30 research outputs found

    Analyse des méthodes par éléments finis et méthodes sans maillage pour la déformation de corps mous en simulation chirurgicale

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    RÉSUMÉ Ce projet de recherche s’intĂ©resse au problĂšme de la simulation chirurgicale qui constitue un des grands dĂ©fis du domaine de l’animation en temps rĂ©el de corps virtuellement dĂ©formables. Le processus de simulation doit reprĂ©senter le comportement d’un organe dĂ©formable qui rĂ©agit aux manipulations de l’utilisateur et de son outil haptique, et ce en temps rĂ©el. La modĂ©lisation repose sur la rĂ©solution d’un systĂšme d’équations aux dĂ©rivĂ©es partielles complexe pour lequel la mĂ©thode des Ă©lĂ©ments finis est gĂ©nĂ©ralement favorisĂ©e. Cependant, cette mĂ©thode nĂ©cessite une discrĂ©tisation du modĂšle dĂ©formable en une suite d’élĂ©ments gĂ©omĂ©triques connectĂ©s entre eux, un processus fastidieux et mal adaptĂ© pour des simulations qui nĂ©cessitent des dĂ©coupes ou autres manipulations entrainant un changement de la topologie initiale de l’objet simulĂ©. Ce travail cherche Ă  confirmer l’hypothĂšse que des mĂ©thodes de discrĂ©tisation basĂ©es sur des particules, et donc sans maillage d’élĂ©ments, sont suffisamment rapides, prĂ©cises et stables pour pallier le problĂšme de l’approche traditionnelle des Ă©lĂ©ments finis. Pour y arriver, deux mĂ©thodes de discrĂ©tisation sans maillage sont construites. Les deux utilisent une formulation faible des Ă©quations d’équilibre de la thĂ©orie de l’élasticitĂ© linĂ©aire en mĂ©canique des milieux continus. Le premier modĂšle, la mĂ©thode basĂ©e sur les points (MBP), utilise une approximation du dĂ©placement d’une particule basĂ©e sur un voisinage compact bĂąti autour de celle-ci Ă  l’aide d’une fonction noyau. Pour intĂ©grer l’équation d’équilibre sur le domaine non dĂ©formĂ©, le modĂšle utilise le volume d’une particule dĂ©crit comme le rapport entre sa masse et la densitĂ© de son voisinage. Deux fonctions d’approximation du dĂ©placement sont formulĂ©es : la fonction de forme “Smooth Particle Hydrodynamics” (SPH) et la fonction de forme “Moving least square” (MLS). Le deuxiĂšme modĂšle est basĂ© sur la mĂ©thode Meshless Total Lagrangian Dymamics (MTLED) qui utilise Ă©galement une approximation du dĂ©placement d’une particule basĂ©e sur un voisinage compact, mais cette fois en utilisant un maillage d’élĂ©ments pour l’intĂ©gration de l’équation d’équilibre sur le domaine non dĂ©formĂ©. Un algorithme intĂ©grant ces deux modĂšles est proposĂ©. Pour valider l’approche sans maillage, un modĂšle de rĂ©fĂ©rence basĂ© sur la mĂ©thode des Ă©lĂ©ments finis avec des Ă©lĂ©ments tĂ©traĂ©driques et hexaĂ©driques linĂ©aires est dĂ©crit et Ă©galement implĂ©mentĂ©. La performance des mĂ©thodes sans maillage et de la mĂ©thode des Ă©lĂ©ments finis est finalement comparĂ©e. La comparaison est effectuĂ©e sur diffĂ©rents scĂ©narios d’étirement et de flĂ©chissement. Une analyse de la rĂ©solution statique du systĂšme d’équilibre et de la matrice de rigiditĂ© est Ă©galement abordĂ©e. Les techniques d’intĂ©gration dans le temps et de gestion des forces de contact sont aussi testĂ©es. Les rĂ©sultats obtenus amĂšnent Ă  l’invalidation de l’hypothĂšse de dĂ©part. Pour arriver Ă  atteindre du temps rĂ©el, seules les mĂ©thodes d’intĂ©gration explicites dans le temps peuvent ĂȘtre utilisĂ©es sur des objets de taille considĂ©rable, c’est-Ă -dire comportant quelques milliers de particules. D’ailleurs, mĂȘme avec une mĂ©thode d’intĂ©gration explicite dans le temps, un nombre trĂšs restreint de voisins est nĂ©cessaire, entrainant ainsi une mauvaise propagation des forces. De plus, si le nombre de particules du volume est diminuĂ© en augmentant la taille du voisinage pour ainsi accĂ©lĂ©rer le temps de calcul, la faible consistance des fonctions d’approximation apporte de graves consĂ©quences sur la prĂ©cision et la stabilitĂ© de l’animation. Pour ces raisons, l’utilisation des deux approches sans maillage Ă©tudiĂ©es lors d’une modĂ©lisation complĂšte du comportement d’un organe dans une simulation en temps rĂ©el n’apporte aucun gain par rapport Ă  la mĂ©thode des Ă©lĂ©ments finis.