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Cardiac diseases are among the most prevalent in the world. The scope and impact of these diseases on society are far-reaching. Therefore, developing tools to aid in identifying and understanding the underlying mechanisms of these diseases is an ongoing and vital field of research in which computational modelling has emerged as an essential tool. Using flexible, open-source software, and modern numerical methods can aid in this endeavour. In this thesis, I have developed a computational platform, for the simulation of bio-physically detailed cardiac tissue models with general cell models. This platform consists of significant additions to the open-source multi-physics finite element library Object Oriented Multi-physics Library (Oomph-lib) and allows for the novel application of Oomph-lib to cardiac modelling. These developments couple single-cell models to tissue and 2D or 3D anatomical models of the heart. The platform can simulate electrical excitation waves and mechanical contraction of cardiac tissue. In addition to this platform, I have also developed methods of applying adaptive operator splitting methods for the stable and efficient numerical solution of cardiac models which I show outperform other more commonly used methods. In conclusion, an efficient, scalable, open-source computational platform applicable to cardiac modelling has been developed and further areas for development have been investigated and noted that form a basis for further model development and validation.

The human hand is a marvel of high dexterity with a sophisticated musculoskeletal structure enabling skilled manipulations and object perception. A deep understanding of its associated biomechanics and tactile sensing mechanisms remains at a primitive level, despite their critical importance for the development of robotic or prosthetic hands. So far, primary studies on hand biomechanics, tactile sensing, and sensorimotor mechanisms have been applied to design and control robotic hands. The overall aim of this project is to define a new and effective method for in-depth studies of the human hand biomechanics and tactile sensing, by overcoming the difficulties of high-demand in-vivo measurements. Toward these goals, the following contributions have been made: (1) creation of the first subject-specific anatomically intact finite-element (FE) hand model; (2) quantification of the extensor mechanism and flexible finer joint effects on the hand grasping quality; (3) creation of a novel integrated numerical model predicting afferent tactile signals and exploring the human tactile sensing mechanism; (4) representation of the human sensorimotor mechanism as a transduction function and its application to an in-house soft robotic system with neuromorphic tactile feedback. A subject-specific FE human hand model was created based on the medical images including the entire hand skeleton, subcutaneous tissue, dermis, and epidermis. In-vivo grasping tests were then performed. Muscle forces and hand kinematics were captured to define the loading and boundary conditions. Simulation results were compared to experimental measurements for validation. The FE hand model can accurately represent the biomechanics and performance of the human hand. It was found that the inter-connected extensor tendon and flexible finger joints are the key anatomical features to maintaining the grasping quality and dexterity of the human hand. To study the human tactile sensing mechanism, a novel numerical system integrating an FE human hand model with a neural dynamic model to predict the cutaneous neural response was created. In contrast to other numerical models, which can only compute the afferent tactile signals under passive stimuli, the integrated model proposed here can effectively predict the group cutaneous response during active touch. A microneurography test was conducted and applied to optimise the neural dynamic model. Group responses from cutaneous neurones during active touch were first computed and related to the resulting perception. Temporal 15 coding may be used for the rapid identification of stimuli and triggering reactions, whereas rate coding can represent the quantities of the stimulus. The dynamic relationship between the afferent tactile input and output efferent motor signals can be represented as transduction functions and applied to the control of the robotic/prosthetic hand. A custom-made artificial tactile sensory system was created to implement the accuracy and implications of sensorimotor functions in robotics/prosthetics. A fully 3D printed tactile sensor array was fabricated and mounted on a tendon-driven biomimetic hand. A neural dynamics model was integrated with a tactile sensor to produce neuromorphic tactile signals. The sensorimotor function was applied to control the biomimetic hand and perform different grasps based on neuromorphic tactile feedback. Similar sensing capability and hand performance were achieved by the artificial tactile sensory system compared to human subjects. This constitutes a step further toward the application of next-generation neuroprosthetics.

Despite recent advances, there are still challenges in solving higher-order partial differential equations using the finite element method. This thesis focuses on finite element techniques for higher-order problems with applications to isogeometric analysis and statistical inference. In both areas, the efficient solution of higher-order partial differential equations is essential. The construction of isogeometric smooth spline basis functions is crucial for solving higher-order partial differential equations on meshes with arbitrary topologies. We introduce a simple blending approach that produces smooth blended B-splines, referred to as SB-splines, on unstructured quadrilateral and hexahedral meshes. We first define a set of mixed smoothness quadratic B-splines that are $C^0$ continuous in the unstructured regions of the mesh but are $C^1$ continuous everywhere else. Subsequently, the SB-splines are obtained by smoothly blending in the physical space the mixed smoothness B-splines with Bernstein basis functions of equal degree. One of the key novelties of our approach is that the required smooth weight functions are assembled from the available smooth B-splines in the geometric parametrisation. The SB-splines are globally smooth, non-negative, have no breakpoints within the elements, and reduce to conventional B-splines away from the unstructured regions of the mesh. Remarkably, the optimal convergence rates are numerically observed for the Poisson and biharmonic problems in one and two dimensions. The statistical finite element method coherently sythesises data and finite element models using Bayesian inference. However, the Gaussian process inference using covariance matrices is computationally expensive and memory-intensive. Consequently, the size of the finite element model is significantly limited. To this end, we introduce a sparse precision formulation by specifying the Gaussian process priors as Matérn random fields. Instead of kernel parametrisation, the Matérn random fields are parametrised as solutions of a higher-order stochastic partial differential equation. Finite element discretisation of the corresponding weak form results in sparse precision matrices. Specifically, the sparse precision matrices for arbitrary Matérn smoothness are obtained using recursive finite element computation and rational approximation. In addition to achieving improved scalability, we demonstrate the extension of the stochastic partial differential equation approach to non-Euclidean domains and the modelling of non-stationary and anisotropic Matérn random fields.

This thesis puts forward methods for the computation of transport of mass, momentum and heat in multicomponent flows, systems which involve the transport of two or more chemical species in a common thermodynamic phase. Although commonplace in nature, problems of this type remain relatively unstudied in the numerical literature. The transport problems considered in this thesis are formulated in terms of the Onsager--Stefan--Maxwell equations, which describe multi-species molecular diffusion in fluids, and the Navier--Stokes equations, which account for convection. Under some mild assumptions, we prove existence and uniqueness of solutions to some linearized systems. Effective numerical methods using finite elements are then obtained and analyzed to provide a general methodology for simulation. The scope of the thesis is broader than numerical analysis. It contains original reformulations of transport problems within the framework of linear irreversible thermodynamics. The theory of fluid thermodiffusion is consolidated and cast into a new form, which allows for straightforward simulation of heat transfer alongside molecular diffusion. In addition we provide original and substantial detail on how to extend the framework to encompass transport in electrolytic materials under the assumption of electroneutrality, which generalizes some of the equations arising in porous electrode theory. The power of the framework developed is illustrated throughout the thesis. We employ it to simulate a diverse range of examples, such as oxygen diffusion in the lungs, the mixing of flowing hydrocarbons streams, thermal separation of gases and transport in electrolytes.

Phase-field theory is a powerful method which is widely used in dealing with multiphase problem in fluid dynamics in recent years. In this thesis, models of moving contact lines and vesicle motion, deformation and interaction would be established with phase-field method. Energy variational approach is used to derive the governing equations from some basic energy assumption. C⁰ finite element scheme is given to perform numerical test. Continuous and discrete energy decaying law are also given to prove the feasibility of the model. Finally, numerical simulation is applied. A number of results in different conditions are shown. By comparing with experimental data from previous research, the models are proven to be with good accuracy.

Cold-formed steel (CFS) members are widely used in the constructional industry, because CFS has high strength-to-weight ratio and can be easily fabricated into different shapes. In order to accommodate services like electric wires and pipelines, perforations are commonly punched into the web of CFS beams. However, the appearance of web openings may reduce the properties of the cross section and hence change the stress distribution along the longitude axis. As a result, the perforated cold-formed steel (PCFS) beam is more susceptible to lateral-torsional buckling. For specific cross sections controlled by distortional buckling, the restraint of web on the flange weakens due to the web perforations and hence the PCFS beam may fail more easily than the CFS beam. Among all the current specifications, the design equations for determining the critical stress of PCFS beams are non-existent. In addition, the design guideline of CFS mainly concentrates on the loading conditions that the members subject to pure bending or compression, while the uniformly distributed load is more common in beams. It is known that singly PCFS beams have low lateral stiffness and torsional rigidity about the weak axis which lead to them suffering from distortional or lateral-torsional buckling. To use PCFS sections with larger scale in structures, back-to-back built-up CFS beams with web perforations are commonly employed. They are connected by two individual PCFS studs using self-drilling screws. However, the application of built-up CFS beams with web perforations in practice is encountering challenges due to the lack of suitable design method. The researchers are prone to modify the design equations of hot-rolled I sections to predict the ultimate strength of built-up CFS sections, but this approach was found to be conservative. This project aims to investigate the buckling behaviour of CFS beams with web perforations. Simplified analytical models based on energy method were proposed to predict the critical stress of distortional buckling of PCFS beams subject to pure bending and uniformly distributed load, and the effect of variant moment distribution along the longitude axis was examined. Li's model proposed in 2004 was modified for the calculation of the lateral-torsional buckling of PCFS beam subject to pure bending and uniformly distributed uplift load, and the influences of lateral and translational restraint provided by sheeting were discussed. Elastic finite element models were developed by using commercial software ANSYS to investigate the influence of hole sizes and cross-section dimensions on the buckling behaviour of PCFS beams. The results have shown a good agreement between the finite element analysis data and theoretical results. In this study, non-linear finite element models including material, geometrical and contact non-linearity were performed to explore the structural behaviour of CFS built-up beams with web perforations subject to pure bending. The numerical results were verified against the existing experimental data in the literature. Afterwards, the validated finite element models were employed for the extensive parametric study. A total of 398 numerical simulations were conducted to examine the influence of hole sizes, hole spacing, beam slenderness and screw arrangements. The current direct strength method for PCFS beams was extended for the design rule of CFS built-up beams with web perforations subject to pure bending. This thesis has contributed to improve the understanding of distortional and lateral-torsional buckling behaviour of PCFS beams subject to pure bending and uniformly distributed load, the data obtained from the numerical investigations provided a thorough grounding for further design of CFS built-up beams with web perforations.

