A shaped charge is an explosive device used to penetrate thick targets using a high velocity jet. A typical shaped charge contains explosive material behind a conical hollow. The hollow is lined with a compliant material, such as copper. Extremely high stresses caused by the detonation of the explosive have a focusing effect on the liner, turning it into a long, slender, stretching jet with a tip speed of up to 12km/s. A mathematical model for the penetration of this jet into a solid target is developed with the goal of accurately predicting the resulting crater depth and diameter. The model initially couples fluid dynamics in the jet with elastic-plastic solid mechanics in the target. Far away from the tip, the high aspect ratio is exploited to reduce the dimensionality of the problem by using slender body theory. In doing so, a novel system of partial differential equations for the free-boundaries between fluid, plastic and elastic regions and for the velocity potential of the jet is obtained. In order to gain intuition, the paradigm expansion-contraction of a circular cavity under applied pressure is considered. This yields the interesting possibility of residual stresses and displacements. Using these ideas, a more realistic penetration model is developed. Plastic flow of the target near the tip of the jet is considered, using a squeeze-film analogy. Models for the flow of the jet in the tip are then proposed, based on simple geometric arguments in the slender region. One particular scaling in the tip leads to the consideration of a two-dimensional paradigm model of a ``filling-flow'' impacting on an obstacle, such as a membrane or beam. Finally, metallurgical analysis and hydrocode runs are presented. Unresolved issues are discussed and suggestions for further work are presented.

The aim of this thesis is to investigate the mathematics and modelling of the industrial crimper, perhaps one of the least well understood processes that occurs in the manufacture of artificial fibre. We begin by modelling the process by which the fibre is deformed as it is forced into the industrial crimper. This we investigate by presuming the fibre to behave as an ideal elastica confined in a two dimensional channel. We consider how the arrangement of the fibre changes as more fibre is introduced, and the forces that are required to confine it. Later, we apply the same methods to a fibre confined to a three dimensional channel. After the fibre has under gone a preliminary deformation, a second process known as secondary crimp can occur. This involves the `zig-zagged' material folding over. We model this process in two ways. First as a series of rigid rods joined by elastic hinges, and then as an elastic with a highly oscillatory natural configuration compressed by thrusts at each end. We observe that both models can be expressed in a very similar manner, and both predict that a buckle can occur from a nearly straight initial condition to an arched formation. We also compare the results to experiments performed on the crimped fibre. Throughout much of the process, the configuration of the fibre does not alter. This part of the process we call the block, and model the material in this region in two ways: as a series of springs; and as an isotropic elastic material. We discuss the coupling between the different regions and the process that occurs in the block, and consider both the steady state and stability of the system.

Inaccurate dose calculation in radiotherapy can lead to errors in treatment delivery and evaluation of treatment efficacy. Respiration can cause of intra-fractional motions, leading to uncertainties in tumor targeting. These motions should therefore be included in dose calculation. The finite element method-based deformable registration platform MORFEUS is able to accurately quantify organ deformations. The dose accumulation algorithm included in MORFEUS takes organ deformation and tumor movement into account. This study has experimentally validated this dose accumulation algorithm by combining 3D gel dosimetry, respiratory motion-mimicking actuation mechanism, and finite element analysis. Results have shown that within the intrinsic measurement uncertainties of gel dosimetry, under normal conformal dose distribution conditions, more than 90% of the voxels in MORFEUS generated dose grids have met the criterion analogous to the gamma test. The average (SD) distance between selected pairs of isodose surfaces on the gel and MORFEUS dose distributions is 0.12 (0.08) cm.

Inaccurate dose calculation in radiotherapy can lead to errors in treatment delivery and evaluation of treatment efficacy. Respiration can cause of intra-fractional motions, leading to uncertainties in tumor targeting. These motions should therefore be included in dose calculation. The finite element method-based deformable registration platform MORFEUS is able to accurately quantify organ deformations. The dose accumulation algorithm included in MORFEUS takes organ deformation and tumor movement into account. This study has experimentally validated this dose accumulation algorithm by combining 3D gel dosimetry, respiratory motion-mimicking actuation mechanism, and finite element analysis. Results have shown that within the intrinsic measurement uncertainties of gel dosimetry, under normal conformal dose distribution conditions, more than 90% of the voxels in MORFEUS generated dose grids have met the criterion analogous to the gamma test. The average (SD) distance between selected pairs of isodose surfaces on the gel and MORFEUS dose distributions is 0.12 (0.08) cm.

Linear problems are possibly the kindest problems in physics and mathematics. Given sufficient information, the linear equations describing such problems are intrinsically solvable. The solution can be written as a vector having undergone a linear transformation in a vector space; extracting the solution is simply a matter of inverting the transformation. In an ideal optical system, the problem of extracting the object under investigation would be well defined, and the solution trivial to implement. However, real optical systems are all aberrated in some way, and these aberrations obfuscate the information, scrambling it and rendering it inextricable. The process of detangling the object from the aberrated system is no longer a trivial problem or even a uniquely solvable one, and represents one of the great challenges in optics today. This thesis provides a review of the theory behind optical microscopy in the presence of absent information, an architecture for the modern physical and computational methods used to solve the linear inversion problem, and three distinct application spaces of relevance. I hope you find it useful.

