechanical and electrical loads is studied. A variational method, which minimises the overall energy of the crystal is developed. A new concept of transitional “pivot states” is introduced which allows the model to capture the feature that the microstructure in ferroelectric crystal switches between possible domain patterns that are energetically favourable, rather than assuming one particular domain pattern throughout. This model is applied to study the hysteresis responses of barium titanate (BaTiO3) single crystals subjected to a variety of loads. The results have good agreement with experimental data in the literature. The relationship between domain patterns and ferroelectric hysteresis responses is discussed.

The aim of this doctoral research is to understand domain evolution processes in ferroelectrics using piezoresponse force microscopy (PFM) and Monte Carlo simulation. The results provide improved knowledge of domain evolution processes, and systematic experimental methods for research on domain evolution. There has been extensive previous research on domain evolution in ferroelectrics, but the research was mainly constrained to simple domain patterns. However, ferroelectric domains tend to form complex patterns that generate low-energy domain configurations. In this research, several methods such as statistical analysis of PFM data, ex situ/in situ PFM observation under electrical/mechanical loading and combining PFM with electron backscatter diffraction are employed to study domain evolution processes in complex domain patterns. The results show that domain switching almost always takes place by the evolution of pre-existing domain patterns, rather than direct flipping of polarization. Also the net effect of domain evolution processes follows a primary principle that positive work is done by external loads. But this principle is not always followed for microscopic switching processes. Multiple types of domain switching occur simultaneously, and occasionally an overwriting process involves unfavourable as well as favourable domain switching. Domain switching is significantly constrained by the pre-existing domain patterns. Meanwhile, angle-resolved PFM is developed for the systematic interpretation of PFM signal. Using lateral PFM images taken from multiple sample orientations, angle-resolved PFM maps are generated based on the angle of phase reversal in the PFM signal. The resulting maps reliably show complex domain patterns which may not appear in vertical and lateral PFM images. A model of domain evolution is developed using Monte Carlo simulation. Polarization switching by electric field and mechanical stress in the model is shown to take place via the motion of domain walls between pre-existing domains. Typical domain broadening processes are reproduced through this simulation.

This thesis aims toward developing strategies in the area of structural optimization and to implement these strategies in design processes. At   GM Powertrain Sweden where powertrains are designed and developed, two designs of a differential housing have been chosen for this thesis. The main tasks have been to perform a topology optimization of a model early in a design process, and a shape optimization on a model late in a design process. In addition the shape optimization strategies have also been applied on a fork shifter. This thesis covers the theory of different optimization strategies in general. The optimization processes are explained in detail and the results from the structural optimization of the differential housings as well as the fork shifter are shown and evaluated. The evaluation of the thesis provides enough arguments to suggest an implementation of the optimization strategies in design processes at GM Powertrain. A Structural Optimization group has great potential of closing the gap between structural designers and structural analysis engineers which in long terms mean that better structures can be developed in less time. To be competitive in the automotive industry these are two of the most important factors for being successful.

Silks are biomaterials made by spiders and silkworms, evolved for natural functions ranging from protection to predation. The research presented in this Thesis combines principles and methods from engineering, physics and biology to study the material properties of single silk fibres from a biological perspective. In particular, the factors that contribute to the variation in properties of single silk fibres are investigated. The first part of the Thesis focuses on silks made by silkworms. Whether naturally spun or forced reeled, the mechanical properties of these silks are sensitive to a range of environmental and processing conditions, such as humidity, stretching and reeling speed. The research presented in this section contributes to the understanding of how these applied conditions affect silk mechanical properties, which can be understood in terms of silk’s protein structure and biological context. The second section compares both silkworm and spider silk single fibres to other materials in terms of their sonic properties – how the materials propagate sound waves, whether following impact, or propagating vibrations. The results are discussed in the context of the silk’s natural function for impact resistance (silkworm cocoon or spider web) and vibrational signalling (spider silks). The Thesis ends with a discussion of how the presented techniques can be applied to help further our understanding of orb web function through studying spider silks. Overall, this interdisciplinary Thesis contributes to our understanding of the structure-property-function links of these fascinating biomaterials.