Solar Energy is one of the most widely used renewable energy sources, with the solar Photovoltaic (PV) module technologies deployed as one of the primary renewable energy sources to replace fossil fuels. However, the R&D challenge for improving the performance and reliability of PV modules has become an urgent and critical agenda for the energy generation industry sector. The interconnection between the solar PV cells is a very important part of the PV module assembly, and its failure can adversely affect the performance and reliability of the PV module. The interconnection failure has been mostly linked to the crack initiation and propagation in the solder joints used to connect the ribbon interconnection to the cell. This research focuses on the study of the thermal failure of PV module solder joint to determine the optimum ribbon interconnection designs that will give improved thermo-mechanical reliability. It develops a virtual reliability qualification process for the assessment of the life expectancy of PV module interconnections. The FEM simulations in ABAQUS 2019 software are implemented to investigate failure of the solder joints in different ribbon interconnection designs under anticipated life cycle loading conditions and high temperature lamination process. For the first time, the extended finite element method (XFEM) technique is used to determine the crack initiation temperature, crack location, direction and growth rate in solder joint of PV module interconnection under lamination process. Furthermore, the research used the Developed Morrow Energy Density lifetime model to determine the number of cycles to creep-fatigue failure, and then it defined a new generic exponent factor using the Coffin-Manson-Arrhenius model to estimate the lifetime for the designs under different thermal cycling conditions. The research also combines the numerical results of XFEM and creep-fatigue investigation to determine the failure lifetime of PV Module interconnection designs. The results show that the Multi-Busbar interconnection design improves solder joint creep-fatigue life (up to 15%) and consequently provides higher thermo-mechanical reliability for the solar PV modules compared to other studied designs (Conventional and the Light Capturing Ribbon interconnections). The results of this PV module interconnections study can be used for evaluating potential design changes and to facilitate design for reliability validation of different configurations for improving the long-term PV module system reliability.

Topology optimization finds the optimal material distribution of a continuum in a domain, subject to PDE and volume constraints. Density-based models often result in a PDE, volume and inequality constrained, nonconvex, infinite-dimensional optimization problem. These problems can exhibit many local minima. In practice, heuristics are used to aid the search for better minima, but these can fail even in the simplest of cases. In this thesis we address two core issues related to the nonconvexity of topology optimization problems: the convergence of the discretization and the computation of the solutions. First, we consider the convergence of a finite element discretization of a fluid topology optimization problem. Results available in literature show that there exists a sequence of finite element solutions that weakly(-*) converges to a solution of the infinite-dimensional problem. We improve on these classical results. In particular, by fixing any isolated minimizer, we show that there exists a sequence of finite element solutions that \emph{strongly} converges to that minimizer. Moreover, these results hold for both traditional conforming finite element methods and more sophisticated divergence-free discontinuous Galerkin finite element methods. We then focus on developing a solver that can systematically compute multiple minimizers of a general density-based topology optimization problem. This leads to the successful computation of 42 distinct solutions of a two-dimensional fluid topology optimization problem. Finally, by developing preconditioners for the linear systems that arise during the optimization process, we are able to apply the solver to three-dimensional fluid topology optimization problems. This culminates in an example where we compute 11 distinct three-dimensional solutions.

Two investigations are described in this thesis on the common theme of applying finite volume methods to simulate structural impact problems. The first investigation is the application of the Eulerian Finite Volume Method (EFVM) to simulate the low-speed impact of ductile materials. Simulation results are validated against experiment showing that it is possible to accurately predict crater deformation profiles over the low speed speed impact regime for different projectile and substrate materials. We demonstrate how the rate dependent Johnson-Cook plasticity model is crucial to ensure correspondence to experiment. The second investigation is concerned with the application of EFVM to simulate impact damage to thin polymeric coatings applied to the surface of metals. The aim of this work is to demonstrate how new simulation methods can help understand coating damage due stone impact. We simulate the debonding phenomenon of single layer coatings under impact by setting boundary conditions at the plate and paint interface. We show how EFVM can capture two limits of interface behaviour, sliding and separation 'slip' at one extreme and zero sliding 'welded' at the other. Results compare well to previously published experimental and simulation work, and our own finite element simulations in Abaqus. We also demonstrate how EFVM brings greater robustness and stability compared to FEM when modelling adhesive failure and higher energy impact penetration.

With an increase in cancer cases seen year on year, developing and improving treatment forms becomes increasingly important. Treatment of cancerous tumours using carbon-ion radiotherapy has shown favourable results compared to conventional treatment methods. However, enabling this treatment form to become more widely available on a world-wise basis remains a key challenge, due to the facility size and cost. In recent years, material and manufacturing developments of superconductors has improved the performance of high temperature superconductors (HTS) while their price has come down. This has allowed more compact accelerator and gantry magnets to be designed. The inherent characteristics of second generation (2G) HTS enable a drastic increase in the current density and magnetic field generated, compared to normal conductors and low temperature superconductors (LTS). For future superconducting applications, HTS has therefore been recognised as the solution. This thesis aims to address the issue of magnet size and associated costs, by employing 2G HTS in the design of a compact magnet through a layer-by-layer design algorithm. This new design resulted in a reduction of 26.3% of superconducting material used compared to other known designs, thus a cost saving of $115835. The thesis begins by presenting a brief overview of particle therapy, and the application of superconducting technology in these facilities, followed by a concise review of superconductors. The important steps and design considerations to design a magnet are then presented. This includes cross-section and coil end design, yoke design, field quality, and field computation modelling. The thesis goes on to present the designed HTS combined function magnet, designed for use in carbon-ion radiotherapy. The six-layer combined function magnet realises both bending and focusing/defocusing components in each layer, thus utilising space and materials effectively. This resulted in a precise and compact magnet, which uses considerably less HTS material compared to other designs. A further size reduction was achieved by the yoke design and optimisation which followed, which utilised COMSOL Multiphysics and Magnet Infolytica to simulate the magnet and iron yoke, using the finite element method (FEM). FEM is implemented for both stationery and time-dependent simulations. An anisotropic homogeneous-medium bulk approximation is adopted with a power law E - J relationship to model the combined function magnet during magnet ramp. This allowed a comprehensive profile of the HTS tape blocks to be obtained, in addition to several important issues such as magnetisation and critical current of the superconducting coils to be addressed.

Paste extrusion is a bulk forming technique used widely in the ceramics, food, metal and polymer industries, amongst others. This dissertation develops (i) measurements of the friction and bulk constitutive behaviour of pastes and (ii) numerical simulations of paste extrusion using these measurements as inputs. Two pastes were used: microcrystalline cellulose, calcium carbonate and water (MCC/CaCO3) and a commercial tungsten carbide-cobalt-based paste (WC-Co). The friction rig developed by Bryan, Rough and Wilson (2018) was used to determine the frictional behaviour of MCC/CaCO3 paste and to separate pressure- and velocity-dependence of the wall shear stress, O!. A new device with temperature control was constructed to test WC-Co paste. O! measurements were fitted to models proposed by Benbow and Bridgwater (1995): both pastes showed strong velocity dependence of O!, MCC/CaCO3 exhibited negligible pressure dependence, and WC-Co observable but small pressure dependence. For MCC/CaCO3 paste, these were compared to alternative friction measurements made using ram extrusion apparatus. Finite element simulations of extrusion were performed using ABAQUS® with an Arbitrary Lagrangian-Eulerian (ALE) formulation and custom friction subroutines. Steady-state velocity profiles and the pressure drop through square-entry geometries were predicted and extended to the extrusion of MCC/CaCO3 through conical-entry and 3D geometries, and WC-Co with a rate-dependent constitutive model. Manual adjustment of input parameters was required to obtain good agreement between experimental and simulated forces. The resulting MCC/CaCO3 parameters gave reasonable prediction of conical-entry experiments. Extrusion dies with ridges along their length were studied. An analytical model was developed using an upper bound method following the work of Khoddam et al. (2011a, b). Benbow-Bridgwater (1995) constitutive and friction parameters were used. Experiments were performed with 3D printed and machined dies for MCC/CaCO3 and WC-Co, respectively. For both pastes, the analytical model underpredicted the measured forces and parameter adjustment was required to improve the fit. This was attributed to greater surface roughness within the dies. A coupled Eulerian-Lagrangian (CEL) simulation was run in ABAQUS® with frictionless contact. This predicted comparable circumferential and vertical die land velocity components to the analytical model. Plastic deformation was observed along the die land, leading to slightly higher measured stresses and estimated pressure drops. The CEL method also led to a loss in paste-die wall contact and non-uniform paste volume fraction in the die land, creating difficulties testing frictional conditions.

Glass and Carbon Fibre Reinforced Polymer (GFRP/CFRP) composites are currently being utilised widely in an increasing range of engineering applications due to their chemical re- sistance, design flexibility, and high stiffness-to-weight and high strength-to-weight ratios during the last few decades. However, the failure of composites is difficult to predict as the onset of damage in the composites does not result in the catastrophic failure of the whole structure instantaneously but progressively because the collective and interactive damages can transform from one mode to another across the length scales. The World-Wide Failure Exercises (WWFE-I, II, III) assessed the most widely used failure criteria and concluded that most of them could only predict the ultimate strength of composites accurately under some loading conditions, however, none is capable of predicting progressive failure process in the composites. Classical continuum mechanics based Finite Element Method (FEM) has been used to tackle the damage propagation problem by setting a degradation factor for several decades, based on the assumption that the material does not fail. Besides, the newly proposed Extended FEM (XFEM) needs a predefined crack path for the crack propagation, lacking the randomness characteristic of real failures. Therefore, a 3D meso-scale Discrete Element Method (DEM) model is developed for unidirectional FRP composite materials to predict the elasticity and strength of FRP composites. With the help of cross-validation between two numerical approaches and experimental findings under static loading conditions, the failure progression problem can be better addressed. To achieve this goal, firstly, a 3D FEM based micro-scale Representative Volume Element (RVE) model which represents the microstructure of composite laminae is developed. This model is utilised to model the mechanical behaviour of FRP composite materials subjected to different combined loading conditions by using Periodic Boundary Conditions (PBC). The Drucker-Prager plastic constitutive material model and the Ductile failure initiation and evolution criteria are applied to simulate the plastic and damage process of matrix. A bilinear mixed-mode softening law is utilised to simulate the mechanical response of the interface between fibre and matrix. In addition, here in this study, fibres are assumed to be transversely isotropic elastic. A weak and a strong interface are considered, and the numerical results are compared to the theoretical results predicted by three popular failure criteria, such as Hashin, Tsai-Wu and Puck failure criteria. An assessment has been made between these criteria, and the Tsai-Wu failure criterion stands out due to its more general formulation and applicability in different cases. Secondly, three different 3D meso-scale DEM based models are developed for the prediction of elasticity of transversely-isotropic materials considering different packing patterns, namely the 3D lattice discrete model, the 3D Hexagonal Close Packing (HCP) model and the extended 2D hexagonal and square models. These DEM models have been validated and assessed by theoretical analysis, FEM simulations and experimental results available in the literature. The extended 2D hexagonal and square models are based on average strain energy method, and are selected for the prediction of progressive failure of the FRP composite laminae in the next stage due to their simplicity, accuracy and relatively short computation time. Thirdly, the bond strengths of the extended 2D DEM hexagonal model of 0◦ and 90◦ com- posite laminae are calibrated from experiments. In contrast, the bond strength of the extended 2D DEM cubic model of 45◦ lamina is calibrated from the failure prediction via the Tsai-Hill failure criterion under plane stress state. The total strain energy release rate is considered for the interfacial bond to model the delamination of composite materials. Quantitative analysis of progressive damage is conducted for a cross-ply composite laminate, including crack density and stiffness degradation with the validation of experimental findings in the literature. Qualita- tive analysis of an Open-Hole Tension (OHT) case is conducted on a quasi-isotropic composite laminate regarding its damage initiation and propagation process with a comparison to the experimental findings, such as Micro-CT images. Finally, a seven-bond interface model is developed based on the energy balance principle and a power-law relation of bond lengths in the interface for the simulation of progressive delamination process in DCB tests. It has been validated that this model is capable of predicting the stiffness and ultimate peak load accurately comparing with experimental findings. Further, this model is adopted for the construction of CFRP cross-ply composite laminates. Experiments are conducted for the validation of the improved DEM model regarding the failure prediction of the CFRP composite laminates, and relatively good agreements are found between the results of the experiments and numerical simulations.

