<p>The rapid growth of fields such as metamaterials, composites, architected materials, porous solids, and micro/nano materials, along with the continuing advancements in design and fabrication procedures have led to the synthesis of complex structures having intricate material distributions and non-trivial geometries. These materials find important applications including biomedical implants and devices, aerospace and naval structures, and micro/nano-electromechanical devices. Theoretical and experimental evidences have shown that these structures exhibit size-dependent (or, nonlocal) effects. This implies that the response of a point within the solid is affected by a collection of points; ultimately a manifestation of the multiscale deformation process. Broadly speaking, at a continuum level, the mathematical description of these multiscale phenomena leads to integral constitutive models, that account for the long-range interactions via nonlocal kernels. </p> <p><br></p> <p>Despite receiving considerable attention, the existing class of approaches to nonlocal elasticity are predominantly phenomenological in nature, following from their definition of the material parameters of the nonlocal kernel based on 'representative volume element' (RVE)-based statistical homogenization of the heterogeneous microstructure. The size of the RVE required for practical simulation, does not achieve a full-resolution of the intricate heterogeneous microstructure, and also implicitly enforces the use of symmetric nonlocal kernels to achieve thermodynamic consistency and mathematically well-posedness. The latter restriction directly limits the application of existing approaches only to the linear deformation analysis of either periodic or isotropic nonlocal structures. Additionally, the lack of a consistent characterization of the nonlocal effects, often results in inconsistent (also labeled as 'paradoxical') predictions depending on the nature of the external loading. In order to address these fundamental theoretical gaps, this dissertation develops a fractional-order kinematic approach to nonlocal elasticity by leveraging cutting-edge mathematical operators derived from the field of fractional calculus.</p> <p><br></p> <p>In contrast to the class of existing class of approaches that adopt an integral stress-strain constitutive relation derived from the equilibrium of the RVE, the fractional-order approach is predicated on a differ-integral (fractional-order) strain-displacement relation. The latter relation is derived from a fractional-order deformation-gradient mapping between deformed and undeformed configurations, and this approach naturally localizes and captures the effect of nonlocality at the root of the deformation phenomena. The most remarkable consequence of this reformulation consists in its ability to achieve thermodynamic and mathematical consistency, irrespective of the nature of the nonlocal kernel. The convex and positive-definite nature of the formulation enabled the use of variational principles to formulate well-posed governing equations, the incorporation of nonlinear effects, and enabled the development of accurate finite element simulation methods. The aforementioned features, when combined with a variable-order extension of the fractional-order continuum theory, enabled the physically consistent application of the nonlocal formulation to general continua exhibiting asymmetric interactions; ultimately a manifestation of material heterogeneity. Indeed, a rigorous theoretical analysis was conducted to demonstrate the natural ability of the variable-order in capturing the role of microstructure in the deformation of heterogeneous porous solids. These advantages allowed the application of the fractional-order kinematic approach to accurately and efficiently model the response of porous beams and plates, with random microstructural descriptions. Results derived from multiphysical loading conditions, as well as nonlinear deformation regimes, are used to demonstrate the causal relation between the kinematics-based fractional-order characterization of nonlocal effects and the natural role of microstructure in determining the macroscopic response of heterogeneous solids. The potential implications of the developed formalism on scientific discovery of material laws are examined in-depth, and different areas for further research are identified.</p>

