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Viscoelastic granular materials are present in several disciplines. One example is asphalt mixture employed in road construction. In the last three decades, discrete element modeling has been positioned as a valid tool for the analysis of this multiphase material at the grain-scale. All this despite the simplification of the shape of the particles used in these studies. In this work, it is proposed a simplified procedure for the generation of viscoelastic granular samples composed of irregular polyhedra. The numerical aggregates were generated by a Poisson-Voronoi tessellation based on the particle size distribution (PSD) and statistic data of aggregates, without using complex imaging technics. This procedure set the porosity of the packing, while controlling the PSD. Using this procedure implies a significant computational-time reduction by skipping several preparation stages for polyhedral samples, such as deposition by gravity and compaction. This approach can be used for the study granular materials as inclusion in a solid matrix as concrete or asphalt mixtures, particle breaking, and fatigue damage of viscoelastic materials.

International audience; Size limitations of geotechnical testing equipment often require that samples of coarse granular materials have to be scaled in order to be tested in the laboratory. Scaling implies a convenient modification of the particle size distribution (PSD) to reduce particle sizes. However, it is well known that particle size and shape may be correlated in nature, due to geological factors (as an example). By means of two-dimensional contact dynamics simulations, we analyzed the effect of altering the size span on the shear strength of granular materials when particle size and shape are correlated. Two different systems were considered: one made of only circular particles, and the second made of size-shape correlated particles. By varying systematically the size span we observed that the resulting alteration of material strength is not due to the change in particle sizes. It results instead from the variation of the particle shapes induced by the modification of the PSD, when particle size and particle shape are correlated. This finding suggests that particle shape distribution is a higher order factor than PSD for the shear strength of granular materials. It also highlights the importance of particle shape quantification in soil classification and the case for its consideration in activities such as sampling, subsampling, and scaling of coarse materials for geotechnical testing

International audience; A very staggering result that has been constantly highlighted in granular media is that the shear strength of granular assemblies is independent of the particle size dispersity. In other words, a packing composed of monodisperse particles has similar strength properties to those of polydisperse systems. This has been shown numerically for the simplified case of disc and polygon assemblies in 2D and spheres in 3D. In this paper, we use three-dimensional contact dynamics simulations to revisit these results for the more complex case of assemblies composed of highly polydisperse rigid polyhedra. Although non-spherical shapes induce more intricated spatial correlations than spherical shapes because of the multiple contact types (i.e., vertex-face, edge-edge, edge-face, face-face), our numerical data provide evidence that the shear strength independence as the particle size dispersity increases still holds up for assemblies of polyhedra. We explain this finding from compensation mechanisms at the micro-scale between geometrical and mechanical anisotropies developed within the assemblies.

International audience; Over the last decades, simulations by discrete elements methods (DEM) have proven to be a reliable analysis tool in various domains of science and engineering. By providing access to the local physical mechanisms, DEM allows the exploration of microscopic based phenomena related to particles properties and interactions in various conditions and to revisit constitutive equations consequently. The growing computer power and memory now allow us to handle large collections of grains of various shapes and sizes by DEM simulations and in particular, it offers new perspectives in the exploration of the behavior of asteroids seen as self-gravitating and cohesive granular aggregates. In this paper we describe the Contact Dynamics (CD) method, a class of DEM based on non-smooth mechanics, and its implementation in the open-source software LMGC90. In contrast to more classical approach, Hard-and Soft-Sphere DEM, the CD method is based on an implicit time integration of the equations of motion and on a non-regularized formulation of mutual exclusion between particles. This numerical strategy is particularly relevant to the study of dense granular assemblies (even of large size) because it does not introduce numerical artefacts due to contact stiffness. So that it can be used for Small Body research, we implement a parallelised kd-tree and monitor the performance of the code as it simulates a number of granular systems. We provide examples of the simulation of the accretion of self-gravitating aggregates as well as their rotational disruption. We use the routines at our disposal in the code to monitor their behaviour through the entire evolution and find agreement with previous research.

International audience; Soft particle materials such as some pharmaceutical and food products are composed of particles that can undergo large deformations under low confining pressures without rupture. The rheological and textural properties of these materials are thus governed by both particle rearrangements and particle shape changes. For the simulation of soft particle materials, we present a numerical technique based on the material point method, allowing for large elasto-plastic particle deformations. Coupling the latter with the contact dynamics method makes it possible to deal with contact interactions between particles. We investigate the compaction of assemblies of elastic and plastic particles. For plastic deformations, it is observed that the applied stress needed to achieve high packing fraction is lower when plastic hardening is small. Moreover, predictive models, relating stress and packing fraction, are proposed for the compaction of elastic and plastic particles. These models fit well our simulation results. Furthermore, it is found that the evolution of the coordination number follows a power law as a function of the packing fraction beyond jamming point of hard particle packings.

