Application of History Matching Tools to Upscaling

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Modelling to predict the reliability of solder joints

The work in this thesis investigates modelling methods to predict the reliability of solder joints under thermo-mechanical cycling. A literature review is presented covering analytical methods, creep laws and fatigue laws, and advanced damage mechanics methods. The use of FEA (Finite Element Analysis) to model creep along with a fatigue law to predict lifetime appears to be the most widely used and validated technique at present. The FEA discretisation of elasticity problems is derived using the principle of minimum potential energy and implemented in the code FATMAN (Finite-element Analysis Tool, Multi-physics And Nonlinear). A novel implicit solution scheme called LENI is proposed to allow modelling of creep in solder. The sinh law for steady-state creep and the Armstrong-Frederick kinematic hardening law to capture primary creep have been implemented in FATMAN using the LENI scheme. The advantage over an explicit discretisation is investigated. An inverse analysis method for determining material properties is used to determine constants for the kinematic hardening law from experimental creep curves. A damage law is presented which allows the prediction of crack propagation through a solder joint. A failure criteria based on the increase in electrical resistance is used, which removes the need for an empirical fatigue law. The steady state creep law, the kinematic hardening law and the damage law are all applied to modelling of tests developed at the NPL (National Physical Laboratory) including novel crack detection tests, an isothermal fatigue test, and accelerated thermal cycling of resistors

Interest rate models with Markov chains

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An efficient implementation of an implicit FEM scheme for fractional-in-space reaction-diffusion equations

Fractional differential equations are becoming increasingly used as a modelling tool for processes with anomalous diffusion or spatial heterogeneity. However, the presence of a fractional differential operator causes memory (time fractional) or nonlocality (space fractional) issues, which impose a number of computational constraints. In this paper we develop efficient, scalable techniques for solving fractional-in-space reaction diffusion equations using the finite element method on both structured and unstructured grids, and robust techniques for computing the fractional power of a matrix times a vector. Our approach is show-cased by solving the fractional Fisher and fractional Allen-Cahn reaction-diffusion equations in two and three spatial dimensions, and analysing the speed of the travelling wave and size of the interface in terms of the fractional power of the underlying Laplacian operator

Proceedings of the Eleventh UK Conference on Boundary Integral Methods (UKBIM 11), 10-11 July 2017, Nottingham Conference Centre, Nottingham Trent University

This book contains the abstracts and papers presented at the Eleventh UK Conference on Boundary Integral Methods (UKBIM 11), held at Nottingham Trent University in July 2017. The work presented at the conference, and published in this volume, demonstrates the wide range of work that is being carried out in the UK, as well as from further afield

Validação do critério ISSF aplicado a juntas adesivas usando métodos numéricos

Due to the limitations presented by conventional joining techniques, like bolted and welded joints, the industry has turned attention to adhesively-bonded joints. The lower weight and decreased stress concentrations are some of the advantages made possible by this technique. Over the years, diverse analytical and numerical approaches to the failure of these joints were investigated. The work presented in this report aims to propose and validate a fracture mechanics based approach to joint failure, named Intensity of Singular Stress Fields (ISSF). With this purpose, aluminium and composite single-lap joints bonded with a brittle adhesive were tested. Different overlap lengths (LO) were also considered in order to evaluate this parameter influence in the final results. The experimental data was treated and the average maximum loads sustained by the joints were collected. Then, a numerical method for joint strength prediction was proposed, consisting of a combination of experimental and numerical information. The numerical data was obtained through simulations resorting to the Finite Element Method (FEM) and a meshless technique, the Radial Point Interpolation Method (RPIM). The validation of the approach was achieved by analysing the polar stress components and comparing the experimental and numerical results. It was experimentally verified that increasing LO leads to an increase in strength of the joints. The proposed technique was successfully applied for both aluminium and composite adherends even though they had different formulations. The results attained with the proposed method were promising given itssimplicity compared with previously proposed methodologies. The method’s application to meshless methods was also confirmed since the RPIM presented very similar results to the FEM, despite presenting some oscillations.Devido às limitações das técnicas de ligação convencionais, tais como as ligações aparafusadas e a soldadura, a indústria virou a sua atenção para as juntas adesivas estruturais. O baixo peso e a redução das concentrações de tensões são algumas das vantagens inerentes a esta técnica. Ao longo dos anos foram investigadas diversas abordagens analíticas e numéricas relativas à fratura deste tipo de juntas. O presente trabalho tem como objetivo propor e validar um método baseado na mecânica da fratura para avaliar a falha destas juntas. Para o efeito, foram testadas juntas de sobreposição simples de alumínio e compósito ligadas por um adesivo frágil. Também foram considerados diferentes comprimentos de sobreposição (LO) de forma a avaliar a influência deste parâmetro nos resultados finais. Os dados experimentais foram tratados e foram recolhidas as cargas máximas médias suportadas pelas juntas. Posteriormente, foi proposto um método numérico para prever a resistência das juntas, que consiste na combinação de informação analítica e numérica. Os dados numéricos foram obtidos através de simulações recorrendo ao Método dos Elementos Finitos (MEF) e a uma técnica meshless, o Radial Point Interpolation Method (RPIM). A validação da abordagem foi conseguida através da análise das componentes polares das tensões e por comparação entre os resultados experimentais e analíticos. Verificou-se experimentalmente que um aumento do comprimento de sobreposição origina um aumento da resistência das juntas. A técnica foi aplicada com sucesso para aderentes de alumínio e de compósito mesmo apresentando formulações distintas. Os resultados obtidos com o método proposto foram promissores dada a simplicidade do mesmo quando comparado com metodologias previamente propostas. A aplicabilidade do método aos métodos sem malha também foi comprovada já que o RPIM apresentou resultados muito similares ao MEF, apesar de apresentar algumas oscilações