The purpose of this master thesis is to determine whether or not it exist, a model that can describethe reduction in strength, due to missing threads in a bond between a bolt and nut. And how thereduction in strength might effect a wall-shoe assembly, used to connect a wall to another wall or aconcrete base plate. This is done by firstly considering the strength of the entire wall-shoe assembly andthe strength of the bond between the nut and the bolt is then considered. The strength of the entire assembly is calculated using some simple analytical models. The strengthof the bolt is the limiting factor for the assembly given the analytical models. Four FEM-models arethen created, three to evaluate the strength of the bolt and nut assembly, for bolt sized from M6to M60 with thread engagement from one thread to seven threads.  An elastic model without a defined tensile stress limit is proposed. The maximum stress at the sharpgeometry changes (stress concentrations) are used to dimension the maximum allowed load accordingto the von Mises yield criterion.  The yield limit is implemented by introducing a elastic-plastic (without hardening) for three different materials. Where the maximum yield force is determined as the maximum reactionforce on the frictionless support boundary condition, when a displacement is applied. Material hardening is applied according to a bi-linear material model (with hardening). Thereaction force is evaluated and the maximum force and displacement can be determined using thedefinition of property class 8.8 that propose a yield limit of 80 percent of maximum load. The behavior of the anchor bolt when it is pulled out of the concrete was also modeled. To obtain anunderstanding of the pull-out behavior. The FEM-models makes it possible to formulate a simple reduction model, where the bolt failure loadis reduced by the calculated reduction factors. The reduction factors are dependent on the amountof missing thread due to damages or insufficient bolt height. The reduction factors are also highlydependent on the ratio between the rise and bolt diameter. The reduction factors are significantlysmaller when a perfect plastic material model is applied. The failure mode is dependent on the material model, when hardening is applied fewer threads areneeded to achieve bolt failure rather then thread failure, compared to when a ideal plastic materialmodel is applied. The reduction factors are not affected by the material yield limit, the maximal load is however highlydependent on the yield limit. The placement of the missing thread does not effect the reduction factors. They can therefor beused regardless of if threads are missing due to damage or due to partial thread engagement. A test of an M8 bolt was performed to attempt to validate the FEM-model. Due to some inherent flawsin the test procedure no clear conclusion, about the validity of the model can be made. It is howeverclear that missing threads induces risk of failure when tightening the assembly, since the bolt or nutcan be damaged without any clear signs that the assembly is compromised, leading to catastrophicfailure. Reducing the load with the reduction factor model should be done with caution. / Den här masteruppsatsen ämnar att besvara frågeställningen huruvida det finns en modell som kan beskriva den reduktion i hållfasthet, som förorsakas av ett bortfall av iskruvade gängor för ett förband mellan en bult och en mutter. Det görs genom att först betrakta styrkan för hela väggskoförbandet och delförbandet mellan bulten och muttern.  Hållfastheten av hela system som förbanden ämnar att sammanfoga (en vägg med grundplatta/vägg) beräknas. Fyra stycken FEM-modeller konstrueras sedan. Tre för att undersöka hållfastheten för bultar i storlekar mellan M6 och M60, med ett antal hela gängor med fullt ingrepp, i spannet från ett till sju. FEM-modell utan sträckgräns där maxlast beräknas med den maximala effektiva spänningen i modellen. En modell som kommer att visa sig vara bristfällig. FEM-modell där sträckgränsen implementeras för tre material, en elastik-plastisk material model utan härdning används. Den maximalt tillåtna kraften utvärderas med hjälp av reaktionskraften på det friktionsfria stödet. Där den maximalt beräknade antas motsvara förbandets sträckgräns.  En modell med bi-linjärt härdning. Reaktionskraften utvärderas och sambandet för Property Class 8.8 används för att bestämma förbandets maximalt tillåtna last. Alltså att sträckgränsen är 80 procent av brottgränsen. FEM model konstrueras för att få förståelse för hur brott för en ankarbult som dras ut ur betongen uppkommer. FEM-modellerna möjliggör en enkel modell baserat på reduktionsfaktorer där lasten reduceras för förbandet när gängvarv saknas, när gängorna är skadad eller när full mutter inte kan uppnås. Reduktionsfaktorn är lägre när den perfekt-plastiska modell används och större vid hårdnande.  Hur brottet sker ändras med materialmodellen. Den perfekt-plastisk model kräver fler gängor i ingrepp innan bulten går av, jämfört med när materialet kan hårdna vid plastisk deformation. Reduktionsfaktorerna är oberoende av materialets sträckgräns, den maximala lasten kommer dock ändras med sträckgränsen.  Placeringen av den avsaknade gängan verkar inte påverka reduktionsfaktorn, givet att en hel gänga saknas och att lika många gängor saknas.  Ett test med M8 gjordes för att testa bekräfta modellen men på grund av brister i testets utformning kunde inga slutsatser om FEM modellens giltighet göras. Det blev uppenbart att saknade gängor ökar riskan att förbandet brister när det spänns, eftersom gängorna kan förstöras utan utvändiga tecken på att det skett. Detta kan leda till ett plötsligt brott. Användandet av reducerings modellen för maxlast bör därför användas med försiktighet.