We develop the equations obeyed by contacts forces in Contact Dynamics algorithm and consider their resolution in two simple cases of cohesive grains, namely two-body and three-body cohesive collisions. We show how equations predict that increasing the time step increases the effective cohesion of the systems. Numerical simulations are performed to verify the predictions, in the case of cohesive granular piles falling in the gravity field, and in the case of a simplified Newton's cradle; predictions are confirmed. We thereby present the details of Contact Dynamics equations in a nutshell, and speculate over the definition of a dimensionless "cohesive time" that would merge considerations over the cohesive properties of the simulations and considerations over their precision.

This paper is devoted to the investigation of the density sorting of grains using water jigging. Experiments achieved in a laboratory scale water jig for two initial binary bed configurations are studied and compared to numerical results. The vertical composition of the deposit is estimated after different number of water pulses to represent the sorting evolution in time. Simulations are based on a multiscale model in which the fluid is solved at a larger scale than the grain diameter using the finite element method, while the grains are considered as rigid bodies and solved using the nonsmooth contact dynamics. Key parameters are numerically varied and observed to determine the sensitivity of the process.

International audience; The interaction of beam-like structures against surfaces is a challenging problem with applications in engineering (wheel-rail contact, pipeline-soil interaction, ropes sliding on the seabed) and in medical applications such as surgical planning and training (catheter navigation, aneurysm coiling, stent deployment). This contact problem is traditionally solved using Total Lagrangian beam formulations, which interact against Lagrangian triangulated surfaces. Overall, the computational speed is affected, due to the nonlinearities of the beam formulation and, as well as due to the expensive search algorithms, required to find the close point projection. In the search towards an efficient beam to surface contact algorithm, this paper explores the combined use of 1) a corotational beam formulation, where the motion of the beam element is decomposed in rigid body and pure deformational parts and 2) an implicit description of the surface by means of discrete signed distance fields (SDF), which can be seen as a Lagrangian beam immersed within an Eulerian (rigid) solid. To do so, a previously reported implicit corotational formulation for beam dynamics is modified to account for frictional contact, by means of a penalty term. The new contributions are fully linearized to update the tangent operator and the system is integrated in time by means of the HHT-α method. Overall, a consistent implicit contact dynamics formulation is provided. A SDF, defined in a voxel-type grid, is used to represent implicitly the surface geometry. The SDF values and derivatives are computed at the Lagrangian point of integration of the beam by means of an efficient tensor product of compact, high order, 1D Kernels, as widely used in immersed Fluid-Structure Interaction techniques. A wide variety of validation tests are presented which prove the accuracy and robustness of the proposed algorithm.

International audience; The Optimal Recycling of Reclaimed Asphalts in low-traffic Pavements (ORRAP) project concerns a cold recycling of 100% Reclaimed Asphalt Pavement (RAP) without binder addition, in base and subbase layers of low-traffic pavements. The mastic coating of aggregates induces a viscoelastic behaviour and changes the resilient modulus with frequency and temperature. This modulus is obtained with repeated load triaxial tests and is a key element for pavement design. In this context, this paper presents a numerical alternative to predict this influence with a discrete approach. Contact Dynamics (CD) simulations are used to reproduce the resilient modulus test on a set of rigid spherical particles with a viscoelastic contact, based on the Burgers’ model. The tests were carried out with cylindrical samples at several frequencies for two temperatures (20 °C and 40 °C). The proposed model is calibrated in a given range of temperatures and frequencies regarding the experimental data, and then used to predict resilient modulus values at unreachable frequencies in the laboratory, with one set of parameters for each temperature. Finally, using the Williams-Landel-Ferry (WLF) equation, a master curve of resilient modulus at 20 °C as a function of the frequency was established. The Time-Temperature Superposition Principle (TTSP) reveals that the values at high frequencies and 40 °C correspond to the data at low frequencies and 20 °C.