Concrete, as the most widely used construction material, has been applied in a variety of engineering structures. To fully understand the mechanisms of macroscopic behaviour and improve concrete design, it is important to carry out numerical modelling of concrete under complex loadings. The highly heterogeneous composition of concrete needs to be considered in order to better understand its mechanical response and damage evolution at macro-scale. A novel computational technology, which models the damage and failure of quasi-brittle materials, e.g. concrete, at meso-scale provides a powerful tool to realistically predict the mechanical behaviour and failure of concrete. The concrete meso-structure includes coarse aggregates, mortar with small sand and aggregates embedded, the interfacial transition zones (ITZ) and air voids. Therefore, the main target of this thesis is to develop an effective and efficient mesoscale modelling framework to represent the constituents of concrete realistically and to better describe the damage and failure process of concrete. Three-dimensional concrete meso-structures with varied shape, size and phase particle size distribution, either generated synthetically or obtained from X-ray Computed Tomography (XCT) scanning, can be meshed in the same image-based modelling approach, which makes it efficient for concrete meso-structure generation. To compare concrete meso-structures with physically realistic and randomly prescribed aggregates and voids, both image-based and parametric (or synthetic) models are generated. They yield mechanical behaviour in good agreement with experimental data only except that the distribution of damage differs between the two models. Concrete models with various representations of ITZ are investigated and compared with experimental data. The combined modelling considering damage-plasticity model for mortar and cohesive zone model for ITZ, whose material properties are calibrated from experiment, is demonstrated to be efficient and reliable. To better understand the effect of ITZ cohesive parameters and clarify the argument on ratio of shear to normal cohesive strength and fracture energy, parametric study is carried out for meso-scale concrete models subject to various loadings. Mortar plasticity and damage dominate the overall energy dissipation, which is linked to stress-strain curve and crack pattern. Localisation of damage in both tension and compression is governed by mortar damage dissipation and concentrated by the presence of ITZ.

Bio-impedance spectroscopy has been increasingly used for medical and food industrial applications as it provides information about cellular structure, composition and integrity of cell membranes of biological samples. This study is focused on analysing how bio-impedance spectrum is affected by cellular structure (cell deformation, shape and orientation) and the integrity of cell membranes during the frozen-thaw injury process. Two measurement systems were designed and built: contact-electrode measurement and non-contact induction measurement system. For the former, the frequency range of measurement is 10 kHz to 10 MHz while the frequency range for the latter is 400 kHz to 6 MHz. Both systems can detect the change in impedance spectrum of biological samples (potato and meat) caused by the poration of the cell membranes during the frozen-thaw injury process. A finite element method (FEM) simulation solver was built and applied for the simulation of BIS. Specifically, the poration of the cell membrane was simulated and it was proved to cause the increase in equivalent conductivity of the cell membrane and this is in agreement with the experimental observation carried out in this thesis work and previous studies reported in literature. The shape and orientation effect of the cell was also simulated and the results were explained with physical insights. In addition, a new acceleration method for simulating thin cell membrane based on FEM was proposed and implemented. The modelling method accelerates the computing progress by reducing the number of meshing elements without reducing the accuracy of the simulation in a significant manner in comparison with analytical solutions. The accuracy of the acceleration modelling (reduced-mesh model) was also validated by the full-meshed FEM model to be within 0.4%-2% while the simulation time was reduced up to 25%.

Steel and concrete composite structures are frequently utilised in multi-story buildings, as they maximise the material merits via composite action, which is achieved by a shear connection between the steel and concrete sections. The fire performance of the shear connection is a primary parameter in composite beam design, which has been investigated with a focus on adopting solid concrete slabs. Despite the popularity of embracing profiled steel sheeting in composite construction, the fire behaviour of shear studs embedded in a transverse deck slab remains to be confirmed. This thesis presents experimental and numerical studies on the behaviour of the shear connection when headed shear studs are incorporated with a transverse deck slab both at ultimate and fire limit states. High-temperature push-out tests were experimentally conducted, and finite element models were developed using a commercial package, Abaqus. Concrete plasticity parameters for high-temperature applications were proposed to simulate a concrete-dominated fracture in the push-out test models. The accuracy of the developed numerical models was verified using experimental data, which demonstrate a strong correlation in the shear resistance and failure modes at different temperatures. The failure mode transforms from a concrete pull-out into stud shearing as the temperature increases in the transverse deck specimen owing to a higher thermal degradation of stud material. The shearing location also approaches the bottom of the shear stud as fire exposure time increases. Parametric studies using the developed numerical models were conducted, including several variables such as the stud welding method, deck thickness, stud location, and number of studs in a trough. Although all the mentioned variables influence the shear resistance in the ultimate limit state, their effects decrease with increasing temperature. Since the current design code of EC4-1-2 (2014) shows a different response in comparison to experimental data, modified design rules for shear resistance calculation in the fire limit state have been proposed herein depending on failure modes.

Guided waves are currently being used to inspect pipelines, aircraft, tanks, bridges and rail structures, for the purpose of assessing their structural integrity. However, the multimodal and dispersive nature of guided waves require the selection of a reliable excitation system. Piezoelectric transducers based on Lead Zirconate Titanate have been extensively employed to excite guided waves. In particular, thickness-shear piezoelectric transducers have found widespread use in industrial applications for plate-like and tubular structures. Research has been continuously carried for shear transducers in the last two decades to improve sensitivity and resolution. Nonetheless, enhancements have been mainly based on post signal processing techniques or the design of arrays to cancel out unwanted modes through backward cancellation. Research in the literature has suggested that the design of the transducer might be introducing unexpected wave modes along with the desired ultrasonic response. The aim of the thesis is to assess the effect of the design of the transducer on ultrasonic guided wave excitation. This is achieved by comparing the output of the transducer in a plate-like structure with the expected design based on the ideal point source hypothesis. The thesis then seeks to provide explanations for the differences between the ideal and real behaviour, based on physical explanations of the phenomena involved. Guidelines are also elaborated to meliorate the existing state of the art on shear transducers. The first theme of the thesis is then the characterisation of a single shear transducer in a plate-like structure. In chapter 4 an experimental analysis based on 3D LDV Vibrometry is combined with a numerical finite element approach where the geometry of the transducer and the electromechanical nature of excitation are both taken into account. A mesh sensitivity analysis is carried out to ensure the convergence of the model. Both experimental and numerical results indicate that an unexpected out-of-plane mode is propagating in the plate, compromising the mode selectivity and purity of the transducer in terms of shear horizontal mode. The second theme is the interpretation of the physical phenomena described in chapter 4. In Chapter 5 the validated numerical model is exploited to provide qualitative and quantitative evidence on the transducer behaviour. The vibration of the piezoelectric element, of the wear-plate and of the backing mass are assessed and discussed. A physical interpretation of the effect of the design on the ultrasonic response is provided. It is proposed that the electrical layout and the geometry heavily influences the propagation of guided waves. An alternative is numerically studied to show the improvement in shear horizontal mode purity with a different electrical configuration. The third theme is the development of alternative designs to provide evidence of possible improvement. Thus, in chapter 6 two prototypes with different electrode layouts are developed and tested according to the procedure developed in Chapter 4. A definite improvement in shear horizontal mode purity is found when an alternative electrical design is considered. However, the effect of the geometry on the excitation remains to be assessed. The fourth theme is the creation of a general methodology to study the influence of the geometrical parameters. In chapter 7 the fundamentals requirement of the transducer are formulated mathematically as design criteria and an objective function is established. The combination of features and the heuristic search of an adequate objective function are described. The integration between a finite element software and the genetic algorithm optimisation approach is also fully discussed. Both a two-dimensional and a three dimensional geometrical optimisation are carried out. The importance of the geometrical parameters and their interdependence in terms of ultrasonic excitation is also discussed. Indications in terms of future design changes to be implemented in industrial applications are provided.

This thesis primarily explores the stability of spherically capped conical shells and secondarily explores the nature of the polygonal folds observed during these deformations. The polygonal folds were classified according to the number of facets observed. The problem is primarily explored using Finite Element Method (FEM) studies of rigid indentations of spherically capped conical shells of varying thickness, cone angle, and slant height. The main finding of the FEM studies is that the capped shells suddenly buckle during the indentation as the ridge approaches the region where the cap and conical shell meet. The geometry of this join region dominates the shell response for all the studied spherically capped conical shells and provides another perspective on how local geometry affects a shell's response to indentation. Experimentally a commercially bought rubber conical shell is qualitatively observed to show that the shell can be poked and folded to remain statically in a wide number of folded shapes. While the thesis does not answer the reason for this stability, the combination of the FEM studies and exploration of the rubber conical shell suggest that the observed stability is likely linked to the interaction between the cap and conical shell.

