<p dir="ltr">Investigating the deformation and failure of human cortical bone under altered hydration contributes to the understanding of bone fracture. Further, studying the impact of hydration on bone deformation can lead to developing fracture prevention strategies that will enhance the lives of the aging population. In addition, characterization of cortical bone water modulation effects on biomechanical behavior helps us understand how bone dynamically changes due to aging, health conditions, and therapeutic interventions.</p><p dir="ltr">The concepts in this thesis are demonstrated on bone specimens of a 75-year-old male human subject. To investigate the potential role of water in bone as modulated by selective estrogen receptor modulators, we used magnetic resonance imaging to characterize bound water in human samples. The behavior of human cortical bone under mechanical loading protocols was tested to analyze the bone failure surface. Bone microstructure, microdamage, and fractures were observed from progressive bending experiments. Earlier evidence suggests that treating human cortical bone with Raloxifene (RAL) toughens bone but does not affect strength.</p><p dir="ltr">Questions remain about how RAL treatment affects bone biomechanics with the consideration of size effects. In this research, experiments were conducted on samples mimicking the thickness of cortical bone. Smaller thickness samples investigated in prior work were also considered, and intrinsic strength and tissue damage were introduced. Additionally, ultra-short echo-time magnetic resonance images were employed to observe 3D spatial information of bound and free water in the bone.</p><p dir="ltr">This research seeks to combine methods in bone biology and the mechanics of materials to solve problems of bone fragility. Linear strength concepts do not distinguish between treatments. However, treatment effects are detected with a nonlinear approach. Furthermore, this study provides valuable insights into quantifying bound water content within in-vitro specimen samples. These findings pave the way for further research into continued advancements addressing skeletal health challenges.</p>

A Natural nEighbours Method (NEM) based on the FRAEIJS de VEUBEKE (FdV) variational principle is developed in the domain of 2D infinitesimal transformations. This method is firstly applied to linear elastic problems and then is extended to materially nonlinear problems and problems of linear elastic fracture mechanics (LEFM). In all these developments, thanks to the FdV variational principle, the displacement field, the stress field, the strain field and the support reaction field are discretized independently. In the spirit of the NEM, nodes are distributed in the domain and on its contour and the corresponding Voronoi cells are constructed. In linear elastic problems the following discretization hypotheses are used: 1. The assumed displacements are interpolated between the nodes with Laplace functions. 2. The assumed support reactions are constant over each edge of Voronoi cells on which displacements are imposed. 3. The assumed stresses are constant over each Voronoi cell. 4. The assumed strains are constant over each Voronoi cell. The degrees of freedom linked with the assumed stresses and strains can be eliminated at the level of the Voronoi cells so that the final equation system only involves the nodal displacements and the assumed support reactions. The support reactions can be further eliminated from the equation system if the imposed support conditions only involve constant imposed displacements (in particular displacements imposed to zero) on a part of the solid contour, finally leading to a system of equations of the same size as in a classical displacement-based method. For the extension to materially non linear problems, similar hypotheses are used. In particular, the velocities are interpolated by Laplace functions and the strain rates are assumed to be constant in each Voronoi cell. The final equations system only involves the nodal velocities. It can be solved step by step by time integration and Newton-Raphson iterations at the level of the different time steps. In the extension of this method for LEFM, a node is located on each crack tip. In the Voronoi cells containing the crack tip, the stress and the strain discretization includes not only a constant term but also additional terms corresponding to the solutions of LEFM for modes 1 and 2. In this approach, the stress intensity coefficients are obtained as primary variables of the solution. The final equations system only involves the nodal displacements and the stress intensity coefficients. Finally, an eXtended Natural nEighbours Method (XNEM) is proposed in which the crack is represented by a line that does not conform to the nodes or the edges of the cells. Based on the hypotheses used in linear elastic domain, the discretization of the displacement field is enriched with Heaviside functions allowing a displacement discontinuity at the level of the crack. In the cells containing a crack tip, the stress and strain fields are also enriched with additional terms corresponding to the solutions of LEFM for modes 1 and 2. The stress intensity coefficients are