International audience; Cohesion forces strongly alter the flow properties of a granular material. To investigate this influence, we focus on a simple configuration: the collapse of a cohesive granular column. To do so, we adopt a numerical approach and implement a peculiar rheology in a Navier-Stokes solver (Basilisk) : the so-called µ(I)-rheology, usually used for dry granular materials, supplemented by a yield stress for cohesion. With this approach, we recover the stability of the column, assuming the classical Mohr-Coulomb criterion for failure. We then compare this approach with a code based on Contact Dynamics, which implies forces at the grain scale: we recover as well the stability of the column. Furthermore, this comparison enables us to estimate the macroscopic yield stress based on the cohesive contacts between grains, which bridges the gap between continuous and discrete approaches of cohesive granular matter.

Paru sous le titre publié :Collective Dynamics of Focal Adhesions Regulate Direction of Cell Motion; International audience; Directed cell motion is essential in physiological and pathological processes such as morphogenesis, wound healing, and cancer spreading. Chemotaxis has often been proposed as the driving mechanism, even though evidence of long-range gradients is often lacking in vivo. By patterning adhesive regions in space, we control cell shape and the potential to move along one direction in another migration mode coined ratchetaxis. We report that focal contact distributions collectively dictate cell directionality, and bias is non-linearly increased by gap distance between adhesive regions. Focal contact dynamics on micro-patterns allow to integrate these phenomena in a model where each focal contact is translated into a force with known amplitude and direction, leading to quantitative predictions for cell motion in new conditions with their successful experimental tests. Altogether, our study shows how local and minute timescale dynamics of focal adhesions and their distribution lead to long-term cellular motion with simple geometric rules.

Squeal of rail-bound vehicles emitted in tight curves is characterized by high sound pressure levels at pure medium and high frequencies. Many models have been proposed in the literature to explain the occurrence of this noise with different instability mechanisms: negative damping due to falling friction or instability with a constant friction coefficient. The aim of the paper is to contribute to the understanding of the instability mechanisms in the case of a constant friction coefficient. A stability analysis of the wheel/rail contact dynamics in curve is performed by using an equivalent point contact model combined with wheel and rail modal bases. Results show that even with an assumption of a constant Coulomb friction coefficient, two types of instabilities may occur in the wheel/rail system: classical mode coupling and instabilities due to negative damping added to a single wheel mode when the track dynamical behavior, especially in the vertical direction, is included. For this second type of instabilities, an 1-degree of freedom model can be formulated. By using this model, it is found that the equivalent damper behavior of the infinite track is the origin of these instabilities.

International audience; Multibody models are often coupled with other domains in order to enlarge the scope of computer-based analysis. In particular, modeling multibody systems (MBSs) in interaction with granular media is of great interest for industrial process such as railway track maintenance, handling of aggregates, etc. This paper presents a strong coupling methodology for unifying a multibody formalism using relative coordinates and a discrete element method based on non-smooth contact dynamics (NSCD). Both tree-like and closed-loop MBSs are considered. For the latter, the coordinate partitioning techniques is applied in the NSCD framework. The proposed approach is applied on the slider-crank mechanism benchmark. Results are in very good agreement with results obtained with other techniques from the literature. Finally, a multibody model of a tamping machine is coupled to a discrete element model of railway ballast in order to analyse efficiency of track maintenance. This application demonstrates that the dynamics of the machine must be taken into account so as to estimate the performance of the maintenance process correctly.

Coarse granular materials exhibit important grain breakage in civil engineering structures, making it more complicated to predict the settlement and collapse of structures. A three-dimensional numerical model is presented using the discrete element method (Non-Smooth Contact Dynamics method). Polyhedral grains are generated, divided into tetrahedral subgrains and glued together using a cohesive law. Samples of breakable grains are subjected to oedometric compression where grains interact via contact and friction processes. Multiple geometrical and physical parameters are tested to analyze the response on the macroscopic and microscopic scales. The tendencies found show the ability of the model to represent the real material’s behavior.

This paper deals with the estimation of pressure at collisions times during the movement of a dense crowd. Through the non-smooth contact dynamics approach for rigid and deformable solids, proposed by Fremond and his collaborators, the value of pressure and contact forces at collisions points, generated through congestion or panic situation are estimated. Firstly, we propose a second-order microscopic model, in which the crowd is treated as a system of rigid solids. Contact forces are rigorously defined by taking into account multiple simultaneous contacts and the non-overlapping condition between pedestrians. We show that for a dense crowd, percussions can be seen as contact forces. Secondly, in order to overcome the restrictive hypothesis related to the geometric form adapted to model the pedestrian, a continuous equivalent approach is proposed where the crowd is modeled as a deformable solid, the pressure is then defined by the divergence of the stress tensor and calculated according to volume and surface constraints. This approach makes it possible to retain an admissible right-velocity, including both the non-local interactions between non-neighbor pedestrians and the choice of displacement strategy of each pedestrian. Finally, the comparison between the two proposed approaches and some other existing approaches are presented on several illustrative examples to estimate the contact forces between pedestrians.