Cervical Spine Injuries (CSIs) arising from collisions are rare in contact sports, such as rugby union, but their consequences can be devastating as they can lead to paraplegia, tetraplegia and death. Finite Element (FE) models have been widely used to give a more in-depth understanding of the biomechanics of injury. Several FE modelling approaches are available in the literature, but a fully calibrated and validated FE modelling framework for cervical spines under compressive dynamic loading is still lacking and material properties are properly not calibrated for such events. This study developed and validated a methodology for specimen-specific FE modelling of the cervical spine under impact loading. Thirty-five (n=35) individual vertebral bodies (VBs) and three (n=3) whole cervical spines (C2 to C7) were dissected from porcine spine segments. Samples were potted in bone cement, mCT scanned and a speckle pattern was applied to the anterior aspect of the bones to allow Digital Image Correlation (DIC). Surface displacements and strains were acquired using DIC. Twenty-seven (n=27) VBs were compressively tested to a load up to 10kN applied at a rate of 1000N/min from the cranial side. Specimen-specific FE models were developed for fourteen (n=14) samples in this group and the material properties were optimised based on the experimental load-displacement data and using a factor (KGSStatic ) to calibrate a density to Young’s modulus equation. Thirteen (n=13) FE models were created from the remaining tested samples: the previously optimised density to Young’s modulus relationship was applied to this group and the resulting vertebral stiffness was compared to experimental findings. This allowed validation of the developed density to Young’s modulus relationship. Eight (n=8) remaining VBs were subjected to an impact load applied via a falling mass of 7.4 kg at a velocity of 3.1ms􀀀1. Surface displacements and strains were acquired from the anterior VB surface via DIC, and the impact load was monitored with two load cells. Specimen-specific FE models were created for this group and material properties were assigned again based on the density-Young’s modulus relationship previously validated for static experiments, supplemented by an additional factor (KGSDynamic ) derived from an iterative comparison between numerical stiffness predictions and experimental findings. Three (n=3) whole cervical spines were subjected to the spine impact loading conditions and surface displacements, strains and force profiles were also acquired. Spine specimen-specific FE models were created for these samples using the previously developed modelling workflow. VBs material properties were assigned via KGSDynamic , grey-scale and the density-Young‘s modulus relationship. Intervertebral discs were defined as homogeneous and isotropic and mechanical properties were assigned to the specimens using a kinematic approach. Experimental and numerical load-displacement curves for these spinal segments were compared using Bland-Altman plots, non-parametric tests and Lin’s concordance coefficient (CCC). The optimised conversion factor for quasi-static loading, KGSStatic , had an average of 0.033. Using this factor, the validation models presented average numerical stiffness value 3.72% greater than experimental. From the dynamic loading experiments, the value for KGSDynamic was found to be 0.14, 4.2 times greater than KGSStatic . Average numerical stiffness was 2.3% greater than experimental. Almost all models presented similar stiffness variation and regions of maximum displacement and strains similar to what observed via DIC. Spine models presented similar biomechanical behaviour to experimental data in terms of predicted peak load, vertebral displacements and strains and three-dimensional spine movements. Strain patterns exhibited a high level of similarity to those recorded via DIC but strain magnitudes were consistently smaller. Deformation by buckling was observed. The developed FE modelling methodology allowed the creation of models which predicted both static and dynamic behaviour of VBs. The same methodology was then applied to the modelling of the whole cervical spine, which resulted in predictions showing agreement with experimental data. Strains and deformation patterns were assessed and evaluated, showing that buckling was the main deformation mode for this type of impact. This methodology is now validated to be fully applied to simulate axial impact scenarios replicating rugby collisions events.

The Helmholtz equation arises in a range of applications, from aircraft design to geophysical exploration, which often involve problems set in infinite domains. Simulating these infinite domains is a major challenge when using the finite element method (FEM). One way to overcome this challenge is by surrounding the finite computational domain with perfectly matched layers (PMLs), which use a coordinate transformation to simulate the effect of an infinite domain. The choice of transformation is key to creating an efficient method and is the central focus of the thesis. Prior work on optimising PML transformations by Bermudez et al. [Journal of Computational Physics, 223, (2007), 469-488] showed that transformations should be unbounded. Cimpeanu et al. [Journal of Computational Physics, 296, (2015), 329-347] then showed that the layer thickness should be as close to zero as practically possible. Our first novel contribution is finding a transformation which has the same effect as a PML with zero thickness. The transformation has the special property that it transforms a 1D planar wave to vary linearly through the PML. This property allows the PML to be resolved with a single linear element and therefore without introducing additional degrees of freedom. We use this property as our definition of an optimal transformation and show that in 1D the optimal transformation is unique. We then extend the idea of optimal transformations to 2D, which apart from the case of a planar wave at an angle of incidence, prove challenging to compute. Our first method is a series solution. It suffers from slow convergence, is expensive to compute, but provides useful insight into the character of the transformations. Our second method formulates the optimal transformation as a root of a non-linear equation, which we solve using Newton's method. We then use the optimal transformation with the FEM to simulate infinite domains in several examples. However, our basic method is not effective when the transformation exhibits discontinuities which we call rips. We then go on to study rips. We show that optimal transformations for fields with a single angular Fourier mode cannot have such rips, but optimal transformations for fields with multiple modes can. We then analyse the behaviour of the transformation around the critical point of the rip. By improving our method to compute the transformation, reformulating the weak form and improving our integration scheme we show that we can use discontinuous optimal transformations with the FEM. The FEM requires solving a system of linear equations. If the system is large, we may have to use an iterative method. One iterative method which is effective for the Helmholtz equation is GMRES with a complex shifted Laplacian preconditioner. We show that the performance of this solver typically deteriorates when used with the PML method, however, we also show that this is not the case when used with our optimal transformation procedure. Finally, we develop a computational model for a specific challenging fluid-structure interaction problem using conventional PMLs. The problem is an infinite vibrating submerged plate with an incomplete elastic coating. The primary challenges we discuss are the fluid-elastic interaction in the PML and the choice of a transformation which is effective in both the fluid and elastic domains. We demonstrate the accuracy of our model by comparing the solution on two domain sizes for an example problem.

Conventional manufacture of prosthetic sockets is artisanal, relying on limited objective data, which often leads to discomfort and tissue damage. Thermal discomfort is a key concern identified by amputees, particularly in hot climates. Despite this, it has had little research attention. This research increases knowledge of the body's heat transfer mechanisms and the effect of amputation and wearing a prosthesis on heat transfer and thermal discomfort through reviewing literature, running a clinical study with amputees and developing a computational bioheat model. A questionnaire on discomfort, completed by 42 amputees in Bangalore, found heat and perspiration in the prosthetic socket were the most prevalent causes of discomfort. Skin temperatures and thermal discomfort measurements were collected from 30 lower-limb prosthesis users during exercise. After exercise, thermal discomfort was greater on the amputated leg, despite the skin on both legs cooling. The discomfort might signal that the heat generated by the muscles in the residual limb during exercise is stored in the muscles. To explore the effect of the environment on muscle temperatures during exercise and post-exercise recovery, a cylindrical isolated-segment bioheat model of the thigh was developed in COMSOL Multiphysics and compared to empirical data of muscle temperatures. This model is the first to use finite element analysis to determine temperature distributions through the thigh during exercise and post-exercise recovery. It showed that thermal responses of individuals are varied and complex. From this understanding of the temperature responses of a healthy leg, the possible effects of amputation and prosthesis-use are discussed. The model increases knowledge of the heat transfer factors to consider in developing user-specific prosthetic sockets that reduce the body's thermal load. The feasibility of integrating simulations, such as this model, with computer-aided design and 3D printing technology to improve customisation of prosthetic sockets was assessed by systematically reviewing the effectiveness of 3D printing prosthetics and other medical devices. The technology shows promise for supporting data-driven prosthetic socket design and manufacture but lacks research and clinical validation.

Undrained deformation of dilative sand generates negative excess pore pressure. It enhances the strength which is called dilative hardening. This increased suction is not permanent. The heterogeneity at the grain scale triggers localisations causing local volume changes and associated drainage. The negative hydraulic gradient drives fluid into dilating shear zones. It loosens the soil and diminishes the shear strength. Continuum-based finite element method cannot apprehend pore-fluid movements at grain scale without extreme mesh refinement. This thesis aims to evaluate the capabilities of the finite element method and existing material models to identify the onset and propagation of localisation in dilatant hardening materials. Then constitutive relations are upgraded to provide mesh-independent results for different drainage conditions. First, the ability of critical state Nor-Sand model to simulate drained and undrained deformation of dense sand is evaluated. Then non-coaxial and non-associative flow theories are integrated. Different flow rules are examined for proportional and non-proportional loading paths. Both theories inhibit the tendency to dilate. Non-coaxial Nor-Sand model reduces the overly stiff response predicted by the original Nor-Sand model during undrained dilative shearing. Secondly, a bifurcation analysis is conducted to evaluate the potential of constitutive models to detect the onset of localisation. Under strict isochoric constraint, the Rice criterion is never met by the Nor-Sand model. Both non-coaxial and non-associative flow rules do not bring destabilising effects in dilative sand. The local drainage is the triggering mechanism of shear bands in globally undrained dense sand. Third, the nonlocal regularisation is applied to Nor-Sand model and its capability to produce mesh objective results is elucidated for drained sand. Along with scaling, nonlocal Nor-Sand model can reduce the mesh sensitivity without extreme mesh refinement. Fourth, a comprehensive parametric study is conducted to examine the rate and mesh dependence of saturated dense sand with closed and open drainage boundaries. In both cases, the hydro-mechanical coupling decides both the onset and propagation of localisation. Depending on the local degree of drainage shear zones can be fully or partially drained. The normalised velocity at the boundary between localised and uniform deformation is mesh dependent. For saturated sand, the nonlocal method is successful only when either all material points or shear band material points are fully drained depending on global boundary conditions. The regularisation of drained soil skeleton is not effective when the hydro-mechanical coupling is active. A mesh-independent, rate-dependent constitutive model is developed to capture the pore fluid diffusion at the grain scale. It describes the macroscopic constitutive behaviour of undrained dense sand in the presence of a locally drained or partially drained shear band.

This thesis focuses on the dynamics and stability of liquid pools (layers) and droplets comprising of binary mixtures of miscible components, where surface tension induced (Marangoni) flows play a prominent role. Specifically, evaporation of thin horizontally heated liquid layers and thin sessile droplets spreading on heated surfaces are investigated using both modelling and experimental approaches. Below the capillary length gravitational effects weaken and surface tension becomes the prominent driving force in the ensuing flow dynamics. Surface tension gradients arise over the liquid-vapour (LV) interface due to either a variation in temperature (thermal Marangoni stress) or, in the case of binary liquids, concentration (solutal Marangoni stress). In our case, we consider both. Solutal Marangoni stresses can suppress or enhance thermal Marangoni, leading to interesting behaviour. First, the stability, flow dynamics and evaporation kinetics of bi-component miscible liquid layers subject to a horizontal temperature gradient are investigated by means of two-phase direct numerical simulations (DNS). Both the liquid and gas phases are fully resolved, with the Volume-of-Fluid (VOF) method used to account for the deformable liquid-vapour (LV) interface. Surface tension varies linearly with both temperature and concentration at the interface. In the bulk liquid, thermophoresis (Soret effect) and mixture thermodynamics are accounted for. It is shown that even in absence of evaporation, thermophoresis can drive subtle component separation. Under certain conditions, flow exhibits the so-called hydrothermal wave instabilities with similar concentration fluctuations also propagating at twice their wavelength. Introduction of evaporation over the interface depletes both overall liquid mass and concentration of the more volatile component while the layer remains well mixed due to return flow sustained by thermal Marangoni stress. In the absence of thermal Marangoni, preferential evaporation of the more volatile component from the hot wall combined with solutal Marangoni stress reverses the return flow. Secondly, the dynamics and stability of thin volatile droplets comprising of binary mixtures deposited on heated substrates are investigated using lubrication theory and linear stability analysis under the quasi-steady-state approximation. Solely the liquid phase is focused on and so a novel one-sided model is developed to predict the spreading and evaporation of a binary axisymmetric drop on a heated substrate with high wettability. A thin drop with a moving contact line is considered, taking into account the variation of liquid properties with concentration as well as the effects of inertia. The parameter space is explored and the resultant effects on wetting and evaporation evaluated. Increasing solutal Marangoni stress enhances spreading rates in all cases, approaching those of superspreading liquids. Preliminary results from the stability analysis indicate that the addition of a second component has a strong destabilising effect on the drop. Quantitative and qualitative agreement is found with experiments. Thirdly, experiments are conducted with binary ethanol-water droplets spreading on hydrophilic glass slides heated from below. The spreading rate is quantified, revealing that preferential evaporation of the more volatile component (ethanol) at the contact line drives superspreading, leading in some cases to a contact line instability.

