The tangential contact stiffness for ground Ti-6Al-4V surfaces is measured to linearly decrease with the application of tangential load. At the beginning of the application of tangential load, for ground surfaces, the ratio of the tangential contact stiffness to the normal contact stiffness is seen to be approximately half the Mindlin ratio. This is consistent with many other published experimental studies. Measurements of normal contact stiffness for ground surfaces conform to a model that posits a linear relationship between normal contact stiffness and normal load. An equivalent surface roughness parameter is defined for two surfaces in contact; and the normal contact stiffness for ground surfaces is observed to be inversely proportional to this parameter. Single asperity models were constructed to simulate the effect of different frictional laws and plasticity on the tangential displacement of an asperity contact. Further, multi-asperity modelling showed the effect of different normal load distributions on the tangential behaviour of interfaces. In addition, normal contact stiffness was modelled for a grid of asperities taking into account asperity interactions. A receding contact problem for which the required form of the distributed dislocations is bounded-bounded was solved. Then, a fundamental 2D frictional receding contact problem involving a homogeneous linear elastic infinite layer pressed by a line load onto a half-plane of the same material was analysed. This was done by the insertion of preformed distributed dislocations (or eigenstrains), which take into account the correct form of the separation of the interface at points away from the area of loading, along with corrective bounded-bounded distributions. The general method of solution was further refined and adapted to solve three other receding contact problems. The solutions demonstrated the robustness and applicability of this new procedure.

Dans un contact pneu/chaussée, le bruit de roulement résulte de l’interaction mécanique entre les aspérités de la chaussée et les pains de la bande de roulement. À l’issue de cette interaction, des forces compressives apparaissent pour repousser les deux corps en contact. Ces forces conduisent à la vibration du pneumatique. Ces vibrations sont à l’origine du bruit rayonné. Le travail de cette thèse s’inscrit dans le cadre de l’évaluation du bruit de roulement. L’objectif est double. Premièrement, il s’agit de comprendre les mécanismes à l’œuvre dans un processus de roulement de deux surfaces rugueuses qui engendrent une vibration puis du bruit. Deuxièmement, on cherche à mettre en évidence l’influence des aspérités de la chaussée sur les forces dynamiques interfaciales et sur le bruit généré. Dans ce contexte, on propose un nouveau modèle 3D de contact dynamique basé sur la décomposition modale de la réponse du pneumatique. Cette nouvelle approche permet de réduire considérablement le temps CPU. Le pneumatique est modélisé par une plaque orthotrope sur fondation élastique. Le problème de contact est résolu par la méthode de pénalité. On a validé ce modèle analytiquement. Cet outil permet de prédire finement ce qui se passe dans la zone de contact. Nous pouvons prédire les forces de contact et les vitesses vibratoires. En outre, il permet de déterminer l’aire de contact et les cartes de pression. À l’échelle locale, les caractéristiques d’un choc sont connues. On est capable de déterminer la force maximale du choc, à partir de l’évolution temporelle de la force de contact, et sa durée mais aussi le pourcentage de temps du choc. / In a tire road contact, the rolling noise results from the mechanical interaction between the asperities of the roadway and the tread pattern. Following this interaction, compressive forces appear to push the two bodies in contact. These forces lead to the vibration of the tyre. These vibrations are the origin of the radiated noise. The work of this thesis falls within the evaluation of rolling noise. The objective is twofold. First, we seek to understanding the mechanisms involved in a rolling process of two rough surfaces that generate vibration and then noise. Second, we aim to show the influence of the road asperities on the interfacial dynamic forces and on the noise generated. In this context, we propose a new 3D model of the dynamic contact based on a modal decomposition of the tyre response. This new approach significantly reduces CPU time. The tyre is modeled by an orthotropic plate on a elastic foundation. The contact problem is solved by the penalty method. This model was validated analytically. This tool allows us to finely predict what happens in the contact area. We can predict contact forces and vibratory velocities. Moreover, it makes it possible to determine the contact area and the pressure maps. At the local scale, the characteristics of a shock are known. We are able not only to determine the maximum force of impact, using time evolution of the contact force, and its duration but also the percentage of shock time.