----------ABSTRACT Virtual reality applications and computer simulations are currently undergoing exponential growth. This project focus on the field of surgery simulation which relies on computer animations concepts and complex physical models in order to realistically animate the behaviour of deformable soft tissues and organs under the manipulations of a haptic device driven by the user. The modelization involves a system of partial differential equations for which the finite element methods (FEM) are well adapted and have been used over the past three decades. Yet, those methods rely on a huge discretization process that breaks the simulated object into a group of geometrical elements connected together within a topology. Avoiding the discretization process would result in a major breakthrough for real time surgical simulation. This research suggests that particle-based discretization methods, also referred to as meshless methods, currently used in other simulation applications are adequately fast, precise and stable to meet the surgery simulation constraints. To sustain this hypothesis, the study and implementation of two meshless discretization models built around the weak form of elasticity equilibrium of the theory of continuum mechanics are performed. The first model, the point-based animation method (MBP), uses an approximation function of a displacement based on a compact neighborhood of particles built from a kernel function. To integrate the weak form of the equilibrium equations formulated within a lagrangian description, the model uses the volume of a particle as the ratio between its mass and the density of its neighborhood. Two approximation functions of the displacement are studied: the Smooth Particle Hydrodynamics (SPH) and the Moving Least Squares (MLS). The second meshless model is based on the Meshless Total Lagrangian Explicit Dynamics (MTLED) method and also uses an MLS approximation function, but takes advantage of a background integration grid to integrate the weak form of the equilibrium equations. To validate the meshless approaches, the implementation of a reference solution based on a finite element method using linear tetrahedral and hexahedral elements is carried out. The finite element and the two meshless models are tested on different stretching and bending behaviours. An analysis of the static case of equilibrium system and thereby the stiffness matrix is performed. Likewise, time integration schemes and contact penalty forces are tested. The results of the trials invalidate the research’s hypothesis. In real time simulations, only the explicit time integration scheme was able to produce fast enough results on simulations involving large objects, that is, with more than a few thousands particles. Those particles were restrained to a low number of neighbours, causing a weak propagation of forces through the objects. Furthermore, because of the low consistency order of the approximations, decreasing the number of particles by extending the neighborhood in order to reduce computation delays will result in severe instabilities inducing in most cases the end of the simulation process. For these reasons, the conclusion is that the two particle based methods presented in this research bring no valuable gains over the finite elements method in the field of real-time simulation of soft tissues deformation required by surgical simulators

    Numerical modelling of additive manufacturing process for stainless steel tension testing samples

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    Nowadays additive manufacturing (AM) technologies including 3D printing grow rapidly and they are expected to replace conventional subtractive manufacturing technologies to some extents. During a selective laser melting (SLM) process as one of popular AM technologies for metals, large amount of heats is required to melt metal powders, and this leads to distortions and/or shrinkages of additively manufactured parts. It is useful to predict the 3D printed parts to control unwanted distortions and shrinkages before their 3D printing. This study develops a two-phase numerical modelling and simulation process of AM process for 17-4PH stainless steel and it considers the importance of post-processing and the need for calibration to achieve a high-quality printing at the end. By using this proposed AM modelling and simulation process, optimal process parameters, material properties, and topology can be obtained to ensure a part 3D printed successfully
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