The development and implementation process of a complete numerical framework for high-fidelity Fluid–Structure Interaction (FSI) simulations of moored floating bodies using Computational Fluid Dynamics (CFD) with the Finite Element Method (FEM) is presented here. For this purpose, the following three main aspects are coupled together: Two-Phase Flow (TPF), Multibody Dynamics (MBD), and mooring dynamics. The fluid–structure problem is two-way and fully partitioned, allowing for high modularity of the coupling and computational efficiency. The Arbitrary Lagrangian–Eulerian (ALE) formulation is used for describing the motion of the mesh-conforming fluid–solid interface, and mesh deformation is achieved with linear elastostatics. Mooring dynamics is performed using gradient deficient Absolute Nodal Coordinate Formulation (ANCF) elements with a two-way mooring–structure coupling and a one-way fluid–mooring coupling. Hydrodynamic loads are applied accurately along mooring cables using the solution of the fluid velocity provided by the TPF solver. For this purpose, fluid mesh elements containing cable nodes that do not conform to the fluid mesh are located with a computationally efficient particle-localisation algorithm. As it is common for partitioned FSI simulations of solids moving within a relatively dense fluid to experience unconditional instability from the added mass effect in CFD, a non-iterative stabilisation scheme is developed here. This is achieved with an accurate and dynamic estimation of the added mass for arbitrarily shaped structures that is then applied as a penalty term to the equations of motion of the solid. It is shown that this stabilisation scheme ensures stability of FSI simulations that are otherwise prone to strong added mass effect without affecting the expected response of structures significantly, even when using fully partitioned fluid–structure coupling schemes. Thorough verification and validation for all aspects of the FSI framework ultimately show that the produced numerical results are in good agreement with experimental data and other inherently stable numerical models, even when complex nonlinear events occur such as vortices forming around sharp corners or extreme wave loads and overtopping on moving structures. It is also shown that the mooring dynamics model can successfully reproduce nonlinearities from high frequency fairlead motions and hydrodynamic loads. The large-scale 3D simulation of a floating semi-submersible structure moored with three catenary lines ties all the models and tools developed here together and shows the capability of the high-fidelity FSI framework to model complex systems robustly and accurately.

In many countries today, cross-laminated timber (CLT) panels are increasingly being used in structural applications. CLT has many key advantages such as high strength-to-weight ratio in comparison to other common construction materials, excellent sustainability credentials, easy handling in construction, quick erection time, and good thermal and sound insulation. CLT exhibits complex behaviour; therefore, powerful theories are required to provide a better understanding of the mechanical behaviour of CLT panels and to enable their efficient and safe application in structural engineering. From that point of view, developing theoretical and numerical solutions for the analysis of CLT panels is an active research topic. A CLT panel is a laminated composite panel and, from an engineering design point of view, it can be considered as an orthotropic composite material with an elastic behaviour. Existing analytical approaches for CLT panels have limitations in applicability and accuracy. Hence, the State Space Approach (SSA) has the potential to improve the accuracy and range of applicability over these existing methods. The SSA provides theoretically accurate three-dimensional solutions that guarantee continuous transverse stress distributions across the thickness of the plates. Also, the boundary conditions and the continuity at the interfaces are satisfied (Ye, 2003). Thus, the research presented in this thesis will investigate CLT panels using the novel application of this approach. Before focusing on the specific application to CLT, the general SSA is explored for simply supported orthotropic composite plates under different types of out-of-plane loads. A new analytical solution by using the SSA for the case of a plate with three sides simply supported and one free edge under different out-of-plane loads will be developed and the derivations for the equations will be shown in detail. Note that this is the first time the SSA formulation for this particular boundary condition has been developed. For both the aforementioned and fully simply supported boundary conditions, the results obtained by using the SSA are compared with existing experimental works, various existing analytical approaches and numerical methods. To provide more knowledge and understanding of this particular application, numerical modelling of CLT using the Finite Element Method (FEM) via ABAQUS is conducted. Although the FEM is very applicable in understanding the general structural behaviour of the panel, it shows discontinuity of the transverse shear stresses at the interfaces of each ply of the CLT since, in the case of solid elements, the transverse stresses are obtained from the displacement field not from the equilibrium equations. Crucially, the SSA overcomes this problem and shows continuous stress distributions between the plies. Ultimately, this work shows that, for the boundary conditions examined, the SSA provides an accurate and efficient way to capture the structural behaviour of CLT panels subject to out-of-plane loads and can outperform some of the existing analytical methods commonly used in practice.

This thesis aims to develop an understanding about swelling and disintegration of multi-component polymeric structures such as pharmaceutical tablets. The thesis presents a model for the diffusion-driven water uptake, swelling deformation and subsequent disintegration of polymer matrix drug-delivery devices. Hygroscopic swelling occurs when a dry tablet enters a humid environment and absorbs water molecules. The modification of tablet structures changes the release profile of the drug in the desired manner. The previous research mostly focused on transport problems related to drug release. This study contributes an understanding of the mechanical behaviour of hydrophilic polymer release matrix materials which are treated as continuum. Modelling of the swelling problem involves concurrent large deformation of the polymer network and diffusion of the solvent through the network. A coupled diffusion-deformation model was created to study the relation between both physics. The coupled diffusion-deformation model was utilised to consider disintegration of polymer matrix through the inclusion of swelling agents. Two cases were presented to illustrate the application of the model: swelling-controlled and immediate-release drug delivery systems. This study used COMSOL Multiphysics®, a finite element commercial software to perform the analysis. Various physical modules: structural mechanics, chemical transport and mathematics were combined for solving coupled diffusion-deformation-damage boundary value problems. The numerical results were validated using existing experimental data from the literature. The model parameters were varied to investigate their sensitivity to the solution. Higher solvent concentration gradient in the matrix produced higher swelling strain, thus increased local stress. Disintegrability was measured by the time taken for the maximum principal stress to reach a given failure. Higher coefficient of water diffusion allows higher amount of water ingression into the matrix. Higher coefficient of hygroscopic swelling generates higher local swelling strain. This study facilitates in understanding the complex phenomena in the application of drug release formulation.

The fluid-structure interactions of wall-mounted slender structures, such as cilia, filaments, flaps, and flags, play an important role in a broad range of physical processes: from the coherent waving motion of vegetation, to the passive flow control capability of hair-like surface coatings. While these systems are ubiquitous, their coupled nonlinear response exhibits a wide variety of behaviours that is yet to be fully understood, especially when multiple structures are considered. The purpose of this work is to investigate, via numerical simulation, the fluid-structure interactions of arrays of slender structures over a range of input conditions. A direct modelling approach, whereby the individual structures and their dynamics are fully resolved, is realised via a lattice Boltzmann-immersed boundary model, which is coupled to two different structural solvers: an Euler-Bernoulli beam model, and a finite element model. Results are presented for three selected test cases - which build in scale from a single flap in a periodic array, to a small finite array of flaps, and finally to a large finite array - and the key behaviour modes are characterised and quantified. Results show a broad range of behaviours, which depend on the flow conditions and structural properties. In particular, the emergence of coherent waving motions are shown to be closely related to the natural frequency of the array. Furthermore, this behaviour is associated with a lock-in between the natural frequency of the array and the predicted frequency of the fluid instabilities. The original contributions of this work are: the development and application of a numerical tool for direct modelling of large arrays of slender structures; the characterisation of the behaviour of slender structures over a range of input conditions; and the exposition of key behaviour modes of slender structures and their relation to input conditions.

In this thesis, we use a combination of experiments and numerical modelling to study the spreading of micro-droplets on 'patterned surfaces', with applications to the manufacture of POLED displays via inkjet printing. The term patterned surfaces is used to refer to surfaces with either micron-sized topographical features or variations in the wettability or a combination of both. We demonstrate that these patterned surfaces provide an effective means to control the spread of fluid deposited using an inkjet method so that liquid films are printed in a pixel shape. It is shown that the spreading of the fluid deposited via the inkjet method can be either locally enhanced or hindered depending on whether the topography gradient ahead of the contact line is positive or negative. Locally enhanced spreading occurs via the formation of thin rivulets through a mechanism similar to the capillary rise in sharp corners. A key feature of the liquid-substrate interaction studied in this work is the presence of significant contact angle hysteresis, which enables the persistence of non-circular fluid morphologies. However, we find that the efficacy of topographical features in restraining the spreading of deposited liquid within the boundaries of a pixel is critically dependent on the accurate positioning of droplets in a pixel. We demonstrate that this dependence on the positioning of droplets is reduced on substrates with both topographical and wettability patterns. Excellent predictions of the evolution of the liquid morphologies on patterned surfaces are provided by a simple model combining quasi-static surface-tension effects within the framework of a thin-film approximation, combined with an experimentally measured dynamic spreading law, which relates the speed of the contact line to the contact angle. We also show that if an experimental spreading law is not available, the spreading of a droplet in a pixel can be adequately predicted by the Cox-Voinov spreading law. This model does not include viscous effects in the bulk of a droplet and hence a given morphology is attained more rapidly in the numerical computations compared to the experiments in which bulk viscous resistance retards the fluid motion. Nonetheless, the model can be used very effectively to predict the areas covered by the liquid and may serve as a useful design tool in the inkjet printing industry.