The aorta, the main and largest artery in the human body, is susceptible for many types of problems. One of the most common aortic disease is the formation of an aneurysm. Endovascular aortic aneurysm repair (EVAR) is a minimally invasive treatment option for aortic aneurysms, involving the deployment of an expandable stent graft within the aorta without operating the aneurysm directly. With 1.5 to 43 % of EVAR patients having postoperative complications, research to help predict these complications of EVAR is of essence. In this study, the deformations of the aorta induced by a deployed stent graft have been investigated and visualized in order to aid understanding of the geometrical behaviour of the aorta post EVAR. This has been carried out by the development and analysis of patient-specific aortic 3D reconstruction models, 3D printed physical models and FE simulation models. A qualitative assessment of the deformations was achieved by superimposing reconstructed geometries, revealing a light straightening of the aorta and iliac vessels, as well as anterior movement of the iliac branches. Based on the good agreement between the simulated and reconstructed geometries, the findings suggest that such deformations could be derived from the pressure being removed from the aneurysm due to the deployed stent graft, in combination with stent radial forces from the proximal and distal landing zones. Despite that the simulation seemed to underestimate distal movement of the iliac vessel, this study emphasizes the potential of 3D printing and FE analysis as promising tools for planning and research of EVAR. / Den stora kroppspulsådern, aortan, kan drabbas av flera olika sjukdomstillstånd. En av de vanligaste är bildandet av en aortaaneurysm. Endovaskulär Aneruysm Reparation (EVAR) är en operationsteknik för att behandla aortaaneurysmer och involverar positionering av ett rörformat, självexpanderande stentgraft innanför aortaaneurysmen via ljumskartärerna. Eftersom 1,5 till 43 % av EVAR-patienter råkar ut för postoperativa komplikationer är det väsentligt att bedriva vidare studier för att förutse dessa. I denna studie har deformationerna av en aorta på grund av positionerade stentar undersökts och visualiserade för att underlätta förståelsen av aortans geometriska beteende efter EVAR. Detta har gjorts genom att utveckla och analysera patientspecifika 3D-rekonstruktioner, 3D-printade fysiska modeller och simulerade modeller av en aorta. En kvalitativ bedömning av deformationerna uppnåddes genom att superpositionering av rekonstruerade geometrier, vilket avslöjade en lätt uträtning av aortan och tarmbensartärerna, samt en framförflyttning av de senare. Baserat på den goda överensstämmelsen mellan de simulerade och rekonstruerade modellerna, antyder resultaten att sådana deformationer kan härledas av att trycket avlägsnats från aneurysmen på grund av stentgraften, i kombination med radiellt tryck från stentar över och under aneurysmen. Trots att simuleringen underskattade framförflyttningen av tarmbensartärerna, belyser denna studie potentialen hos 3D-printing och FE-analyser som ett värdefullt verktyg för att planera och studera EVAR.

<p dir="ltr">This thesis focuses on the study of wave propagation in architected material systems. Specifically of interest is wave propagation in topologically interlocking material (TIM) systems made of tetrahedra and bio-inspired blocks. TIM systems are assemblies of composed of blocks in which the block geometry constrains blocks in place. Individual blocks can only be removed by disassembling the system. This interlocking of block geometry allows these systems to bear loads without the need for adhesives. Overall, load bearing is affected by block geometry, contact interaction, and assembly architecture. Wavefronts and wave velocities are computed using an explicit finite element code. Wave propagation is investigated first in a row of interlocking tetrahedra, then in 3D planar TIM systems of tetrahedra and bio-inspired scutoid blocks.</p><p dir="ltr">The propagation of linear traveling waves through a row of interlocking tetrahedra is demonstrated by the use of finite element simulations. The wave velocity was found to be independent of wave amplitude for ideal contact conditions but dependent on impact velocity for an exponential pressure-overclosure relationship between surfaces. For a frictionless, constant contact stiffness model, the effective wave velocity is about 50% of the 1D material wave speed. In the presence of friction, the wave velocity increases to about 80% of the 1D material wave speed. The wave velocity is attributed to wave-guiding set by the geometry of the tetrahedra. The wave velocity is further modulated by the rocking motion of the tetrahedra about an axis perpendicular to the wave propagation direction. The rocking motion is affected by friction and is reduced as friction is increased. Experimental results on wave propagation in a row of 3D-printed triangular prisms demonstrate pulse-like voltage versus time wave responses. With rough and tacky surfaces, the velocity of the linear traveling waves is measured as approximately 20% the 1D material wave speed. For smooth and low friction surface conditions, significantly higher wave velocities are measured. Similarly, reducing the number of contact surfaces by fusing pairs of building blocks also results in higher measured wave velocities. Experiments on rectangular prisms lack the wave-guiding geometry and provide a reference configuration. Finite element models are used to gain detailed insight into the wave propagation process. Wave-guide models are defined to predict wave speeds based on the effective path of wave propagation. The proposed models closely predict measured and computed wave speeds for the tetrahedra and triangular prisms.