Methods of component mode synthesis, such as Craig and Bampton reduction, are known to generally yield more accurate results in deformable multibody dynamics. The main shortcoming of those methods is that they are intuitively based. Recently Nikravesh developed a reduction method called mode condensation which is derived from the equations of motion and yields the same results as Craig and Bampton reduction. In this dissertation, it is proven that these two methods span the same column space; therefore, they should yield identical results. We propose that mode condensation provides an analytical justification for Craig and Bampton reduction. Test results suggest that Craig and Bampton reduction and mode condensation are appropriate for a broader range of applications because their column space matches up well with the conditions under which the deformable body is restrained. Although Guyan reduction preserves exact solutions for static problems, its applications shall be limited to low frequency excitation because of raised eigen-frequencies. Modal truncation is not recommended for use in multibody dynamic settings because it lacks the ability to receive forces and displacements at the moving boundary. Another issue addressed in this dissertation is the misconception that if mean axes are adopted as the moving reference frame, only free-free modes should be used for model reduction. It was not clear how a restrained deformable body with mean axes can be condensed properly. We have shown that the conventional (nodal-fixed) mode shapes can be used with mean axes as long as the transformation matrix has full rank and contains complete rigid-body mode shapes.

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One of the common research goals in disciplines such as computer graphics and robotics is to understand the subtleties of human motion and develop tools for recreating natural and meaningful motion. Physical simulation of virtual human characters is a promising approach since it provides a testbed for developing and testing control strategies required to execute various human behaviors. Designing generic control algorithms for simulating a wide range of human activities, which can robustly adapt to varying physical environments, has remained a primary challenge. This dissertation introduces methods for generic and robust control of virtual characters in an interactive physical environment. Our approach is to use the information of the physical contacts between the character and her environment in the control design. We leverage high-level knowledge of the kinematics goals and the interaction with the surroundings to develop active control strategies that robustly adapt to variations in the physical scene. For synthesizing intentional motion requiring long-term planning, we exploit properties of the physical model for creating efficient and robust controllers in an interactive framework. The control design leverages the reference motion capture data and the contact information with the environment for interactive long-term planning. Finally, we propose a compact soft contact model for handling contacts for rigid body virtual characters. This model aims at improving the robustness of existing control methods without adding any complexity to the control design and opens up possibilities for new control algorithms to synthesize agile human motion.

Dans le cadre du procédé de revêtement de surface Cold Spray, un modèle numérique d’impact de particule sur substrat à haute vitesse est créé, ainsi qu’une nouvelle interaction adhésive, dans le logiciel de dynamique explicite du CEA Europlexus. Le modèle utilise des Éléments Finis et la méthode sans maillage SPH (Smoothed Particle Hydrodynamics) avec la loi matériau de Johnson-Cook, couramment utilisée pour modéliser les métaux à des vitesses de déformation élevées et prenant en compte le durcissement plastique, le durcissement en vitesse de déformation, et l’assouplissement thermique. L’interaction adhésive est basée sur les modèles de zone cohésive de Dugdale-Barenblatt et Griffith, avec une limite sur la contrainte cohésive et la rupture de l’adhésion dictée par l’énergie dissipée. L’étude de cette interaction dans le cas des corps déformables à haute vitesse de déformation montre que le type de modèle cohésif utilisé impacte directement et de façon très prononcée les résultats du calcul. L’interaction adhésive est ensuite liée à un mécanisme physique connu pour être la raison majeure de l’adhésion entre métaux lors du procédé Cold Spray : l’instabilité en cisaillement à l’interface de contact (présente dans la simulation grâce à une loi d’endommagement). Pour ce faire, un critère d’activation de l’adhésion est créé, basé sur une chute de la valeur locale de limite élastique du matériau. Ce critère permet de retrouver le phénomène de vitesse critique nécessaire pour l’adhésion de la particule lors du procédé. Un critère de rupture de l’adhésion supplémentaire est ajouté, basé sur la valeur de l’endommagement dans les éléments collés, et permet de retrouver le phénomène de vitesse maximale pour l’adhésion de la particule. Le modèle complet, construit sur des principes physiques, est ainsi capable de simuler le phénomène d’adhésion Cold Spray. Des tests de dureté et images EBSD sont aussi présentés et comparés aux résultats numériques. / In the context of the Cold Spray process, a numerical model of a single particle impact is developed. The point of interest is the adhesion of the particle to the substrate, thus an adhesive interaction model is also created. The impact model uses the Smooth Particle Hydrodynamics and/or the Finite Elements methods, with a Johnson-Cook material law, commonly used for metals at high strain rates, which takes into account strain hardening, strain rate hardening and thermal softening. The adhesive interaction is a Griffith and Dugdale-Barenblatt cohesive model with energy dissipation and a limit on the cohesive stress. Using this model it is shown that in the case of fast dynamics and deformable bodies, not only the adhesion parameters but also the type of model has an influence on the results. The adhesion model is also, contrary to previous works, linked with an actual physical mechanism known to induce adhesion in Cold Spray: a shear stress instability at the interface. This is done by adding an activation criterion to the cohesive model. This criterion is defined as a local drop in yield strength on either element in contact. Only when this criterion is locally met are the cohesive stresses applied and cohesive energy dissipated. The result is the apparition of a critical velocity, under which adhesion cannot occur due to either not enough initial kinetic energy to create an instability at the interface, or not enough adhesive surface created to keep the particle from rebounding. For the model to localize and undergo shear banding/shear instability, a damage value is added to the material law. An erosion criterion is then implemented in the cohesive model to remove the cohesive stresses from highly damaged parts of the adhesive surface. This results at high impact speeds in a maximal velocity above which the interfacial material is too damaged to sustain adhesion and prevent the particle from rebounding. A deposition behavior similar to the Cold Spray process is then observed, with a range of low velocities without any adhesion of the particle, then a critical speed initiating a velocity range of adhesion of the particle, and finally a maximum speed above which the interface is too damaged to sustain the adhesion. A set of experimental observations is also carried out to better understand the actual microstructural dynamics and changes at the interface of 1 mm copper particles impacted on copper. The results are compared to simulations and the use of the macroscopic Johnson-Cook law at a microscopic level is validated.