Automotive tyres are one of the main components of a vehicle and have an extremely complex structure consisting of several types of steel reinforcing layers embedded in hyperelastic rubber materials. They serve to support, drive - accelerate and decelerate - and steer the vehicle, and to reduce transmitted road vibrations. However, driving is associated with certain types of pollution due to CO2 emissions, various particles due to tyre wear, as well as noise. The main source of CO2 emissions is the tyre rolling resistance, which accounts for roughly 30% of the fuel consumed by cars. The phenomenon becomes more pronounced in off-road conditions, where truck vehicles are responsible for about a quarter of the total CO2 emissions. Appropriate legislation has been introduced, to control all of these pollution aspects. Therefore, tyre simulation (especially in off-road conditions) is essential in order to achieve a feasible design of a vehicle, in terms of economy and safety. After a concise literature review and critical evaluation of the state-of-the-art models related to simulation and analysis of off-road tyres, the various limitations of the existing tyre models in terms of representing the rolling response and driving behaviour of actual tyres have been identified (e.g. utilization of non-invariant soil parameters). Finite element models for the terrain have been developed in which invariant soil parameters have been designated which are used for the description of the tyre-terrain interaction. Similar to the development of the soil models, a realistic tyre model was established via a novel coupled MATLAB-ABAQUS optimisation algorithm. The agreement of the tyre structure with reality was achieved through matching of its eigen properties with analogous data from actual tyres. Subsequently, the interaction between a 235/75R17 tyre and a road - which is considered to be either rigid or deformable - was modelled with the finite element method and the rolling response of towed and driven wheels under various driving conditions was investigated. Regarding the limitations of the models used, it should be noted that the soil material is described by the linear Drucker-Prager constitutive model and the tyre parameters have been obtained via an optimisation procedure. More accurate soil constitutive models and calibration of their corresponding parameters, as well as realistic tyre properties can be used for further development of the various models involved in the thesis, the results of which can be validated with experimental data. Additionally, a novel semi-analytical solution for the estimation of the response of a pneumatic tyre rolling on deformable terrain has been introduced, which involves substantial improvements compared to other existing semi-analytical solutions. Among others, lateral forces as well as the effects of treaded pattern and multi-pass have been taken into account. Although the developed analytical model is based on invariant soil parameters, it remains a semi analytical approach, as it involves empirical parameters such as the shear deformation modulus and empirical parameters related to distribution of the pressures between the tyre and the soil. Furthermore, it is assumed that the pressures at the tyre-soil interface are uniform along the width of the tyre which can lead to significant deviation of the results, especially for low inflated tyres (< 15kPa) with large contact area.

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.

Hot spotting of automotive disc brakes is an undesired thermal localisation phenomenon, which is a challenge for numerical modelling in terms of both accuracy and efficiency especially for complex disc geometry. In this research, the aim was to develop a computationally efficient finite element (FE) approach for 2-piece pin-mounted ventilated disc hot spot prediction with acceptable accuracy enabling parametric studies to contribute to the knowledge of the complex mechanisms. A time reduction strategy for the simulations was established by incorporating an axisymmetric brake pad assumption with material scaling factor and the friction characteristics were defined by a user-subroutine. The computing accuracy and efficiency of this method were then verified by comparing with traditional FE models. 2D in-plane, 2D out-of-plane, and 3D models were performed to investigate the effects of ventilated disc hot spotting, radial hot spot/band migration, and hot spotting of realistic complex disc geometry respectively. Both 2D and 3D results were validated using experimental results based on a laboratory dynamometer and showed good correlation. The results suggested that adequate modelling of friction pair contact pressure distribution and the subsequent non-uniform heat generation is essential for hot spot simulation; speed was identified as the determinant for the number of hot spots, whereas hot spot temperature was determined by energy level. Furthermore, recommendations for vent design, pins, disc run-out, cooling, material selection, wear rate, pad length and loading distribution were given. Finally, hot spotting and hot band migration cause-effect chains were established based on the results and discussion.

The central theme of this thesis is the design of optimal balanced black-box stopping criteria in iterative solvers of symmetric positive-definite, symmetric indefinite, and nonsymmetric linear systems arising from finite element approximation of stochastic (parametric) partial differential equations. For a given stochastic and spatial approximation, it is known that iteratively solving the corresponding linear(ized) system(s) of equations to too tight algebraic error tolerance results in a wastage of computational resources without decreasing the usually unknown approximation error. In order to stop optimally-by avoiding unnecessary computations and premature stopping-algebraic error and a posteriori approximation error estimate must be balanced at the optimal stopping iteration. Efficient and reliable a posteriori error estimators do exist for close estimation of the approximation error in a finite element setting. But the algebraic error is generally unknown since the exact algebraic solution is not usually available. Obtaining tractable upper and lower bounds on the algebraic error in terms of a readily computable and monotonically decreasing quantity (if any) of the chosen iterative solver is the distinctive feature of the designed optimal balanced stopping strategy. Moreover, this work states the exact constants, that is, there are no user-defined parameters in the optimal balanced stopping tests. Hence, an iterative solver incorporating the optimal balanced stopping methodology that is presented here will be a black-box iterative solver. Typically, employing such a stopping methodology would lead to huge computational savings and in any case would definitely rule out premature stopping. The constants in the devised optimal balanced black-box stopping tests in MINRES solver for solving symmetric positive-definite and symmetric indefinite linear systems can be estimated cheaply on-the- fly. The contribution of this thesis goes one step further for the nonsymmetric case in the sense that it not only provides an optimal balanced black-box stopping test in a memory-expensive Krylov solver like GMRES but it also presents an optimal balanced black-box stopping test in memory-inexpensive Krylov solvers such as BICGSTAB(L), TFQMR etc. Currently, little convergence theory exists for the memory-inexpensive Krylov solvers and hence devising stopping criteria for them is an active field of research. Also, an optimal balanced black-box stopping criterion is proposed for nonlinear (Picard or Newton) iterative method that is used for solving the finite dimensional Navier-Stokes equations. The optimal balanced black-box stopping methodology presented in this thesis can be generalized for any iterative solver of a linear(ized) system arising from numerical approximation of a partial differential equation. The only prerequisites for this purpose are the existence of a cheap and tight a posteriori error estimator for the approximation error along with cheap and tractable bounds on the algebraic error.

The field of paleomagnetism attempts to understand in detail the the processes of the Earth by studying naturally occurring magnetic samples. These samples are quite unlike those fabricated in the laboratory. They have irregular shapes; they have been squeezed and stretched, heated and cooled and subjected to oxidation. However micromagnetic modelling allows us to simulate such samples and gain some understanding of how a paleomagnetic signal is acquired and how it is retained. Micromagnetics provides a theory for understanding how the domain structure of a magnetic sample alters subject to what it is made from and the environment that it is in. It furnishes the mathematics that describe the energy of a given domain structure and how that domain structure evolves in time. Combining micromagnetics and ever increasing computer power, it has been possible to produce simulations of small to medium size grains within the so-called single to pseudo single domain state range. However processors are no longer built with increasing speed but with increasing parallelism and it is this that must be exploited to model larger and larger paleomagnetic samples. The purpose of the work presented here is twofold. Firstly a micromagnetics code that is parallel and scalable is presented. This code is based on FEniCS, an existing finite element framework, and is shown to run on ARCHER the UK’s national supercomputing service. The strategy of using existing libraries and frameworks allow future extension and inclusion of new science in the code base. In order to achieve scalability, a spatial mapping technique is used to calculate the demagnetising field - the most computationally intensive part of micromagnetic calculations. This allows grain geometries to be partitioned in such a way that no global communication is required between parallel processes - the source of favourable scaling behaviour. The second part of the theses presents an exploration of domain state evolution in increasing sizes of magnetite grains. This simulation, whilst a first approximation that excludes magneto-elastic effects, is the first attempt to map out the transition from pseudo-single domain states to multi domain states using a full micromagnetic simulation.

This thesis investigates tsunami impact on shore-based, low-rise structures in coastal areas. The aims are to investigate tsunami wave inundation in built-up coastal areas with reference to structural response to wave inundation, to assess the performance of current design codes in comparison with validated state-of-the-art numerical models and to improve structural design of residential buildings in tsunami risk areas. Tsunami events over the past few decades have shown that a significant proportion of fatalities can be attributed to the collapse of building infrastructure due to various actions of the incident waves. Although major tsunami events have demonstrated the potential catastrophic effects on built infrastructure, current building codes have no detailed or consistent guidance on designing structures in tsunami-prone regions. Furthermore, considerable differences in existing empirical formulae highlight that new research is necessary to appropriately address the particularities of the tsunami-induced forces and structure response into the design standards. In this thesis, numerical modelling methods are used to simulate hydrodynamic impact on shore-based coastal structures. The hydrodynamic simulations were conducted using a novel meshless numerical method, smoothed particle hydrodynamics (SPH), which is coupled with the finite element (FE) method to model structural behaviour. The SPH method was validated with experimental data for bore impact on an obstacle using a convergence study to identify the optimum particle size to capture the hydrodynamics. The FE model was validated against experimental data for plates under transient blast loads which have similar load characteristics with impulsive tsunami-induced bore impacts. One of the contributions of the thesis is the use of a new coupling method of the SPH-based software DualSPHysics and FE-based software ABAQUS. Using SPH particle spacing of the same size as the FE mesh size, enables the SPH output pressure to be directly applied as an input to the structural response model. Using this approach the effects of arrangement and orientation of single and multiple low rise structures are explored. Test cases were performed in 2-D and 3-D involving a discrete structure and multiple structures. The 3-D SPH simulations with single and multiple structures used an idealised coastal structure in the form of a cube with different on-plan orientations (0°, 30°, 45° and 60°) relative to the oncoming bore direction. The single structure cases were intended to study the improvement of the resilience of coastal structures by reducing the acting pressures on the vertical surfaces by changing the structure’s orientation. It was found the pressure exerted on the vertical surface of structure can be reduced by up to 50% with the 60° orientation case. The multiple structure models were conducted to examine shielding and flow focusing phenomena in tsunami events. The results reveal that the distance between two adjacent front structures can greatly influence the pressure exerted on the rear structure. This thesis also demonstrates the capability of SPH numerical method in simulating standard coastal engineering problems such as storm waves impact on a recurve wall in 2-D. The idealised structures were represented as standard timber construction and the finite element modelling was used to determine the corresponding stress distributions under tsunami impact. Following the comparison of the method used in this thesis with commonly used design equations based on the quasi-static approach, large differences in stress prediction were observed. In some cases the loads according to the design equations predicted maximum stresses almost one order of magnitude lower. This large discrepancy clearly shows the potential for non-conservative design by quasi-static approaches. The new model for the simulation of tsunami impact on discrete and multiple structures shows that the resilience of a coastal structure can be improved by changing the orientation and arrangement. The characteristics of tsunami waves during propagation and bore impact pressures on structures can be assessed in great detail with the combined SPH and FE modelling strategy. The techniques outlined in this thesis will enable engineers to gain a better insight into tsunami wave-structure interaction with a view towards resilience optimisation of structures vulnerable to tsunami impact events.