The tangential contact stiffness for ground Ti-6Al-4V surfaces is measured to linearly decrease with the application of tangential load. At the beginning of the application of tangential load, for ground surfaces, the ratio of the tangential contact stiffness to the normal contact stiffness is seen to be approximately half the Mindlin ratio. This is consistent with many other published experimental studies. Measurements of normal contact stiffness for ground surfaces conform to a model that posits a linear relationship between normal contact stiffness and normal load. An equivalent surface roughness parameter is defined for two surfaces in contact; and the normal contact stiffness for ground surfaces is observed to be inversely proportional to this parameter. Single asperity models were constructed to simulate the effect of different frictional laws and plasticity on the tangential displacement of an asperity contact. Further, multi-asperity modelling showed the effect of different normal load distributions on the tangential behaviour of interfaces. In addition, normal contact stiffness was modelled for a grid of asperities taking into account asperity interactions. A receding contact problem for which the required form of the distributed dislocations is bounded-bounded was solved. Then, a fundamental 2D frictional receding contact problem involving a homogeneous linear elastic infinite layer pressed by a line load onto a half-plane of the same material was analysed. This was done by the insertion of preformed distributed dislocations (or eigenstrains), which take into account the correct form of the separation of the interface at points away from the area of loading, along with corrective bounded-bounded distributions. The general method of solution was further refined and adapted to solve three other receding contact problems. The solutions demonstrated the robustness and applicability of this new procedure.

In the last decade, traumatic brain injuries (TBIs) and spinal cord injuries (SCIs) has become one of the most scrutinised medical challenges of our time. However, the lower quality of life experienced by the sufferer and the associated socio-economic cost of both TBI and SCI remain a huge burden for society. There is currently no reliable way to evaluate the level of functional damage caused by TBI and SCI related mechanical forces without invasive examination. The types of axonopathy involved in such injuries are the combinations of coupled mechanical-electrophysiological phenomena at multiple length and time scales, extremely challenging to approach by experimental means alone. It is therefore highly desirable to complement experimental studies with computational work to further the understanding of such multiscale problems. This thesis firstly proposes a novel 3D finite element framework coupling mechanics and electrophysiology to model cellular and subcellular phenomena, such as nerve dislocation and membrane damage by micropipette. The former study shows that 1D simulations focussing solely on the stretch component of the axonal damage are unable to capture the same electrophysiological damage that a 3D framework predicts. The latter study shows that local membrane deformation can lead to electrophysiological alterations at the axonal level solely through geometrical effects and without the need to account for ion channel activity alterations. This was demonstrated for micropipette suction in a patch clamp where the consideration of the 3D flow of current was sufficient to alter its electrophysiology, offering an alternative explanation to the damage mechanism hypothesised by published experimental work. At the axonal and tissue scale, previous models have often simplified the modelling of damage by using a single axon model. It is however unclear whether an altered axonal electrophysiology can truly be representative of the compound electrophysiology of multiple axons or fibre. Three different models: axonal, fibre and tissue level models, were evaluated and compared for their ability to model macroscale electrophysiology deficits. The results of the three models suggest that the recovery of compound action potential amplitude post-mechanical stretch can not be straightforwardly scaled from axonal level to fibre level. Furthermore, the electrophysiological recovery may not be solely dependent on mechanical recovery of the tissue. This thesis identified the need for scale specific models in the context of TBI and SCI. In particular, lipid bilayer membrane geometrical distortion following mechanical insult at the subcellular scale and functional tissue alteration at the tissue scale both require a different approach. The models proposed herein successfully identify mechanisms overlooked in previous experimental literature. In order to fully capture experimental behaviour, future models will need to account for other mechanisms such as mechanoporation, reorganisation of paranodal junctions and injury related Calcium ion imbalance.