Simulation tools for biomechanical applications with PGD-based reduced order models

Cotutela Universitat Politècnica de Catalunya i Università degli Studi di PaviaNumerical simulation tools are generally used in all modern engineering fields, especially those having difficulties in performing large number of practical experiments, such as biomechanics. Among the computational methods, Finite Element (FE) is an essential tool. Nowadays, the fast-growing computational techniques, from the upgrading hardware to the emerging of novel algorithm, have already enabled extensive applications in biomechanics. For applications that require fast response and/or multiple queries, Reduced Order Modelling (ROM) methods have been developed based on existing methods such as FE, and have eventually enabled real-time numerical simulation for a large variety of engineering problems. In this thesis, several novel computational techniques are developed to explore the capability of Proper Generalised Decomposition (PGD), which is an important approach of ROM. To assess the usability of the PGD-based ROM for biomechanical applications, a real human femur bone is chosen to study its mechanical behaviour as an example. Standard image-based modelling procedure in biomechanics is performed to create an FE model which is then validated with in vitro experimental results. As a basis of this work, the medical image processing has to be performed, in order to generate an available FE model. This model is validated according to data collected from a previously performed \textit{in vitro} experimental test. The full procedure of image-based model generation and the validation of generated model is described in Chapter 2. As a major objective of this thesis, a non-intrusive scheme for the PGD framework is developed in Chapter 3. It is implemented using in-house developed Matlab (Mathworks, USA) code to conduct the PGD work flow, and calling Abaqus as an external solver for devised fictitious mechanical problems. The transformation of data from computed tomography (CT) image set to FE model including inhomogeneous material properties is subjected to some physical constraints, and when applying the load, there are also geometric constraints limiting the locations where load could be applied. These constraints will lead to a constrained parameter space, which possibly has difficulty to be separated in a Cartesian fashion. Therefore, a novel strategy to separate the parameters in a collective manner is proposed in Chapter 4. Chapter 5 details a comprehensive application in biomechanics, the methodologies proposed in Chapter 3 and 4 are applied on the practical model generated in Chapter 2. As a typical application of the PGD vademecum, a material property identification problem is discussed. Further PGD vademecum is generated using the identified material properties with variable loading locations, and with this vademecum, real-time mechanical response of the femur is available. In addition, for the purpose of extending the methodologies to orthotropic materials, which is commonly used in biomechanics, in Chapter 6 another linear elastic model is investigated with the non-intrusive PGD scheme. Nowadays, isogeometric analysis (IGA) is a very popular tool in computational mechanics. It is appealing to take advantage of non-uniform rational B-splines (NURBS) to discretise the model. For PGD, using B-splines for the discretisation of the parameter space could improve the quality of vademecum, especially for problems involving sensitivities with respect to the parameters during the online computations. It is important and necessary to extend the PGD framework to nonlinear solid mechanics, because most biological soft tissues have been observed nonlinear mechanical behaviours. Consequently, in Chapter 7 we have developed a PGD framework for the St.Venant-Kirchhoff constitutive model using the Picard linearisation which is consistent with the fixed-point iteration algorithm commonly used in PGD. In Chapter 8, conclusive remarks are addressed as well as forecasts of possible future works.Postprint (published version

Simulating 3D Radiation Transport, a modern approach to discretisation and an exploration of probabilistic methods

Light, or electromagnetic radiation in general, is a profound and invaluable resource to investigate our physical world. For centuries, it was the only and it still is the main source of information to study the Universe beyond our planet. With high-resolution spectroscopic imaging, we can identify numerous atoms and molecules, and can trace their physical and chemical environments in unprecedented detail. Furthermore, radiation plays an essential role in several physical and chemical processes, ranging from radiative pressure, heating, and cooling, to chemical photo-ionisation and photo-dissociation reactions. As a result, almost all astrophysical simulations require a radiative transfer model. Unfortunately, accurate radiative transfer is very computationally expensive. Therefore, in this thesis, we aim to improve the performance of radiative transfer solvers, with a particular emphasis on line radiative transfer. First, we review the classical work on accelerated lambda iterations and acceleration of convergence, and we propose a simple but effective improvement to the ubiquitously used Ng-acceleration scheme. Next, we present the radiative transfer library, Magritte: a formal solver with a ray-tracer that can handle structured and unstructured meshes as well as smoothed-particle data. To mitigate the computational cost, it is optimised to efficiently utilise multi-node and multi-core parallelism as well as GPU offloading. Furthermore, we demonstrate a heuristic algorithm that can reduce typical input models for radiative transfer by an order of magnitude, without significant loss of accuracy. This strongly suggests the existence of more efficient representations for radiative transfer models. To investigate this, we present a probabilistic numerical method for radiative transfer that naturally allows for uncertainty quantification, providing us with a mathematical framework to study the trade-off between computational speed and accuracy. Although we cannot yet construct optimal representations for radiative transfer problems, we point out several ways in which this method can lead to more rigorous optimisation