La simulation de la dynamique des systèmes multicorps avec contact frottant joue un rôle important dans un grand nombre d'applications industrielles.Elle est même devenue une partie importante du développement de nouveaux produits, de la vérification et même de l'optimisation de leur conception pour améliorer les anciens produits.Les travaux présentés dans cette thèse font partie d'une collaboration entre l'équipe BiPoP, équipe de recherche de l'INRIA Grenoble, et Schneider Electric.Le but principal de ces travaux est de comprendre l'influence du jeu dans les articulations, ainsi que l'influence du dimensionnement industriel et les tolérances géométriques sur lecomportement global des liaisons mécaniques. Plus spécifiquement nous avons étudié le mini-disjoncteur C-60 (domaine dans lequel la sécurité humaine doit être garantie), pour répondre à cette demande de robustesse, tout en respectant les tolérances sur les pièces constituant le disjoncteur C-60.Le jeu radial dans les articulations pivot est une source de variabilité dans les conditions initiales du système, mais également dans la dégradation de ses performances.La dégradation du système se présente toujours sous forme de vibrations, de bruit, de forces de réactions très grandes dans les articulations, de mauvaise précision et exactitude de la sortie.Le but est d'étudier l'influence des conditions initiales et le déplacement hors-plan, ainsi que l'effet de polarisation en trois dimensions.Un objectif supplémentaire est de développer un banc d'essai virtuel efficace pour reproduire les mesures obtenues sur un vrai banc d'essai en laboratoire, en utilisant la plateforme logicielle SICONOS qui utilise la méthode NSCD (Non Smooth Contact Dynamic) introduite par J.J. Moreau et M. Jean.Le schéma NSCD a prouvé son efficacité numérique: il est capable de traiter des problèmes de complémentarité, le contact ainsi que les impacts et les lois de frottement multivaluées.Le but est de comprendre quelle est la meilleure description géométrique pour simuler de très petits jeux.L'étude complète est divisée en deux parties. La progression part du cas planaire pour arriver au cas spatial, et la complexité suit le même chemin.Dans le cas planaire, on analyse un mécanisme à quatre barres avec du jeu quand une des articulations est commandée en boucle ouverte, ou par retour d'état linéaire ou non-linéaire(PD, linéarisation par retour d'état, ou commande passive).L'accent est mis sur la quantification de la dégradation des performances quand du jeu est ajouté dans les articulations. On montre alors que les commandes par retour d'état se comportent de façon robuste.Dans le cas spatial, le mécanisme C-60 est analysé précisément pour explorer les possibilités de relaxer les tolérances industrielles sur les pièces sans compromettre ni les performances ni la sécurité. L'influence de l'entrée, du modèle et des incertitudes numériques sur le modèle C-60 est étudiée.L'influence induite par le jeu et le coefficient de frottement dans les articulations sur la performance du produit est étudiée.Pour valider le modèle de simulation, des expériences sont effectuées sur des prototypes d'essai et les résultats sont comparés avec les simulations numériques.Nous avons trouvé une bonne correlation entre les résultats numériques et expérimentaux.L'analyse statistique~(analyse du pire cas, et par des simulations basées sur la méthode de Monte-Carlo) a été réalisée pour trouver la dispersion des conditions fonctionnelles.En plus des variations dimensionnelles, la tolérence aux variations géométriques comme la forme, l'orientation et la position, est analysée.Ce travail de recherche devrait aider les concepteurs à simuler le comportement du système mécanique avec une articulation de révolution imparfaite,depuis l'étape de conception préliminaire jusqu'à la fin de la conception pour avoir une amélioration significative de la planification et du budget. / Dynamic simulation of multibody systems with unilateral contact and friction plays an important role in a wide range of industrial applications. It has become an integral part of new product development, verification/optimization of the design and to enhance the old products.This work is a part of collaboration between the BiPoP research team of INRIA Grenoble and the Schneider Electric company.The main goal of this thesis is to understand the influence of clearances in the revolute joints on the overall behaviour of the linkage mechanisms and specifically on the C-60 miniature circuit breaker where human safety must be guaranteed.In other words, the objective is to address the robustness of the C-60 breaker with respect to the production tolerances, which areexpressed in the form of dimensional and geometrical variations on the parts. These variations are the source of clearance in the joints of the mechanism.The radial clearance in the revolute joints is a source of variability in the initial conditions of the system and also the degradation of the system's performance. The degradation of the system isalways in the form of vibration, noise, very high reaction forces at the joints.The aim is to study the influence of initial conditions and the out-of-plane motion, so the polarization effect in three dimensional case.Another objective is to develop the time efficient virtual test bench to reproduce the measurements of real test bench in the laboratory using the open-source simulation software SICONOS which is based on the NonSmooth Contact Dynamic method (NSCD) introduced by J.J. Moreau and M. Jean.The NSCD scheme is proven to be a quite efficient numerical method, capable of handling complementarity conditions, as well as impacts and set-valued friction laws.The goal is to understand what is the most appropriate geometricdescription which allows to simulate very small clearances.The complete study is divided in two main sections.The progress through these partsgoes from the planar to the spatial case, the complexity follows the same advance.In the planar case, a four-bar mechanism with joint clearance, when one joint is actuated by collocated open-loop or state feedback controllers (PD, statefeedback linearization, passivity-based) is analysed. The focus is put on how much the performancedeteriorates when clearances are added in the joints. It is shown that collocated feedback controllersbehave in a robust way.In the spatial case, the C-60 mechanism is analysed precisely to explore the possibilities to relax the manufacturing tolerances on the parts withoutany compromise on either performance or the human safelyThe influence of the input, model and numerical uncertainties on the C-60 model is studied. The joint-wise influences of the clearance and coefficient of friction on theproduct performance are studied.To validate the simulation model, experiments are carried-out on the prototype samples and the results are compared with the simulations.We found quite good correlation between the virtual and experimental results.A statistical analysis~(worst-case and Monte Carlo simulation) has been carried out to find out the dispersion of the functional conditions.In addition to dimensional variations, the geometrical variations such as form, orientation and position tolerances are also analyzed.This research work shall help the designers to simulate the real time behaviour of the mechanical systems with the imperfect revolutejoint from the pre-design stage till the end of the design, to have good improvement on schedule and budget.