Trabecular bone has a complex and porous microstructure. This study develops approaches to determine the mechanical behaviour of this material at the macroscopic level through the use of homogenisation-based multiscale methods using micro-finite element simulations. In homogenisation-based finite element methods, a simulation involving a representative volume element of the microstructure of the considered material is performed with a specific set of boundary conditions. The macroscopic stresses and strains are retrieved as averaged quantities defined over this domain. Most of the homogenisation-based work on trabecular bone has been performed to study its macroscopic elastic regime, and therefore define its constant macroscopic stiffness tensor. The rod and plate-shaped microstructure of trabecular bone can be precisely identified with advanced scanning tools, such as micro-computed tomography devices. Taking into account the size requirements to achieve a certain independence of boundary conditions for trabecular bone in a homogenisation-based multiscale setting, the resulting stack of images can have around ten million solid voxels after binarisation. Although a completely linear finite element simulation with such a large system may be feasible with commercial packages (with the proper time and memory requirements), it is not possible to perform a nonlinear simulation for such a mesh in a reasonable time frame, and the amount of required memory may not be available. A highly scalable parallel driver program which solves finite strain elastoplastic systems was developed within the framework of the existing parallel code ParaFEM. This code was used throughout this study to evaluate the yield and post-yield properties of trabecular bone. It was run on cutting edge high performance computing platforms (BlueGene/Q at the Hartree Centre, Science and Technology Facilities Council; and ARCHER, UK National Supercomputing Service, at Edinburgh Parallel Computing Centre). Micro-finite element simulations require definition of properties at the microscopic scale and it is unclear how these properties affect the macroscopic response. This study examines the effect of compressive hydrostatic yield at the microscopic scale on the macroscopic behaviour. Two different microscopic yield criteria, one permitting yielding at compressive hydrostatic stresses and the other not, were considered. A large number of load cases were examined. It was found that these two microscopic yield criteria only influence macroscopic yield behaviour in load scenarios which are compression-dominated; for other load cases, macroscopic response is insensitive to the choice of the microscopic yield criterion, provided it has an appropriate strength asymmetry. Also, in compression-dominated load cases, high density bone is much more sensitive as it is more like a continuum, resulting in the microscopic properties being more directly upscaled. Only a few previous studies have employed homogenisation to evaluate the macroscopic yield criterion of trabecular bone. However, they either used a simplified microscopic yield surface or examined only a small number of load cases. A thorough multiaxial evaluation of the macroscopic yield surface was performed by applying a wide range of loading scenarios (160 load cases) on trabecular bone samples. Closed-form yield surfaces with different symmetries (isotropy, orthotropy and full anisotropy) were fitted to the numerically obtained macroscopic yield points in strain space, and the fitting errors were evaluated in detail for different subsets of load cases. Although orthotropy and full anisotropy showed the smallest fitting errors, they were not significantly superior to the isotropic fit. Thus, isotropy in strain space presents itself as the most suitable option due to the simplicity of its implementation. The study showed that fitting errors do depend on the chosen set of load cases and that shear load cases are extremely important as it was found that even for these highly aligned samples, trabecular bone presents some degree of shear asymmetry, i.e. different strength in clockwise and counter-clockwise shear directions. There have been no previous attempts to evaluate the post-yield behaviour of trabecular bone through homogenisation-based studies on detailed micro-finite element trabecular bone meshes. A damage and plasticity constitutive law for the microscale based on existing data in the literature was considered. A homogenisation-based multiscale approach was used to evaluate the hardening and stiffness reduction at the macroscale when uniaxial load scenarios are applied to trabecular bone samples, for a small range of plastic strain Euclidean norms. Results show that damage progression at the macroscale for trabecular bone is not isotropic, which is contrary to what has been assumed previously, and that both the evolution of the yield surface and damage are different for tension, compression and shear. Nonetheless, they can be correlated with plastic strain Euclidean norms by using linear relationships. It was also observed that macroscopic damage in a specific load case affects differently the on-axis orthotropic stiffness and the off-axis orthotropic stiffness components. The findings of this study will permit the use of a more rigorous definition of the post-elastic macroscopic behaviour of trabecular bone in finite element settings.

Orientador: João Antonio Pereira / Banca: Gilberto Pechoto de Melo / Banca: Sérgio Sartori / Resumo: O presente trabalho propõe o estudo e implementação de uma metodologia para a estimação dos parâmetros modais de estruturas utilizando uma técnica de identificação baseada apenas na resposta do modelo, denominada Decomposição no Domínio da Freqüência (DDF). Para tal são abordados os conceitos básicos envolvidos na análise modal, análise modal baseada apenas na resposta e métodos de identificação. A formulação do algoritmo é baseada na decomposição da matriz densidade espectral de potência utilizando a técnica da decomposição em valores singulares (SVD). A decomposição da matriz densidade espectral nas linhas de freqüências correspondentes aos picos de amplitude, permite a estimativa dos modos de vibrar do sistema. Tem-se ainda que, o primeiro vetor singular obtido com a decomposição da matriz densidade espectral, para cada linha de freqüência, na região em torno do modo, contém as respectivas informações daquele modo e o correspondente valor singular leva a uma estimativa da função densidade espectral de um sistema de um grau de liberdade (1GL) equivalente. Neste caso, a matriz densidade espectral de saída é decomposta em um conjunto de sistemas de 1 grau de liberdade. Posteriormente, esses dados são transformados para o domínio do tempo, utilizando a transformada inversa de Fourier, e as razões de amortecimento são estimadas utilizando o conceito de decremento logaritmo. A metodologia é avaliada, numa primeira etapa, utilizando dados simulados e posteriormente utilizando dados experimentais. / Abstract: The present work proposes the study and implementation of a methodology for the estimating of the modal parameters of structures by using the output-only data. The technique called Frequency Domain Decomposition (DDF) identifies the modal parameters without knowing the input. For that, it is discussed the basic concepts involved in identification, modal analysis and output-only modal analysis. The formulation of the algorithm is based on the decomposition of the power spectral density matrix by using the singular values decomposition technique (SVD). The decomposition of the spectral density matrix for the lines of frequency corresponding to the amplitude peaks, allows the estimating of the modes shape of the system. Additionally, the first singular vector obtained with the decomposition of the spectral density matrix, for each line of frequency, in the area around of the peak, contains the respective information of that mode. The corresponding singular value leads to an estimating of the spectral density function of an equivalent system of one degree of freedom. Therefore, the output spectral density matrix is decomposed in a set of one degree of freedom system. Later on, those data are transformed for the time domain by using the inverse Fourier transform and the damping ratios estimated from the crossing times and the logarithm decrement of the corresponding single degree of freedom system correlation function. The methodology is evaluated using simulated and experimental data. / Mestre