</p><p dir="ltr">Scutoids are prism-like shapes containing lateral vertices between two parallel polygonal surfaces. With the lateral vertices at the midplane, scutoid blocks can be periodically and densely packed. Scutoid-based planar arrays are demonstrated to behave mechanically as TIM systems. Under quasi-static transverse loads, assembly properties (stiffness, strength, toughness) match or exceed those of the corresponding tetrahedra-based TIM systems. The scutoid-based TIM systems have unique chiral characteristics. Chirality is attributed to the combination of building block and assembly symmetry. Chirality leads to asymmetric internal load transfer patterns resulting in unbalanced in-plane reaction forces and reaction moments. Experiments confirm the computational findings. Under transverse indentation, these systems have nonlinear force-displacement responses and measurable torque responses.</p><p dir="ltr">Wave propagation following transverse impact on planar arrays of interlocking tetrahedra and scutoids is investigated. Unique wave speed and wavefront development are demonstrated to occur in these systems. The 1D material wave speed emerges as the limiting wave speed of the TIM systems, rather than the dilatational wave speed. In tetrahedra assemblies, waves propagate with a velocity of approximately 25% of the 1D material wave speed. The wave velocity is attributed to wave-guiding from the interlocking tetrahedra geometry. Tetrahedra are not perfectly space-filling and block-to-block interactions are not limited to one direction. In the scutoid assemblies, waves propagate at velocities between 80% and 90% of the 1D material wave speed. These velocities are along directions associated with dominant load paths. The wave velocities in the scutoid-based TIM systems approach the 1D material wave speed as the contact surfaces are substantially orthogonal to the assembly surface. In comparison to monolithic plates, wavefronts develop with significant spatial non-uniformity. Wave patterns exhibit the symmetry or asymmetry also observed in the quasi-static response. Overall, contact surface orientation, block geometry, and assembly architecture affect wave velocity and wavefront development.</p>

Solar sails are an innovative propulsion mechanism for space exploration, harnessing the momentum of photons from the Sun to propel spacecraft. As material science advances and launch costs continue to fall, opportunities utilising the novel characteristics of solar sails become more and more feasible. Due to the inherit connection between mass and acceleration, it is of great importance to reduce mass to gain acceleration. This thesis investigates the structure of solar sails and provides an analysis of the forces they encounter. The study examines the forces acting on circular solar sails in space, as well as the unique challenges they face on Earth and during the launch phase. The membrane and supporting composite structure is analysed using mathematical models in MATLAB in order to develop and optimize structures for strength and reduced mass. Dimensioning forces were found and a preliminary structure discussed. By understanding these forces, it is possible to optimize the design and deployment of solar sails, paving the way for more efficient space missions. / Solsegel är en innovativ framdrivningsmekanism för rymdforskning som utnyttjar fotoners rörelsemängd från solen fotoner för att driva rymdfarkoster. I takt med att materialvetenskapen utvecklas och uppskjutningskostnader fortsätter att sjunka, blir möjligheterna att anv¨anda solsegels unika egenskaper alltmer genomförbara. På grund av det naturliga sambandet mellan massa och acceleration är det av stor vikt att minska massan för att öka accelerationen. Detta examensarbete undersöker strukturen hos solsegel och ger en analys av de krafter de utsätts för i olika stadier under dess livscykel. Studien granskar de krafter som verkar på seglen i rymden, samt de unika utmaningar de står inför på jorden och under uppskjutningsfasen. Membranet och den stödjande kompositstrukturen analyseras med hjälp av modeller i MATLAB för att utveckla och optimera strukturer med avseende pästyrka och vikt. Genom att förstå dessa krafter är det möjligt att optimera utformningen och utplaceringen av solsegel, vilket banar väg för allt mer effektiva och unika rymduppdrag.