also obtained as primary variables of the solution. A set of applications are performed to evaluate these developments. The following conclusions can be drawn for all cases (linear elastic, nonlinear, fracture mechanics). In the absence of body forces, the numerical calculation of integrals over the area of the domain is avoided: only integrations on the edges of the Voronoi cells are required, for which classical Gauss numerical integration with 2 integration points is sufficient to pass the patch test. The derivatives of the nodal shape functions are not required in the resulting formulation. The patch test can be successfully passed. Problems involving nearly incompressible materials can be solved without incompressibility locking in all cases. The numerical applications show that the solutions provided by the present approach converge to the exact solutions and compare favourably with the classical finite element method. / Une méthode des éléments naturels (NEM) basée sur le principe variationnel de FRAEIJS de VEUBEKE (FdV) est développée dans le domaine des transformations infinitésimales 2D. Cette méthode est dabord appliquée aux problèmes élastiques linéaires puis est étendue aux problèmes matériellement non linéaires ainsi quà ceux de la mécanique de la rupture élastique linéaire (LEFM). Dans tous ces développements, grâce au principe variationnel de FdV, les champs de déplacements, contraintes, réformations et réactions dappui sont discrétisés de façon indépendante. Dans lesprit de la NEM, des noeuds sont distribués dans le domaine et sur son contour et les cellules de Voronoi associées sont construites. En domaine élastique linéaire, les hypothèses de discrétisation sont les suivantes : 1. Les déplacements sont interpolés entre les noeuds par des fonctions de Laplace. 2. Les réactions dappui sont supposées constantes sur chaque côté des polygones de Voronoi le long desquels des déplacements sont imposés. 3. Les contraintes sont supposées constantes sur chaque cellule de Voronoi. 4. Les déformations sont supposées constantes sur chaque cellule de Voronoi. Les degrés de liberté associés aux hypothèses sur les contraintes et les déformations peuvent être éliminées au niveau des cellules de Voronoi de sorte que le système déquations final nimplique que les déplacement nodaux et les réactions dappui supposées. Ces dernières peuvent également être éliminées de ce système déquations si les conditions dappui nimposent que des déplacements constants (en particulier égaux à zéro) sur une partie du contour du domaine étudié, ce qui conduit à un système déquations de même taille que dans une approche basée sur la discrétisation des seuls déplacements. Pour lextension aux problèmes matériellement non linéaires, des hypothèses similaires sont utilisées. En particulier, les vitesses sont interpolées par des fonctions de Laplace et déformations sont supposées constantes sur chaque cellule de Voronoi. Le système déquations final nimplique que les vitesses nodales. Il peut être résolu pas à pas par intégration temporelle et itérations de Newton-Raphson à chaque pas de temps. Pour lextension de cette méthode aux problèmes de LEFM, un noeud est localisé à chaque pointe de fissure. Dans les cellules de Voronoi correspondantes, la discrétisation des contraintes et des déformations contient non seulement un terme constant mais aussi des termes additionnels correspondant aux solutions de la LEFM pour les modes 1 et 2. Avec cette approche, les coefficients dintensité de contraintes constituent des variables primaires de la solution. Le système déquations final ne contient que les déplacements nodaux et les coefficients dintensité de contraintes. Finalement, une méthode des éléments naturels étendue (XNEM) est proposée dans laquelle la fissure est représentée par une ligne indépendante des noeuds ou des côtés des cellules de Voronoi. La discrétisation utilisée en domaine élastique linéaire est enrichie par des fonctions de Heaviside qui autorisent une discontinuité des déplacements au niveau de la fissure. Dans les cellules contenant une pointe de fissure, les contraintes et les déformations sont aussi enrichies par des termes additionnels correspondant aux solutions de la LEFM pour les modes 1 et 2. Ici aussi, les coefficients dintensité de contraintes constituent des variables primaires de la solution. Une série dapplications numériques sont réalisées afin dévaluer ces développements. Les conclusions suivantes peuvent être tirées. Elles sappliquent à tous les cas (élastique linéaire, non linéaire, mécanique de la rupture) : En labsence de force volumique, le calcul numérique dintégrales sur laire du domaine est évité : seules sont nécessaires des intégrales numériques sur les côtés des cellules de Voronoi. Lutilisation de 2 points de Gauss suffit pour passer le patch test. Les dérivées des fonctions dinterpolation nodales ne sont pas nécessaires dans cette formulation. La formulation passe le patch test. Les problèmes impliquant des matériaux quasi incompressibles sont résolus sans verrouillage. Les applications numériques montrent que les solutions fournies par lapproche développée convergent vers les solutions exactes et se comparent favorablement avec celles de la méthode des éléments finis.