Micromagnetics is a continuum mechanics theory of magnetic materials widely used in industry and academia. In this thesis we describe a complete numerical method, with a number of novel components, for the computational solution of dynamic micromagnetic problems by solving the Landau-Lifshitz-Gilbert (LLG) equation. In particular we focus on the use of the implicit midpoint rule (IMR), a time integration scheme which conserves several important properties of the LLG equation. We use the finite element method for spatial discretisation, and use nodal quadrature schemes to retain the conservation properties of IMR despite the weak-form approach. We introduce a novel, generally-applicable adaptive time step selection algorithm for the IMR. The resulting scheme selects error-appropriate time steps for a variety of problems, including the semi-discretised LLG equation. We also show that it retains the conservation properties of the fixed step IMR for the LLG equation. We demonstrate how hybrid FEM/BEM magnetostatic calculations can be coupled to the LLG equation in a monolithic manner. This allows the coupled solver to maintain all properties of the standard time integration scheme, in particular stability properties and the energy conservation property of IMR. We also develop a preconditioned Krylov solver for the coupled system which can efficiently solve the monolithic system provided that an effective preconditioner for the LLG sub-problem is available. Finally we investigate the effect of the spatial discretisation on the comparative effectiveness of implicit and explicit time integration schemes (i.e. the stiffness). We find that explicit methods are more efficient for simple problems, but for the fine spatial discretisations required in a number of more complex cases implicit schemes become orders of magnitude more efficient.

Phase change in solidification and melting can be described with the aid of discontinuous functions. The aim of this project is to establish effective methodologies for the solution of discontinuous phase-change problems. The classic capacitance method, which distributes the effect of any discontinuity present over a finite region (typically an element), can suffer from inaccurate energy transport. Improvement is possible with the application of the classic non-physical enthalpy method. However, this approach is known to suffer with the imposition of material velocity, which gives rise to negative thermal capacitance providing a source of error and instability. In order to improve on the performance of the capacitance method and the classic non-physical enthalpy method, this research introduces a series of new non-physical variables. Firstly, a new non-physical enthalpy is defined via the weak form of the energy transport equation. The classical non-physical enthalpy was defined using a temporal integral term. In the new definition, the non-physical enthalpy involves both a temporal and an advection term, which is shown to avoid the generation of negative capacitance and improve the stability of advection heat transfer in numerical methods. Secondly, control volume analysis is performed on weighted and unweighted forms of the governing energy equation involving non-physical enthalpy. The analysis is shown to reveal non-physical source terms that facilitate the removal of phase-change discontinuities. Thirdly, it is demonstrated in the thesis how a non-physical heat source must be introduced into the governing non-physical transport equation to remove discontinuities arising from non-physical terms related to advection. To demonstrate the accuracy and stability of the new method, it is implemented in the finite element method for both one-dimensional linear rod elements and two dimensional triangular elements. Update techniques and root finding methods, such as the predictor-corrector method, the secant method and the homotopy method, are applied to solve the non-linear system of equations, which are constructed with the new theory. Results returned from the one-dimensional numerical experiments are compared with exact solutions, which show reasonable accuracy. Numerical experiments for isothermal solidification with advection-diffusion in both one and two dimensions demonstrate the feasibility of the new methodology.

Thin-walled cold-formed steel (CFS) has exhibited inherent structural and architectural advantages over other constructional materials, for example, high strength-to-weight ratio, ease of fabrication, economy in transportation and the flexibility of sectional profiles, which make CFS ideal for modern residential and industrial buildings. They have been increasingly used as purlins as the intermediate members in a roof system, or load-bearing components in low- and mid-rise buildings. However, using CFS members in building structures has been facing challenges due to the lack of knowledge to the fire performance of CFS at elevated temperatures and the lack of fire design guidelines. Among all available design specifications of CFS, EN1993-1-2 is the only one which provided design guidelines for CFS at elevated temperatures, which, however, is based on the same theory and material properties of hot-rolled steel. Since the material properties of CFS are found to be considerably different from those of hot-rolled steel, the applicability of hot-rolled steel design guidelines into CFS needs to be verified. Besides, the effect of non-uniform temperature distribution on the failure of CFS members is not properly addressed in literature and has not been specified in the existing design guidelines. Therefore, a better understanding of fire performance of CFS members is of great significance to further explore the potential application of CFS. Since CFS members are always with thin thickness (normally from 0.9 to 8 mm), open cross-section, and great flexural rigidity about one axis at the expense of low flexural rigidity about a perpendicular axis, the members are usually susceptible to various buckling modes which often govern the ultimate failure of CFS members. When CFS members are exposed to a fire, not only the reduced mechanical properties will influence the buckling capacity of CFS members, but also the thermal strains which can lead additional stresses in loaded members. The buckling behaviour of the member can be analysed based on uniformly reduced material properties when the member is unprotected or uniformly protected surrounded by a fire that the temperature distribution within the member is uniform. However if the temperature distribution in a member is not uniform, which usually happens in walls and/or roof panels when CFS members are protected by plaster boards and exposed to fire on one side, the analysis of the member becomes very complicated since the mechanical properties such as Young’s modulus and yield strength and thermal strains vary within the member. This project has the aim of providing better understanding of the buckling performance of CFS channel members under non-uniform temperatures. The primary objective is to investigate the fire performance of plasterboard protected CFS members exposed to fire on one side, in the aspects of pre-buckling stress distribution, elastic buckling behaviour and nonlinear failure models. Heat transfer analyses of one-side protected CFS members have been conducted firstly to investigate the temperature distributions within the cross-section, which have been applied to the analytical study for the prediction of flexural buckling loads of CFS columns at elevated temperatures. A simplified numerical method based on the second order elastic – plastic analysis has also been proposed for the calculation of the flexural buckling load of CFS columns under non-uniform temperature distributions. The effects of temperature distributions and stress-strain relationships on the flexure buckling of CFS columns are discussed. Afterwards a modified finite strip method combined with the classical Fourier series solutions have been presented to investigate the elastic buckling behaviour of CFS members at elevated temperatures, in which the effects of temperatures on both strain and mechanical properties have been considered. The variations of the elastic buckling loads/moments, buckling modes and slenderness of CFS columns/beams with increasing temperatures have been examined. The finite element method is also used to carry out the failure analysis of one-side protected beams at elevated temperatures. The effects of geometric imperfection, stress-strain relationships and temperature distributions on the ultimate moment capacities of CFS beams under uniform and non-uniform temperature distributions are examined. At the end the direct strength method based design methods have been discussed and corresponding recommendations for the designing of CFS beams at elevated temperatures are presented. This thesis has contributed to improve the knowledge of the buckling and failure behaviour of CFS members at elevated temperatures, and the essential data provided in the numerical studies has laid the foundation for further design-oriented studies.

In this research, the finite element method (FEM) was used to solve the nonlinear, incompressible, transient, three dimensional Navier-Stokes equations in their non-conservative form. Linear tetrahedron elements were employed with the elegant, equal order interpolation for both pressure and velocity. The characteristic based split scheme was formulated in a fully implicit manner to circumvent the time step restrictions of the classical explicit formulations. The monolithic (single step, fully coupled solution procedure for pressures and velocity) form of the CBS scheme was also derived and its suitability was positively demonstrated. Casting the CBS scheme in a monolithic framework, results in the generation of a pressure stabilization term in the mass conservation equation, thereby circumventing the LBB restriction by the elimination of the zero pressure block. An account of all the steps involved in discretizing the Navier-Stokes equations (both in split and monolithic frameworks) was presented in meticulous detail, which included the derivation of the convective and pressure stabilization terms, linearization of the non-linear terms and the consequent derivation of the highly efficient analytical jacobian matrix, along with the temporal and spatial discretizations of the corresponding terms. The monolithic and the split version of the CBS scheme were integrated into a parallel, scalable and extensible Fortran90 software called IFENs. The development of IFENs started during the course of this research and all of its components have been designed and implemented by the author of this thesis. Multi processor parallelism was achieved using the Intel implementation of the most widely used/preferred, Message Passing Interface (MPI) standard. The parallel support needed for the use of a variety of parallel, linear, iterative solvers belonging to the Krylov subspace family (e.g. GMRES and its variants, CG, BiCG, BiCG- stab, etc.), parallel non linear solvers belonging to the Newton-Krylov family (line search newton, trust region newton, nonlinear GMRES, etc.) and parallel preconditioners (incomplete LU, Additive Shwarz Method - ASM, algebraic multigrid, etc.), was provided by the incorporation of PETSc into IFENs. PETSc is a state of the art, non-trivial toolkit, which represents a collection of several parallel libraries useful in high performance scientific computing. Keeping in mind the specific requirements of IFENs, a custom mesh partitioner was implemented. It operated on meshes that were renumbered using bandwidth reducing algorithms like Revere Cuthill Mckee. The possibility of using established domain decomposition libraries like ParMETIS was explored and demonstrated to be counter productive for the demands of this research. After the preliminary testing and validation of the procedures adopted before and during the execution of IFENs, large, high definition domains representative of human arteries (specifically, carotid bifurcations, found in the neck) were considered and the complete incompressible set of Navier-Stokes equations were solved for pressure and velocity fields. During the tenure of this research more than 1000 recorded parallel test cases were executed to test various components of IFENs, as well as various simulations representative of a wide variety of problems. IFENs can easily handle meshes with tens of millions of elements. The largest mesh used for the purpose of this research contained 14.58 million tetrahedrons and 2.489 million nodes, which on average required just 7 minutes per timestep, while executing the classical split framework of the CBS scheme. Results from the simulation of 9 carotid meshes, representative of 4 carotid geometries were presented and found to be in good agreement with the available ultrasound data. The flow fields were analysed and post processed using different techniques for each case. The haemodynamic wall parameters like time averaged wall shear stress and oscillatory shear index were calculated and mapped onto the corresponding boundary nodes. The region in the carotid bifurcation susceptible to the deposition of plaques and consequent stenosis were pointed out and other anomalies were highlighted.