International audience; Many materials can be described as granular materials composed of soft or ultra-soft grains. Mostfood products, metal powders, microgels and many suspensions are soft-grain systems. Despite their different mechanisms of deformability, depending on their composition and structure, their common feature is that they can undergo large strains without rupture. As a result, these materials can reach high packing fractions beyond random close packing through both grain rearrangements and grain shape change. Until now, because of the lack of proper numerical and experimental tools, their compaction behavior under stress, volume change behaviour under shear and microstructure have mostly remained unexplored.In this work, we present a numerical technique to model soft granular materials in which the grains can undergo extensive shape change and large deformations. It combines an implicit formalism of the Material Point Method and the Contact Dynamics method [1-3]. In this framework, the large deformations of individual grains as well as their collective interactions are treated consistently. In order to reduce the computational cost, this method is parallelised using the Message Passing Interface (MPI) strategy. Using this approach, we investigate the uniaxial compaction of 2D packings composed of elastic grains. We consider compressibility rates ranging from fully compressible to incompressible grains. The packing deformation mechanism is a combination of both grain rearrangements and large deformations, and leads to high packing fractions beyond the jamming state. We show that the packing strength declines when the grain compressibility decreases, and the packing can deform considerably. We also investigate the evolution of the connectivity of the grains and grain deformation distributions in the packing.REFERENCES[1] S. Nezamabadi, F. Radjai, J. Averseng, J.-Y. Delenne, “Implicit frictional-contact model for soft particle systems”, Journal of the Mechanics and Physics of Solids, 83: 72-87, 2015.[2] S. Nezamabadi, T.-H. Nguyen, J.-Y. Delenne, F. Radjai, “Modeling soft granular materials”, Granular Matter, 19: 8, 2017.[3] S. Nezamabadi, X. Frank, J.-Y. Delenne, J. Averseng, F. Radjai, “Parallel implicit contact algorithm for soft particle systems”, Computer Physics Communications, In press.

International audience; We investigate the dynamic fracture of a single particle impacting a flat surface using 3D DEM simulations based on a fragmentation model involving both a stress threshold and a fracture energy. The particle is assumed to be perfectly rigid and discretized into polyhedral Voronoï cells with cohesive interfaces. A cell-cell interface loses its cohesion when it is at a normal or tangential stress threshold and an amount of work equal to the fracture energy is absorbed as a result of the relative cell-cell displacements. Upon impact, the kinetic energy of the particle is partially consumed to fracture cell-cell contacts but also restituted to the fragments or dissipated by inelastic collisions. We analyze the damage and fragmentation efficiency as a function of the impact energy and stress thresholds and their scaling with fracture energy and impact force. In particular, we find that the fragmentation efficiency, defined as the ratio of the consumed fracture energy to the impact energy, is unmonotonic as a function of the impact energy, the highest efficiency occurring for a specific value of the impact energy.

International audience; This paper presents a numerical technique to model soft particle materials in which the particles can undergo large deformations. It combines an implicit finite strain formalism of the Material Point Method and the Contact Dynamics method. In this framework, the large deformations of individual particles as well as their collective interactions are treated consistently. In order to reduce the computational cost, this method is parallelised using the Message Passing Interface (MPI) strategy. Using this approach, we investigate the uniaxial compaction of 2D packings composed of particles governed by a Neo-Hookean material behaviour. We consider compressibility rates ranging from fully compressible to incompressible particles. The packing deformation mechanism is a combination of both particle rearrangements and large deformations, and leads to high packing fractions beyond the jamming state. We show that the packing strength declines when the particle compressibility decreases, and the packing can deform considerably. We also discuss the evolution of the connectivity of the particles and particle deformation distributions in the packing.

International audience; By means of extensive three-dimensional contact dynamics simulations, we analyse the strength properties and microstructure of a granular asteroid, modelled as a self-gravitating cohesive granular aggregate composed of spherical particles, and subjected to di-ametrical compression tests. We show that, for a broad range of system parameters (shear rate, cohesive forces, asteroid diameter), the behaviour can be described by a modified inertial number that incorporates interparticle cohesion and gravitational forces.