Computer gamers demand more realistic effects for each release of a new game. This final year project is concerned with deforming the geometry in a terrain rendering environment. The intension is to increase the resolution where the original resolution of the terrain is not enough to cater for all the details associated with a deformation, such as an explosion. An algorithm for extending the maximum available resolution was found, the DEXTER algorithm, but calculations have shown that it has a too high memory consumption to be feasible in a game environment. In this project, an algorithm has been implemented, based on the DEXTER algorithm, but with some structural changes. The algorithm which has been implemented increases the resolution, if needed, where a deformation occurs. The increased resolution is described by b-spline surfaces, whereas the original resolution is given by a height map. Further, graphics primitives are only allocated to a high resolution region, when needed by the refinement process. It has been found that by using dynamic blocks of graphics primitives, the amount of RAM consumed can be lowered, without a severe decrease in rendering speed. However, the algorithm implemented has been found to suffer from frame rate drops, if too many high resolution cells need to be attached to the refinement process during a single frame. Is has been concluded that the algorithm, which is the result of this final year project, is not suitable for a game environment, as the memory consumption is still too high. The amount of time spent on refining the terrain can also be considered too much, as no time is left for other aspects of a game environment. The algorithm is however considered a good choice concerning deformations, as the updates needed in association with a deformation, can be kept small and localized, according to the DEXTER structure. Also, the b-spline surfaces offer more freedom over the deformation, compared to using a height map.

Ces travaux de recherche sont réalisés dans le cadre d’une thèse CIFRE en collaboration entre Schlumberger et le LURPA de l’ENS Cachan. Schlumberger est une entreprise de service pétrolier. Elle développe des outils de mesures fonctionnant sous des conditions sévères de température et pression élevées mais aussi des effets dynamiques tels que des accélérations produisant des chocs entre les différentes pièces.L’objectif de la thèse est de déployer de nouvelles règles de cotation, pour des assemblages hyperstatiques déformables, basées sur la méthode CLIC et les normes ISO. La déformation des pièces dépend considérablement des défauts géométriques. Nous avons donc couplé des modèles de chaînes de cotes 3D avec des modèles RdM de type poutre afin d’optimiser les tolérances. Ces modèles doivent permettre la prise en compte des jeux d’assemblage dans les liaisons, la rigidité des pièces et les différents types de contact entre les sous-ensembles des outils étudiés.Ces modèles multi-physiques ont permis de caractériser le comportement mécanique en fonction des écarts géométriques des pièces. Enfin, pour des études plus complexes, des modélisations et simulations éléments finis, sur Abaqus, ont été réalisés puis validées par une campagne expérimentale de comportement au choc. / This research is carried out within a CIFRE doctoral thesis in collaboration between Schlumberger and the LURPA of ENS Cachan. Schlumberger is an oil service company. It develops measurement tools operating under severe conditions of high temperature and pressure but also dynamic effects such as accelerations producing shocks between the different parts.The objective of the thesis is to deploy new dimensioning and tolerancing rules for deformable hyperstatic assemblies, based on the CLIC method and the ISO standards. The deformation of the parts greatly depends on the geometrical defects. We have coupled 3D dimension chains with beam models to optimize tolerances. These models must allow the taking into account of the assembly clearances between parts, their rigidity and the different types of contact between the subassemblies of the studied tools.These multi-physical models allowed to characterize the mechanical behavior as a function of the geometrical deviations of parts. Finally, for more complex studies, finite element models and simulations on Abaqus were carried out and then validated by an experimental campaign of impact behavior.

This thesis is concerned with model-based non-rigid registration of single-modality magnetic resonance images of compressed and uncompressed breast tissue in breast cancer diagnostic/interventional imaging. First, a volumetric registration algorithm is developed which solves the registration as a state estimation problem. Using a static deformation model. To reduce computations, the similarity measure is calculated at some specific points called control points. These control points can be from a low resolution image grid or any irregular image grid. Our numerical analysis has shown that control points placed in the area without much information; i.e with small or no changes in image intensity, yield negligible deformation. Therefore, the selection of the control points can significantly impact the accuracy and computation complexity of the registration algorithms. An extension of the speeded up robust features (SURF) to 3D is proposed for enhanced selection of the control points in deformable image registration. The impact of this new control point selection method on the performance of the registration algorithm is analyzed by comparing it to the case where regular grid control points are used. The results show that the number of control points could be reduced by a factor of ten with new selection methodology without sacrificing performance. Second image registration method is proposed in which, based on a segmented pre-operative image, a deformation model of the breast tissue is developed and discretized in the spatial domain using the method of finite elements. The compression of the preoperative image is modeled by applying smooth forces on the surface of the breast where compression plates are placed. Image registration is accomplished by formulating and solving an optimization problem. The cost function is a similarity measure between the deformed preoperative image and intra-operative image computed at some control point and the decision variables are the tissue interaction forces. / Thesis / Master of Applied Science (MASc)

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