Compressive residual stresses (CRS) are beneficial for enhancing the fatigue life of metal components. Shot Peening (SP) is an industrial cold working process that is applied to induce a field of CRS and modify the mechanical properties of the metal component. The SP process involves impacting a surface with tiny shots with forces sufficient to create plastic deformation. The process is governed by a number of important parameters such as the shot size, angle of attack, initial velocity, mass flow rate and the distance from the shot nozzle to the surface being peened. The relationship between the optimal peening outcome, particularly the residual stress distribution of the treated surface, and the peening parameters is still unknown and needs to be investigated further. Manufacturers are interested in producing a uniform peening process for complex geometries which optimises the SP parameters. Modelling the process is complex as it involves the interaction of a metallic surface with a large number of shots of very small diameter. Conventionally, such problems are solved using finite element software to predict stresses and strains of a single shot impact then applying superposition. At the moment there are no Finite Element Method (FEM) modelling solutions involving more than tens of shots. The number of shots and elements required for such a modelling process made the approach unfeasible prior to the work described herein. The objective of this work is to develop an appropriate numerical modelling approach that can better simulate the real SP process. The model will be provided by combining Discrete Element Method (DEM) with FEM. The DEM is employed to get a distribution of impact velocities over space and time which are then implemented into a FEM analysis. A discrete element model with randomly distributed steel shots bombarding a steel component at various velocities has been developed as benchmark example. With this model the SP shot - shot interaction, the shot - target interaction, the surface coverage, angle of impingement, shot size, impact velocity and the overall shot flow can be parametrically studied in details and with little computational effort. The novel approach also proposes a new method to dynamically change the coefficient of restitution for repeated impacts during the simulation and predicts the CRS more effectively. The effects of SP on different materials of relevance to gas turbine engine components will be investigated in order to improve the understanding of the interaction between the shots and the targeted material. Initially, an uncoupled analysis was peforned, in order to assess the capabilities of the two modelling systems, DEM and FEM, to delivery an improved solutuion when combining two commercially available codes. This parametric analysis is performed using the state-of-the-art Discrete Element (DE) application EDEM. In the subsequent part of this work, a dynamic Finite Element (FE) application Abaqus will be used to investigate single shot impacts and to obtain the residual stress distribution. This gives us a prescribed residual stress distribution and peening coverage. A Combined DEM/FEM tool (DEST) is proposed that eliminates any manual pre-processing required for linking/coupling, eliminating the use of two different applications and provide an integrated solution for the simulation of the Shot Peening process. In the subsequent chapter, the implementation of essential tools for the enchanced modelling of Shot Peening process functionalities, such as the nozzle, bounding box, coverage and intensity is described. A number of computational improvements are also implemented to reduce the computation time. The existing binary search is enhanced to self-balancing search tree and further improved to allow insertion and deletion of elements. A bounding box feature which removes shots that move out of the domain during the course of the simulation is also implemented. Experiments featuring single shot impacts are performed to gain better understanding the deformation process in the target material subjected to impact conditions to those occurring in the production peening. The single shot impacts are experimentally examined using SEM and EBSD. During final chapter, case studies are performed to compare the results of the simulations with large-scale experimental work. The coverage of peening of single and multiple nozzles with different angle of impingements are assessed. Finally, possible directions for further research concerning the accurate quantification of material responses to SP are identified in the report.

Incremental Sheet Forming (ISF) is a progressive metal forming process, where the deformation occurs locally around the point of contact between a tool and the metal sheet. The final work-piece is formed cumulatively by the movements of the tool, which is usually attached to a CNC milling machine. The ISF process is dieless in nature and capable of producing different parts of geometries with a universal tool. The tooling cost of ISF can be as low as 5–10% compared to the conventional sheet metal forming processes. On the laboratory scale, the accuracy of the parts created by ISF is between ±1.5 mm and ±3mm. However, in order for ISF to be competitive with a stamping process, an accuracy of below ±1.0 mm and more realistically below ±0.2 mm would be needed. In this work, we first studied the ISF deformation process by a simplified phenomenal linear model and employed a predictive controller to obtain an optimised tool trajectory in the sense of minimising the geometrical deviations between the targeted shape and the shape made by the ISF process. The algorithm is implemented at a rig in Cambridge University and the experimental results demonstrate the ability of the model predictive controller (MPC) strategy. We can achieve the deviation errors around ±0.2 mm for a number of simple geometrical shapes with our controller. The limitations of the underlying linear model for a highly nonlinear problem lead us to study the ISF process by a physics based model. We use the elastoplastic constitutive relation to model the material law and the contact mechanics with Signorini’s type of boundary conditions to model the process, resulting in an infinite dimensional system described by a partial differential equation. We further developed the computational method to solve the proposed mathematical model by using an augmented Lagrangian method in function space and discretising by finite element method. The preliminary results demonstrate the possibility of using this model for optimal controller design.

The world population is expected to increase to approximately 11 billion by 2100. The ageing population (aged 60 and over) is projected to exceed the number of children in 2047. This will be a situation without precedent. The number of citizens with disorders of old age like Dementia will rise to 115 million worldwide by 2050. The estimated cost of Dementia will also increase, from $604 billion in 2010, to $1,117 billion by 2030. At the same time, medical expertise, evidence-driven policymaking and commissioning of services are increasingly evolving the definitive architecture of comprehensive long-term care to account for these changes. Technological advances, such as those provided by computational science and biomedical engineering, will allow for an expansion in our ability to model and simulate an almost limitless variety of complex problems that have long defied traditional methods of medical practice. Numerical methods and simulation offer the prospect of improved clinically relevant predictive information, and of course optimisation, enabling more efficient use of resources for designing treatment protocols, risk assessment and urgently needed management of a long term care system for a wide spectrum of brain disorders. Within this paradigm, the importance of the relationship of senescence of cerebrospinal fluid transport to dementia in the elderly make the cerebral environment notably worthy of investigation through numerical and computational modelling. Hydrocephalus can be succinctly described as the abnormal accumulation (imbalance between production and circulation) of cerebrospinal fluid (CSF) within the brain. Using hydrocephalus as a test bed, one is able to account for the necessary mechanisms involved in the interaction between cerebral fluid production, transport and drainage. The current state of knowledge about hydrocephalus, and more broadly integrative cerebral dynamics and its associated constitutive requirements, advocates that poroelastic theory provides a suitable framework to better understand the disease. In this work, Multiple-network poroelastic Theory (MPET) is used to develop a novel spatio-temporal model of fluid regulation and tissue displacement in various scales within the cerebral environment. The model is discretised in a variety of formats, through the established finite difference method, finite difference – finite volume coupling and also the finite element method. Both chronic and acute hydrocephalus was investigated in a variety of settings, and accompanied by emerging surgical techniques where appropriate. In the coupled finite difference – finite volume model, a key novelty was the amalgamation of anatomically accurate choroid plexuses with their feeding arteries and a simple relationship relaxing the constraint of a unique permeability for the CSF compartment. This was done in order to account for Aquaporin-4 sensitisation. This model is used to demonstrate the impact of aqueductal stenosis and fourth ventricle outlet obstruction. The implications of treating such a clinical condition with the aid of endoscopic third (ETV) and endoscopic fourth ventriculostomy (EFV) are considered. It was observed that CSF velocity in the aqueduct, along with ventricular displacement, CSF pressure, wall shear stress and pressure difference between lateral and fourth ventricles increased with applied stenosis. The application of ETV reduced the aqueductal velocity, ventricular displacement, CSF pressure, wall shear stress and pressure difference within nominal levels. The greatest reversal of the effects of atresia come by opting for ETV rather than the more complicated procedure of EFV. For the finite difference model incorporating nonlinear permeability, qualitatively similar results were obtained in comparison to the pertinent literature, however, there was an overall amplification of ventriculomegaly and transparenchymal pressure difference using this model. A quantitative and qualitative assessment is made of hydrocephalus cases involving aqueductal stenosis, along with the effects to CSF reabsorption in the parenchyma and subarachnoid space. The finite element discretisation template produced for the nth- dimensional transient MPET system allowed for novel insight into hydrocephalus. In the 1D formulation, imposing the breakdown of the blood-CSF barrier responsible for clearance resulted in an increase in ventricular displacement, transparenchymal venous pressure gradient and transparenchymal CSF pressure gradient, whilst altering the compliance proved to markedly alter the rate of change of displacement and CSF pressure gradient. The influence of Poisson's ratio was investigated through the use of the dual-grid solver in order to distinguish between possible over or under prediction of the ventricular displacement. In the 2D model based on linear triangles, the importance of the MPET boundary conditions is acknowledged, along with the quality of the underlying mesh. Interesting results include that the fluid content is highest in the periventricular region and the skull, whilst after longer time scales, the peak CSF content becomes limited to the periventricular region. Venous fluid content is heavily influenced by the Biot-Willis constant, whilst both the venous and CSF/ISF compartments show to be strongly influenced by breakdown in the blood-CSF barrier. Increasing the venous compliance effects the arterial, capillary and venous compartments. Decreasing the venous compliance shows an accumulation of fluid, possibly helping to explain why the ventricles can be induced to compress rather than expand under decreased compliance. Finally, a successful application of the 3D-MPET template is shown for simple geometries. It is envisaged that future observations into the biology of cerebral fluid flow (such as perivascular CSF-ISF fluid exchange) and its interaction with the surrounding parenchyma, will demand the evolution of the MPET model to reach a level of complexity that could allow for an experimentally guided exploration of areas that would otherwise prove too intricate and intertwined under conventional settings.

In an era of intensified market competition, the demand for cost-effective, high-quality, high-performance, and reliable products continues to rise. Meeting this demand necessitates the mass production of premium products through the integration of cutting-edge technologies and advanced materials while ensuring their integrity and safety. In this context, Nondestructive Testing (NDT) techniques emerge as indispensable tools for guaranteeing the integrity, reliability, and safety of products across diverse industries. Various NDT techniques, including ultrasonic testing, computed tomography, thermography, and acoustic emissions, have long served as cornerstones for inspecting materials and structures. Among these, ultrasonic testing stands out as the most prevalent method, owing to its versatility, accuracy, portability, and cost-effectiveness. However, traditional ultrasonic testing presents inherent limitations, all of which are directly or indirectly related to the need for contact with the structure. Therefore, Laser Ultrasonic Testing (LUT) has been introduced as a noncontact NDT technique, harnessing lasers and optical devices for wave generation and detection. In LUT, the material acts as an emitting transducer, and the ultrasonic waves are generated through the photoacoustic effect. LUT's non-contact nature eliminates the need for coupling mediums, enhances inspection speed, and enables automation and application in hostile environments (e.g., radioactive, high-pressure, high-temperature). Yet, LUT encounters its own hurdles. Low signal-to-noise ratios (SNRs) due to the low amplitude of generated waves, and the intricacies of wave generation and propagation pose significant challenges. Meeting these challenges requires precise simulations to understand the mechanisms behind laser-induced wave generation, optimize laser parameters, and explore innovative solutions. Therefore, this dissertation delves into the accurate modeling and simulation of laser-induced elastic waves in both isotropic and composite materials. Additionally, it presents a novel approach to addressing the challenges faced by LUT. Initially, a new theory of thermoelasticity capable of capturing intricacies due to ultrafast heating of material using short and ultrashort laser pulses is presented. Next, the root cause of numerical solution issues in simulating laser-induced elastic waves is explored, and a new guideline for spatial discretization of the domain is proposed. Subsequently, simulations are verified by analytical results. Furthermore, a new model for light absorption in composite materials, considering distinct optical absorptivities for different constituents, is proposed. Lastly, the dissertation thoroughly examines the effects of laser beam shaping on wave convergence and unveils the dynamics of laser-induced elastic waves in composite materials.