International audience; In order to investigate the mechanical behavior of systems with complex architecture and a large number of contacting bodies, a finite element software, named LiToTac, has been developed by using the object-oriented programming technique. This software, with an interactive graphical user interface, is able to handle highly non-linear problems including multiple contacts and large deformation. More importantly, the contact detection based on a hybrid three-stages methodology can be performed automatically, which is more efficient than the common strategies of pre-defining contact zones in commercial FEM software like ANSYS, ABAQUS, etc. In addition, the contact solver in LiToTac is portable between dynamic and quasi-static codes and can accurately solve contact coupled with friction in a reduced system. Several numerical examples are carried out to illustrate the functionality and capacity of the software package.

The modeling of contact is one of the main features of contact dynamics in the context of friction-induced vibrations. It can have a strong impact on the numerical results and consequently on the design choices during the optimization or specification of industrial mechanical systems. This is particularly the case for scientific studies interested in brake squeal. The objective of the paper is to recall and to promote developments concerning the use of non smooth contact dynamics approach for numerical simulations based on finite element method. The specific problem of the prediction of self-excited vibration in the context of brake squeal is discussed. In order to illustrate the potential benefit for the mechanical community of using formulations and theoretical developments from the mathematical community, the stability analysis and the estimation of nonlinear vibrations of a brake system with multiple frictional interface is investigated.

We propose a new way to estimating interparticle contact forces in granular materials, based on the combination of experimental measurements and numerical techniques that take the contact laws respectively from Molecular Dynamics and Non-Smooth Contact Dynamics discrete element methods. Tests are performed in quasi-static conditions on a two-dimensional granular assembly; 80 MPixel pictures of the assembly are shot throughout each test. Image processing and Digital Image Correlation are used in order to get information on the geometry of the assembly (particles and contact points position) and the rigid-body motion of particles (displacements and rotation); based on this information, numerical methods can be applied to assess contact forces. 2D DEM simulations are also performed and the same information is extracted and used for contact force estimation, so that the numerical methods can be validated. The reproducibility of the original set of contact forces is shown to be dependent on the displacement history for the first method, based on contact elasticity, and on the degree of force indeterminacy for the Contact Dynamics-based one. The validation phase also includes a perturbation analysis to predict the influence of measurement error (bad contact detection) when applying the Contact Dynamics-based method, which shows the robustness of this method. After this validation phase, the methods are applied to experimental data. Measurement error on kinematic measurements turns out to be quite significant for the first approach, while it does not affect the second, for which the accuracy of the force estimation can be assumed to be mainly dependent on the degree of force indeterminacy of the system.

In this work, we discuss experiments and discrete element simulations of wall-bounded shear flows of slightly polydisperse spheres under gravity. Experiments were performed in an annular shear cell in which the bottom bumpy wall rotates at fixed velocity, while a pressure is applied at the top bumpy wall. The coaxial cylinders delimiting the flow are flat, frictional and transparent, allowing visualization of the flow. Velocity profiles were obtained by particle image velocimetry, and are characterized by an exponential profile, the decay length of which depends on the applied load, but not on the wall velocity. A force sensor was installed at different vertical positions on the outer sidewall in order to measure wall forces. The effective streamwise and transverse wall friction coefficients were thus estimated, showing wall friction weakening in creep zones. In order to better understand these results, contact dynamics simulations were carried out in a simplified configuration (Artoni & Richard, Phys. Rev. Lett., vol. 115 (15), 2015, 158001). In this case, profiting from the possibility of varying the particle–wall friction coefficient, different flow regimes were observed. In particular, shear can either be localized (1) at the bottom or (2) at the top of the shear cell, or (3) it can be quite evenly distributed in the vertical direction. Through an averaging technique that explicitly takes into account gradient effects (Artoni & Richard, Phys. Rev. E, vol. 91 (3), 2015, 032202), relevant, coarse-grained, continuum fields (solid fraction, velocity, stresses, velocity fluctuations) were obtained. They allow a discussion of the relevance of velocity fluctuations (i.e. granular temperature) for describing non-locality in granular flow. The case of solid-like fluctuations is also addressed. Finally, a simplified stress analysis is devoted to explain the emergence of complex shear localization patterns by the heterogeneity of effective bulk friction, which is due to the joint effect of gravity and wall friction.

