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.

Les géomatériaux tels les roches et le béton ont la particularité de s’amollir sous chargement dynamique, c.-à-d. que la vitesse du son diminue avec l’amplitude de forçage. Afin de reproduire ce comportement, un modèle de milieu continu à variables internes est proposé. Il est composé d’une loi de comportement donnant l’expression de la contrainte, et d’une équation d’évolution pour la variable interne. La viscoélasticité non linéaire de type Zener est prise en compte par l’ajout de variables internes supplémentaires. Les équations du mouvement forment un système de lois de conservation non linéaire et non homogène. Le système d’équations aux dérivées partielles est résolu numériquement à l’aide de la méthode des volumes finis. Une solution analytique du problème de Riemann de l’élastodynamique non linéaire est explicitée. Elle est utilisée pour évaluer les performances des méthodes numériques. Les résultats numériques sont en accord qualitatif avec les résultats expérimentaux d’expériences de résonance (NRUS) et d’acousto-élasticité dynamique (DAET). Des méthodes similaires sont développées en 2D pour réaliser des simulations de propagation d’ondes. Dans le cadre des méthodes de continuation reposant sur la décomposition en harmoniques, une méthode numérique est développée pour le calcul de solutions périodiques. Sur la base d’une discrétisation éléments finis des équations du mouvement, cette méthode fréquentielle donne des simulations de résonance rapides, ce qui est utile pour mener des validations expérimentales. / Geomaterials such as rocks and concrete are known to soften under a dynamic loading, i.e., the speed of sound diminishes with forcing amplitudes. To reproduce this behavior, an internal-variable model of continuum is proposed. It is composed of a constitutive law for the stress and an evolution equation for the internal variable. Nonlinear viscoelasticity of Zener type is accounted for by using additional internal variables. The equations of motion write as a nonlinear and nonhomogeneous system of conservation laws. This system of partial differential equations is solved numerically using finite-volume methods. An analytical solution to the Riemann problem of nonlinear elastodynamics is provided, which is used to benchmark the performances of the numerical methods. Numerical results are in qualitative agreement with experimental results from resonance experiments (NRUS) and dynamic acousto-elastic testing (DAET). Similar methods are developed in 2D to perform wave propagation simulations. In the framework of harmonic-based continuation methods, a numerical method is developed for the computation of periodic solutions. Based on a finite element discretization of the equations of motion, this frequency-domain method provides fast resonance simulations, which is useful to carry out experimental validations.

<p><p><p>This thesis aims toward developing strategies in the area of structural optimization and to implement these strategies in design processes. At</p><p> </p><em>GM Powertrain Sweden </em>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 <em>GM Powertrain</em><p>. 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.</p></p></p>

This dissertation concerns failure modelling with material imperfections and element erosion in finite element analyses. The aim has been to improve the element erosion technique, which is simple to use and implement and also computationally inexpensive. The first part of the dissertation serves as an introduction to the topic and as a summary of the methodologies presented in the following part. The second part consists of seven appended papers. In paper A the standard element erosion technique is used for projectile penetration. In papers B and C a methodology that accounts for size effects is developed and applied to crack initiation in armour steel and tungsten carbide. A methodology to better predict the stress state at crack tips with coarse meshes is presented and applied to armour steel in paper D. Papers E and F concern the development of selective mass scaling which allows for larger time steps in explicit methods. Finally, in paper G the previously presented methodologies are used in combination and validated against experimental results on tungsten carbide. The computations show good agreement with the experimental results on failure initiation for both materials, while the computational results on the propagation of cracks show better agreement for the armour steel than for the tungsten carbide. / On the day of the public defence of the doctoral thesis, the status of articles I, III and IV was Accepted and article VII was Submitted.

This thesis concerns the analysis of dynamical systems suitable to be modelled by piecewise-smooth differential equations. In such systems the continuous-in-time dynamics is interrupted by discrete-in-time jumps in the state or governing equations of motion. Not only can this framework be used to describe existing systems with strong nonlinear behaviour such as impacts and friction, but the non-smooth properties can be exploited to design new mechanical devices. As suggested in this work it opens up the possibility of, for example, fast limit switches and energy transfer mechanisms. Particularly, the dynamics at the onset of low-velocity impacts in systems with recurrent dynamics, so called grazing bifurcations in impact-oscillators, are investigated. As previous work has shown, low-velocity impacts is a strong source of instability to the dynamics, and efforts to control the behaviour is of importance. This problem is approached in two ways in this work. One is to investigate the influence of parameter variations on the dynamic behaviour of the system. The other is to implement low-cost control strategies to regulate the dynamics at the grazing bifurcation. The control inputs are of impulsive nature, and utilizes the natural dynamics of the system to the greatest extent. The scientific contributions of this work is collected in five appended papers. The first paper consists of an experimental verification of a map that captures the correction to the smooth dynamics induced by an impact, known in the literature as the discontinuity map. It is shown that the lowest order expansion of the map accurately captures the transient growth rate of impact velocities. The second paper presents a constructive proof of a control algorithm for a rather large class of impact oscillators. The proof is constructive in the sense that it gives control parameters which stabilizes the dynamics at the onset of low-velocity impacts. In the third paper a piecewise-smooth quarter-car model is derived, and the control strategy is implemented to reduce impact velocities in the suspension system. In the fourth and fifth papers the grazing bifurcation of an impact oscillator with dry friction type damping is investigated. It turns out that the bifurcation is triggered by the disappearance of an interval of stable stick solutions. A condition on the parameters of the system is derived which differentiates between stable and unstable types of bifurcation scenarios. Additionally, a low-cost control strategy is proposed, similar to the one previously mentioned, to regulate the bifurcation scenario. / QC 20100811

In this work the influence of Under Sleeper Pads on the dynamic forces on a railway track is investigated. A special interest is devoted to the effect of using Under Sleeper Pads in a railway track with changing vertical stiffness. The contact force between wheel and rail and the ballast contact forces are examined. For the investigation a finite element model with the length of thirty sleepers is created and calculations are performed with the software LS-DYNA. Three different cases of varying vertical track stiffness are studied: the transition from an embankment to a bridge, a randomly varying track stiffness along the railway track and hanging sleepers.

This thesis presents a continuum model for asphalt concrete incorporating non- linear viscoelasticity, viscoplasticity, mechanically-induced damage and moisture- induced damage. The Schapery single-integral viscoelastic model describes the nonlinear viscoelastic response. The viscoplastic model of Perzyna models the time- dependent permanent deformations, using a Drucker-Prager yield surface which is modified to depend on the third deviatoric stress invariant to include more complex dependence on state of stress. Mechanically-induced damage is modeled using continuum damage mechanics, using the same modified Drucker-Prager law to determine damage onset and growth. A novel moisture damage model is proposed, modeling moisture-induced damage using continuum damage mechanics; adhesive moisture- induced damage to the asphalt mastic-aggregate bond and moisture-induced cohesive damage to the asphalt mastic itself are treated separately. The analytical model is implemented numerically for three-dimensional and plane strain finite element analyses, and a series of simulations is presented to show the performance of the model and its implementation. Sensitivity studies are conducted for all model parameters and results due to various simulations corresponding to laboratory tests are presented. In addition to the continuum model, results are presented for a micromechanical model using the nonlinear-viscoelastic-viscoplastic-damage model for asphalt mastic and a linear elastic model for aggregates. Initial results are encouraging, showing the strength and stiffness of the mix as well as the failure mode varying with moisture loading. These initial results are provided as a an example of the model's robustness and suitability for modeling asphalt concrete at the mix scale.