<p>Injection to the subcutaneous (SC) tissue is one of the preferred methods for drug delivery of pharmaceuticals, from small molecules to monoclonal antibodies. Delivery to SC has become widely popular in part thanks to the low cost, ease of use, and effectiveness of drug delivery through the use of auto-injector devices. However, injection physiology, from initial plume formation to the eventual uptake of the drug in the lymphatics, is highly dependent on SC mechanics, poroelastic properties in particular. Yet, the poroelastic properties of SC have been understudied. In this thesis, I present a two-pronged approach to understanding the poroelastic properties of SC. Experimentally, mechanical and fluid transport properties of SC were measured with confined compression experiments and compared against gelatin hydrogels used as SC-phantoms. It was found that SC tissue is a highly non-linear material that has viscoelastic and porohyperelastic dissipation mechanisms. Gelatin hydrogels showed a similar, albeit more linear response, suggesting a micromechanical mechanism may underline the nonlinear behavior. The second part of the thesis focuses on the multiscale modeling of SC to gain a fundamental understanding of how geometry and material properties of the microstructure drive the macroscale response. SC is composed of adipocytes (fat cells) embedded in a collagen network. The geometry can be characterized with Voroni-like tessellations. Adipocytes are fluid-packed, highly deformable and capable of volume change through fluid transport. Collagen is highly nonlinear and nearly incompressible. Representative volume element (RVE) simulations with different Voroni tesselations shows that the different materials, coupled with the geometry of the packing, can contribute to different material response under the different kinds of loading. Further investigation of the effect of geometry showed that cell packing density nonlinearly contributes to the macroscale response. The RVE models can be homogenized to obtain macroscale models useful in large scale finite element simulations of injection physiology. Two types of homogenization were explored: fitting to analytical constitutive models, namely the Blatz-Ko material model, or use of Gaussian process surrogates, a data-driven non-parametric approach to interpolate the macroscale response.</p>

This thesis concerns optimization of structures considering various uncertainties. The overall objective is to find methods to create solutions that are optimal both in the sense of handling the typical load case and minimising the variability of the response, i.e. robust optimal designs. Traditionally optimized structures may show a tendency of being sensitive to small perturbations in the design or loading conditions, which of course are inevitable. To create robust designs, it is necessary to account for all conceivable variations (or at least the influencing ones) in the design process. The thesis is divided in two parts. The first part serves as a theoretical background to the second part, the two appended articles. This first part includes the concept of robust design, basic statistics, optimization theory and meta modelling. The first appended paper is an application of existing methods on a large industrial example problem. A sensitivity analysis is performed on a Scania truck cab subjected to impact loading in order to identify the most influencing variables on the crash responses. The second paper presents a new method that may be used in robust optimizations, that is, optimizations that account for variations and uncertainties. The method is demonstrated on both an analytical example and a Finite Element example of an aluminium extrusion subjected to axial crushing. / ROBDES

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.