In turbomachinery, it is well known that tighter operating clearances improve the efficiency. However, this leads to unwanted potential unilateral and frictional contact occurrences between the rotating (blades) and stationary components (casings) together with attendant thermal excitations. Unilateral contact induces discontinuities in the velocity at impact times, hence the terminology nonsmooth dynamics. Current modeling strategies of rotor-stator interactions are either based on regularizing penalty methods or on explicit time-marching methods derived from Carpenter’s forward Lagrange multiplier method. Regularization introduces an artificial time scale in the formulation corresponding to numerical stiffness which is not desirable. Carpenter’s scheme has been successfully applied to turbomachinery industrial models in the sole mechanical framework, but faces serious stability issues when dealing with the additional heat equation. This work overcomes the above issues by using the Moreau–Jean nonsmooth integration scheme within an implicit θ-method. This numerical scheme is based on a mathematically sound description of the contact dynamics by means of measure differential inclusions and enjoys attractive features. The procedure is unconditionally stable opening doors to quick preliminary simulations with time-steps one hundred times larger than with previous algorithms. It can also deal with strongly coupled thermomechanical problems.

In the beginning of the 80s, a rigorous mathematical framework was developed for the dynamics of multibody systems with perfect unilateral contacts, particularly due to the contributions of Schatzman and Moreau. Efficient numerical methods have been proposed, for instance Moreau’s NonSmooth Contact Dynamics (NSCD) (Moreau, 1999), which was then extended by Jean to cases with friction (Jean, 1999). But the algorithm, in the latter case, is no longer the time discretization of an evolution problem. In this work, we derive a new algorithm from the time discretization of an evolution problem for multibody dynamics with contacts and friction. Our algorithm has many points in common with the one of Jean and Moreau, but it converges reliably and fixes some energetic inconsistencies. The similarities and differences between the algorithms are illustrated on three planar archetypal examples.

International audience; Collisions in musical string instruments play a fundamental role in explaining the sound production in various instruments such as sitars, tanpuras and electric basses. Contacts occuring during the vibration provide a nonlinear effect which shapes a specific tone due to energy transfers and enriches the hearing experience. As such, they must be carefully simulated for the purpose of physically-based sound synthesis. Most of the numerical methods presented in the literature rely on a compliant modeling of the contact force between the string and the obstacle. In this contribution, numerical methods from nonsmooth contact dynamics are used to integrate the problem in time. A Moreau-Jean time-stepping scheme is combined with an exact scheme for phases with no contact, thus controlling the numerical dispersion. Results for a two-point bridge mimicking a tanpura and an electric bass are presented, showing the ability of the method to deal efficiently with such problems while invoking, as compared to a compliant approach, less modelling parameters and a reduced computational burden.

International audience; Friction-induced vibrations are a complex phenomenon, arising when two surfaces undergo relative sliding. During the last decades many studies on friction-induced vibrations have been carried out, where the simulation of the contact dynamic excitation has always been a challenge to face. This work proposes a new method to reproduce the local dynamic excitation from the contact and its effect on the vibrational response of the system. A friction law including a perturbative term of the friction coefficient is introduced. The evolution of the perturbative term, recovered by dedicated experiments, allows for simulating and analysing the contact excitation mechanisms. The comparisons between numerical and experimental results show good correlation between the measured vibrations and the ones simulated numerically, validating the proposed friction law.

International audience; This article is devoted to the analysis of the influence of the joint clearances in a mechanism of a circuit breaker, which is a forty-two degrees of freedom mechanism made of seven links, seven revolute joints, and four unilateral contacts with friction. Spatial (3D) revolute joints are modelled with both radial and axial clearances taking into account contact with flanges. Unilateral contact, Coulomb's friction and Newton impact laws are modeled within the framework of nonsmooth mechanics without resorting to some regularizations or compliance/damping at contact. The nonsmooth contact dynamics method based on an event-capturing time–stepping scheme with a second order cone complementarity solver is used to perform the numerical integration. Futhermore, the stabilization of the constraints at the position level is made thanks to the stabilized combined projected Moreau–Jean scheme. The nonsmooth modeling approach together with an event–capturing time–stepping scheme allows us to simulate, in an efficient and robust way, the contact and impacts phenomena that occur in joints with clearances. In particular, comparing with the event–detecting time–stepping schemes, the event–capturing scheme enables to perform the time–integration with large number of events (impacts, sliding/sticking transitions, changes in the direction of sliding) and possibly with finite time accumulations with a reasonable time–step length. Comparing with compliant contact models, we avoid stiff problems related with high stiffnesses at contact which generate some issues in contact stabilization and spurious oscillations during persistent contact periods. In the studied mechanisms of the circuit breakers, the numerical methods deals more than seventy contact points without any problems. Furthermore , the number of contact parameters is small : one coefficient of restitution and one coefficient of friction. Though they are sometimes difficult to measure accurately, the sensitivity of the simulation result with respect to contact parameters is low in the mechanism of the circuit breaker. It is demonstrated that this method, thanks to its robustness and efficiency allows to perform a sensitivity analysis using a Monte Carlo method. The numerical results are also validated by careful comparisons with experimental data which show a very good correlation.