This DPhil project is set in the context of single crystal elasticity-plasticity finite element modelling. Its core objective was to develop and implement a methodology for predicting the evolution of texture in single and dual-phase material systems. This core objective has been successfully achieved. Modelling texture evolution entails essentially modelling large deformations (as accurately as possible) and taking account of the deformation mechanisms that cause texture to change. The most important deformation mechanisms are slip and twinning. Slip has been modelled in this project and care has been taken to explore conditions where it is the dominant deformation mechanism for the materials studied. Modelling slip demands that one also models dislocations since slip is assumed to occur by the movement of dislocations. In this project a model for geometrically necessary dislocations has been developed and validated against experimental measurements. A texture homogenisation technique which relies on interpretation of EBSD data in order to allocate orientation frequencies based on representative area fractions has been developed. This has been coupled with a polycrystal plasticity RVE framework allowing for arbitrarily sized RVEs and corresponding allocation of crystallographic orientation. This has enabled input of experimentally measured initial textures into the CPFE model allowing for comparison of predictions against measured post-deformation textures, with good agreement obtained. The effect of texture on polycrystal physical properties has also been studied. It has been confirmed that texture indeed has a significant role in determining the average physical properties of a polycrystal. The thesis contributes to the following areas of micro-mechanics materials research: (i) 3D small deformation crystal plasticity finite element (CPFE) modelling, (ii) geometrically necessary dislocation modelling, (iii) 3D large deformation CPFE modelling, (iv) texture homogenisation methods, (v) single and dual phase texture evolution modelling, (vi) prediction of polycrystal physical properties, (vii) systematic calibration of the power law for slip based on experimental data, and (viii) texture analysis software development (pole figures and Kearns factors).

The aim of this thesis was to improve the understanding of microstructure in single crystal ferroelectrics. This was achieved through macroscopic testing of Lead Magnesium Niobate – Lead Titanate (PMN-PT) and microscopic observations of Barium Titanate (BT) single crystals. Multi-axial polarization rotation tests on PMN-PT showed a gradual increase in the change in dielectric displacement due to ferroelectric switching as the electric field is applied at increasing angles to the initial polarization direction. A relatively high remnant polarization for loading angle near to 90° suggested that PMN-PT is more polarizable in certain directions. Strains measured in two directions, parallel to the electric field and perpendicular to the electric field, showed a noticeable variation on two opposite faces of the specimen suggesting an effect of local domain configurations on macroscopic behaviour. A micromechanical model gave an insight into the switching systems operating in the crystal during the polarization rotation test. Domain structure in BT was mapped using synchrotron X-ray reflection topography. By making use of the angular separation of the diffracted reflections and specimen rocking, different domain types could be unambiguously identified, along with the relative tilts between adjacent domains. Fine needle domains (width ≈ 10μm) were successfully mapped providing a composite topograph directly comparable with optical micrograph. The domain structure was confirmed using other techniques such as piezoresponse force microscopy and atomic force microscopy/scanning electron microscopy and optical observations on the etched crystal. Results show that combined use of multiple techniques is necessary to gain a consistent interpretation of the microstructure. Finally, domain evolution in BT under compressive mechanical loading was observed in-situ using optical and X-ray diffraction techniques providing a series of images that show ferroelastic transition. The domain configurations influence the switching behaviour and constitutive models that can account for such effects need to be developed. Quantitative and qualitative data presented in this thesis can assist model development and validation.

Although the tensile mechanical properties of tendon have been well characterised, the viscoelastic and anisotropic properties remain uncertain. This thesis addresses the anisotropic and viscoelastic material properties of tendon. A method to characterise the three-dimensional shape of tendon is reported and experiments to characterise the fibre-aligned and fibre-transverse viscoelastic properties of tendon are presented. The cross-sectional profiles of bovine digital extensor tendons were determined by a laser-slice method. Linear dimensions were measured within 0.15 mm and cross-sectional areas within 1.7 mm². Tendons were compressed between two glass plates in creep loading at multiple loads. Compression was then modelled in a finite element environment. Tendon was found to be nearly incompressible and reproduction of its isochronal load-displacement curve was achieved with a neo-Hookean material model (E ≃ 0.3 MPa). The fibre-aligned tensile mechanical properties were described using a Quasi-Linear Viscoelastic model. The model was effective at reproducing cyclic loading; however, it was ineffective at predicting stress relaxation outside the scope of data used to fit the model. When all experimental results are considered together, two significant conclusions are made: (1) tendon is much stiffer in fibre-aligned tension than in fibre-transverse compression and (2) the fibre-aligned tensile response is strain dependant, while the transverse response is not.