In 2005, Park et al. demonstrated that the 2-fold surface of a d-AlNiCo quasicrystal exhibits an 8-fold frictional anisotropy, as measured by atomic-force microscopy, between the periodic and aperiodic directions [40, 41]. It has been well known that quasicrystals exhibit lower friction than their crystalline counterparts [38, 18, 51, 30, 12, 54]; however, the discovery of the frictional anisotropy allows for a unique opportunity to study the effect of periodicity on friction when chemical composition, oxidation, and wear are no longer variables. The work presented herein is focused on obtaining an understanding of the mechanisms of friction and the dependence of friction on the periodicity of a structure at the atomic level, focusing on the d-AlNiCo quasicrystal studied by Park et al. Using the LAMMPS [44] package to simulate the compression and sliding of an 'adamant' tip, see section 3.3, on a d-AlNiCo quasicrystalline approximant substrate, we have demonstrated, in preliminary results, an 8-fold frictional anisotropy, but in more careful studies the anisotropy is found to be much smaller. The simulations were accomplished using Widom-Moriarty pair potentials to define the interactions between the atoms [36, 56, 55, 9]. The studies presented in this work have shown a clear velocity dependence on the measured frictional response of the quasicrystalline approximant's surface. The final results show between a 1.026-fold and 1.127-fold anisotropy between sliding in the periodic and 'aperiodic' directions, depending on the sliding velocity.

The benefits of intentional friction damping to reduce the occurrence of wear and premature failure of turbomachinery bladed-disk assemblies are well known and many studies on this topic have focused on the analysis and prediction of the complicated nonlinear forced response exhibited by these structures. In this research, extensions of the recently introduced multi-harmonic Hybrid Frequency-Time method are proposed for the efficient analysis of the response of realistic structures featuring displacement-dependent nonlinearities, such as the friction and impact phenomena that may occur in the presence of friction dampers or when two parts of the same structure periodically contact each other. These theoretical extensions are adapted to the study of large scale, industrial bladed-disk structures that may feature cyclic symmetry or mistuning. Two analysis techniques are developed for the modeling of displacement-dependent nonlinearities. In the first technique friction dampers are modeled as nonlinear operators representing the contact forces acting on the blades, from the simple case of monodirectional friction with constant normal load to the more complex case of three dimensional contact with variable normal load. The analysis of the forced response of several nonlinear systems illustrates the capabilities of this approach as well as the complexity of the typical behavior exhibited by friction damped structures. The second technique introduced helps analyze structures experiencing intermittent contact or friction between two parts or sub-components of the same assembly. This method is applied to the study of the forced response of several simple systems and is used with great efficiency to predict the nonlinear behavior of a beam with a crack. This approach also allows the dampers to be modeled realistically as stand-alone components appended to the bladed disk assembly. In this case the bladed disk assembly as well as the friction dampers are modeled as independent structures that interact at their contacting interfaces. This allows the use of detailed finite element models of dampers rather than having to make simplifying assumptions regarding their geometry. These two methods are applied to the study of the nonlinear forced response a realistic bladed-disk assembly featuring a wedge damper model and a structure-like damper model.