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Dentre os materias comumente utilizados hà um destaque especial para os materiais compÃsitos polimÃricos, desde a fabricaÃÃo de brinquedos a artÃficios bÃlicos. Dessa forma faz-se necessÃrio uma investigaÃÃo ampla sobre todos os aspectos referentes a esses materiais. Assim, a presente pesquisa objetiva avaliar os processos de danificaÃÃo de um compÃsito polimÃrico ( polimetil metacrilato â PMMA, reforÃado com fibra de vidro) atravÃs de um modelo matemÃtico para a tensÃo normal. Primeiramente, foi realizada uma bateria de ensaios de traÃÃo e simulados numericamente, onde foram encontrados os parÃmetros matemÃticos caracterÃsticos deste material, foram apresentados tambÃm, os aspectos relativos a caracterizaÃÃo quÃmica e metalogrÃfica. A seguir foi realizado AnÃlises Computacionais pelo mÃtodo dos elementos finitos em um cÃdigo de cÃlculo internacionalmente conhecido, com o objetivo de verificar a relaÃÃo existente entre o comprimento de trincas e o valor da variÃvel dano. De posse destes dados foram determinados os valores para a variÃvel D0, e os intervalos de validade da expressÃo apresentada. Finalmente concluÃmos a importÃncia de estudos como este a fim de que se possa obter histÃricos de degradaÃÃo do material, para posterior anÃlise de vida remanescente do mesmo. Ainda nesta tÃnica determinou-se a relaÃÃo dano x comprimento da trinca, algo original em nossa literatura nacional, alÃm da apresentaÃÃo de sugestÃes para novos trabalhos, relacionados com a mecÃnica do dano em diversos materiais. / Dentre os materias comumente utilizados hà um destaque especial para os materiais compÃsitos polimÃricos, desde a fabricaÃÃo de brinquedos a artÃficios bÃlicos. Dessa forma faz-se necessÃrio uma investigaÃÃo ampla sobre todos os aspectos referentes a esses materiais. Assim, a presente pesquisa objetiva avaliar os processos de danificaÃÃo de um compÃsito polimÃrico ( polimetil metacrilato â PMMA, reforÃado com fibra de vidro) atravÃs de um modelo matemÃtico para a tensÃo normal. Primeiramente, foi realizada uma bateria de ensaios de traÃÃo e simulados numericamente, onde foram encontrados os parÃmetros matemÃticos caracterÃsticos deste material, foram apresentados tambÃm, os aspectos relativos a caracterizaÃÃo quÃmica e metalogrÃfica. A seguir foi realizado AnÃlises Computacionais pelo mÃtodo dos elementos finitos em um cÃdigo de cÃlculo internacionalmente conhecido, com o objetivo de verificar a relaÃÃo existente entre o comprimento de trincas e o valor da variÃvel dano. De posse destes dados foram determinados os valores para a variÃvel D0, e os intervalos de validade da expressÃo apresentada. Finalmente concluÃmos a importÃncia de estudos como este a fim de que se possa obter histÃricos de degradaÃÃo do material, para posterior anÃlise de vida remanescente do mesmo. Ainda nesta tÃnica determinou-se a relaÃÃo dano x comprimento da trinca, algo original em nossa literatura nacional, alÃm da apresentaÃÃo de sugestÃes para novos trabalhos, relacionados com a mecÃnica do dano em diversos materiais.