This thesis considered the design of new and improved foldcore sandwich panels suitable for high-performance energy absorption applications. This was achieved by utilising origami geometry design techniques to alter foldcore structures such that they possessed different mechanical behaviours and failure modes. The major findings of this thesis were in three areas as follows. First, a modified planar foldcore geometry was developed by introducing sub-folds into a standard foldcore pattern. The new geometry, deemed the indented foldcore, successfully triggered a high-order failure mode known as a travelling hinge line failure mode. This was found to have a much higher energy absorption than the plate buckling failure mode seen in an unmodified foldcore structure. A comprehensive numerical, theoretical, and experimental analysis was conducted on the indented core, which included the development of a new foldcore prototyping method that utilised 3D printed moulds. It was shown that compared to available commercial honeycomb cores, the indented foldcore had an improved uniformity of energy absorption, but weaker overall peak and crushing stresses. Second, rigid origami design principles were used to develop extended foldcore geometries. New parametrisations were presented for three patterns, to complete a set of Miura-derivative geometries termed first-level derivatives. The first-level derivative parametrisations were then combined to create complex, piecewise geometries, with compatible faceted sandwich face geometry also developed. Finally, a method to generate rigid-foldable, curved-crease geometry from Miura-derivative straight-crease geometry was presented. All geometry was validated with physical prototypes and was compiled into a MATLAB Toolbox. Third, the performance of these extended foldcore geometries under impact loadings was investigated. An investigation of curved-crease foldcores showed that they were stronger than straight-crease foldcores, and at certain configurations can potentially match the strength, energy-absorption under quasi-static impact loads, and out-of-plane stiffness of a honeycomb core. A brief investigation of foldcores under low-velocity impact loadings showed that curved-crease foldcores, unlike straight-crease foldcores, strengthened under dynamic loadings, however not to the same extent as honeycomb. Finally, an investigation of single-curved foldcore sandwich shells was conducted. It was seen that foldcore shells could not match the energy-absorption capability of an over-expanded honeycomb shell, but certain core types did exhibit other attributes that might be exploitable with future research, including superior initial strength and superior uniformity of response.

Engineering assemblies are very frequently subject to fretting fatigue, which is a damage process that results when very small slip displacements arise at nominally stationary frictional interfaces. Fretting accelerates the initiation and early propagation of fatigue cracks, thereby causing significant reductions in the fatigue performance of many critical engineering components. A majority of the previous research on fretting fatigue has focused on incomplete (i.e. smooth-edged) contacts, while complete (i.e. sharp-edged) contacts have received less attention. The aim of this thesis is to contribute to the theoretical understanding of complete contacts, especially when they are subject to fatigue conditions. This problem is addressed in two separate ways. First, because fretting failures almost invariably initiate from the edge of contact, a detailed understanding of the conditions in this region should enable more accurate assessments of fatigue performance to be made. Thus, an asymptotic analysis is presented, which provides an accurate description of the contact edge under many conditions. This is done by using the elasticity solution for a semi-infinite notch to represent the state of stress near the contact edge in an asymptotic sense. Attention is then placed on the fact that cyclically loaded frictional contacts tend toward a steady-state response in which less frictional slip (and energy dissipation) occurs than in the first few load cycles. To investigate this effect, a numerical sub-structuring procedure is described, which significantly reduces the number of degrees of freedom in finite element models of frictional contact. This reduced model is then used to calculate the shakedown limit, i.e. the amplitude of cyclic load above which frictional slip is guaranteed to persist in the steady state. The sensitivity of the steady-state solution to the initial residual displacement state is then investigated, and it is shown that initial conditions can have a large influence on the steady-state behaviour of complete contacts.