The main objective of this research is the development of a volumetric wheel-soil ground contact model that is suitable for mobile robotics applications with a focus on efficient simulations of planetary rover wheels operating on compliant and irregular terrains. To model the interaction between a rover wheel and soft soil for use in multibody dynamic simualtions, the terrain material is commonly represented by a soil continuum that deforms substantially when in contact with the locomotion system of the rover. Due to this extensive deformation and the large size of the contact patch, a distributed representation of the contact forces is necessary. This requires time-consuming integration processes to solve for the contact forces and moments during simulation. In this work, a novel approach is used to represent these contact reactions based on the properties of the hypervolume of penetration, which is defined by the intersection of the wheel and the terrain. This approach is based on a foundation of springs for which the normal contact force can be calculated by integrating the spring deflections over the contact patch. In the case of an elastic foundation, this integration results in a linear relationship between the normal force and the penetration volume, with the foundation stiffness as the proportionality factor. However, due to the highly nonlinear material properties of the soft terrain, a hyperelastic foundation has to be considered and the normal contact force becomes proportional to a volume with a fractional dimension --- a hypervolume. The continuous soil models commonly used in terramechanics simulations can be used in the derivation of the hypervolumetric contact forces. The result is a closed-form solution for the contact forces between a planetary rover wheel and the soft soil, where all the information provided by a distributed load is stored in the hypervolume of interpenetration. The proposed approach is applied to simulations of rigid and flexible planetary rover wheels. In both cases, the plastic behaviour of the terrain material is the main source of energy loss during the operation of planetary rovers. For the rigid wheel model, a penetration geometry is proposed to capture the nonlinear dissipative properties of the soil. The centroid of the hypervolume based on this geometry then allows for the calculation of the contact normal that defines the compaction resistance of the soil. For the flexible wheel model, the deformed state of the tire has to be determined before applying the hypervolumetric contact model. The tire deformation is represented by a distributed parameter model based on the Euler-Bernoulli beam equations. There are several geometric and soil parameters that are required to fully define the normal contact force. While the geometric parameters can be measured, the soil parameters have to be obtained experimentally. The results of a drawbar pull experiment with the Juno rover from the Canadian Space Agency were used to identify the soil parameters. These parameters were then used in a forward dynamics simulation of the rover on an irregular 3-dimensional terrain. Comparison of the simulation results with the experimental data validated the planetary rover wheel model developed in this work.

The first part of this dissertation focuses on the development, implementation and validation of models that capture the behavior of joints in a realistic manner. These models are presented within the framework of finite element based, nonlinear multibody dynamics formulations that ensure unconditional nonlinear stability of the computation for systems of arbitrary topology. The proposed approach can be divided into three parts. First, the joint configuration: this purely kinematic part deals with the description of the configuration of the joint and the evaluation of the relative distance and relative tangential velocity between the contacting bodies. Second, the contact conditions: in most cases, contact at the joint is of an intermittent nature. And finally, the contact forces: this last part deals with the evaluation of the forces that arise at the interface between contacting bodies. The advantage of the proposed approach is that the three parts of the problem can be formulated and implemented independently. Many articulated rotor helicopters use hydraulic dampers, which provide high levels of damping but are also associated with high maintenance costs and difficulties in evaluating their conditions due to the presence of seals, lubricants and numerous moving parts, all operating in a rotating frame. To avoid problems associated with hydraulic dampers, the industry is now switching to elastomeric lead-lag dampers that feature simpler mechanical design, lower part count, and result in "dry" rotors. However, the design of robust elastomeric dampers is hampered by the lack of reliable analytical tools that can predict their damping behavior in the presence of large multi-frequency motions experienced by the rotor and thus the damper. The second part of this dissertation focuses on the development of an elastomeric damper model which predicts the behavior of the elastomeric damper based on a continuum mechanics approach: the configuration of the damper is modeled using a finite element approach, and material behavior is represented by a set of nonlinear constitutive laws and material parameters. The validated finite element model of the elastomeric damper is then coupled with a comprehensive, multibody dynamics analysis code to predict the behavior of complex systems featuring elastomeric components.

Rod seals are one of the most critical components of hydraulic systems. However, the fundamental physics of seal behavior is still poorly understood and the seal designers have virtually no analytical tools with which to predict the behavior of potential seal designs. In pursuit of a comprehensive physics based seal analysis/ design tool, in this work, a multi-scale multi-physics (MSMP) seal model is developed. The model solves the transient problem involving macro-scale viscoelastic deformation mechanics, macro-scale contact, micro-scale two phase fluid mechanics in the sealing zone, micro-scale asperity contact mechanics and micro-scale deformation mechanics of the sealing edge in a strongly coupled manner. The model takes into account surface roughness, mixed lubrication, cavitation and two phase flow, transient squeeze film effects and the dynamic operation as well as the effect of macro/micro/nano scale viscoelasticity. A hybrid finite element-finite volume-statistical computational framework is developed to solve the highly coupled multi-physics interactions of the MSMP model simultaneously. Surface characterization experiments are performed to extract the parameters like RMS roughness, asperity density, autocorrelation length and asperity radius needed by MSMP. To remove the high frequency noise without removing the high frequency real surface features, a wavelet transform based adaptive surface extraction method is implemented. Dynamic mechanical analysis (DMA) is performed to extract the macro-scale viscoelastic parameters of the seal. Through atomic force microscopy (AFM) experiments, the local micro/nano scale elastic moduli were found to be varying within two orders of magnitude higher than the bulk of the polymer. Significant differences in local stiffness, adhesion and the relaxation time scales of individual surface asperities were also observed. With the MSMP model, dynamic seal performance was analyzed. The results confirmed the mixed lubrication and the effect of surface roughness. Thicker fluid films during instroke and cavitation during the outstroke were found to be important for non-leakage. Seal behavior was a function of the complex dual dependence on the time varying sealed pressure and hydrodynamic effects. Viscoelasticity is seen to critically affect the leakage and friction characteristics. It produces thicker fluid films and produces a significant increase in Poiseuille component of flow during instroke. Ignoring viscoelasticity leads to under-prediction of the time required to reach the zero leakage state. Several high pressure - high frequency sealing applications were analyzed. In such applications, a new phenomenon of "secondary contact" was observed. Viscoelastic creep was seen to critically affect the contact pressure and hence the friction characteristics. In high frequency applications, viscoelasticity induced significant differences in Poiseuille flow and friction force from cycle to cycle. Cycle frequency was seen to play an important role in governing visco-elastohydrodynamics and the leakage of such seals. The seals need to be designed by considering the relationship between relaxation time scales of the polymer and the cycle frequencies. Study also revealed the presence of characteristics like "critical temperature" and "critical frequency". Using the multi-physics modeling capability of MSMP framework, several novel seal designs using smart materials like piezo-ceramic embedded polymers are proposed and analyzed. The MSMP computational framework developed here has a great potential to be used as a stand-alone seal design and analysis software in academic and industrial research.

Nowadays, high demands are made on filling materials in modern dentistry: Durability, Reliability &Aesthetic Requirements Thus, a group of physicists and an independent practicing dentist investigated 11 different teeth fillings (composite materials) as used in modern dental practices according to their stability and ability to withstand contact loadings.

<p>In the finite element simulation of problems with contact there arises</p><p>the need to change the mesh and continue the simulation on a new mesh.</p><p>This is encountered when the mesh has to be changed because the original mesh experiences severe distortion or the mesh is adapted to minimize errors in the solution. In such instances a crucial component is the transfer of data from the old mesh to the new one. </p><p>This work proposes a strategy by which such remeshing can be accomplished in the presence of mortar-discretized contact, </p><p>focusing in particular on the remapping of contact variables which must occur to make the method robust and efficient. </p><p>By splitting the contact stress into normal and tangential components and transferring the normal component as a scalar and the tangential component by parallel transporting on the contact surface an accurate and consistent transfer scheme is obtained. Penalty and augmented Lagrangian formulations are considered. The approach is demonstrated by a number of two and three dimensional numerical examples.</p> / Dissertation