International audience; For investigating the mechanical behavior of granular materials by means of the discrete element approach, it is desirable to be able to simulate representative volume elements with macroscopically homogeneous deformations. This can be achieved by means of fully periodic boundary conditions such that stresses or displacements can be applied in all space directions. We present a general framework for periodic boundary conditions in granular materials and its implementation more specifically in the Contact Dynamics method.

International audience; When velocity jumps are occurring, the dynamics is said to be nonsmooth. For instance, in collections of contacting rigid bodies, jumps are caused by shocks and dry friction. Without compliance at the interface, contact laws are not only non-differentiable in the usual sense but also multi-valued. Modeling contacting bodies is of interest in order to understand the behavior of numerous mechanical systems such as flexible multi-body systems, granular materials or masonry. These granular materials behave puzzlingly either like a solid or a fluid and a description in the frame of classical continuous mechanics would be welcome though far to be satisfactory nowadays. Jean-Jacques Moreau greatly contributed to convex analysis, functions of bounded variations, differential measure theory, sweeping process theory, definitive mathematical tools to deal with nonsmooth dynamics. He converted all these underlying theoretical ideas into an original nonsmooth implicit numerical method called Contact Dynamics (CD); a robust and efficient method to simulate large collections of bodies with frictional contacts and impacts. The CD method offers a very interesting complementary alternative to the family of smoothed explicit numerical methods, often called Distinct Elements Method (DEM). In this paper developments and improvements of the CD method are presented together with a critical comparative review of advantages and drawbacks of both approaches.; Lorsque des sauts de vitesse se produisent, la dynamique est dite non régulière. Par exemple, dans les collections de solides supposés rigides rentrant en contact, les sauts sont causés par les chocs et le frottement sec. L'absence de déformabilité fait que les lois de contact sont, non seulement non différentiables au sens usuel, mais aussi multi-valuées. Élaborer des modèles de solides en contact est un moyen de comprendre le comportement de nombreux systèmes mécaniques tels que les systèmes multi-corps flexibles, les matériaux granulaires ou les maçonneries. Les matériaux granulaires se comportent de manière étrange, soit comme des solides, soit comme des fluides, et une description dans le cadre de la mécanique classique des milieux continus, qui serait souhaitable, est loin d'être encore satisfaisante. Jean-Jacques Moreau a contribué, de façon fondamentale, à l'analyse convexe, à la théorie des fonctions à variations bornées et des mesures différentielles ainsi qu'au processus de rafle, outils mathématiques décisifs pour traiter la dynamique non régulière. Il a converti ces idées théoriques sous-jacentes en une méthode numérique originale appelée Contact Dynamics (CD), qui est une méthode non régulière implicite et aussi une méthode robuste et efficace pour simuler de larges collections de solides avec du contact frottant et des impacts. Le méthode CD offre une alternative très intéressante à la famille de méthodes usuelles régularisées explicites, comme la méthode des éléments distincts (DEM). Dans cet article, des développements et des perfectionnements de la méthode CD sont présentés ainsi qu'une étude critique comparative des avantages et inconvénients des deux approches.

International audience; This work is devoted to the numerical modeling of contact problems in the context of multibody dynamics. Non-linearities including large deformation and frictional contact are modeled based on the finite element method. An improved approach by means of a semi-explicit calculation is applied to integrate the equation of motion. The frictional contact forces and the relative velocity establish an implicit relationship within the bi-potential framework. A hybrid methodology consisting of the Octree structure and the bounding volume hierarchy is proposed to reduce exhaustive contact inspections. Two numerical examples implemented in our in-house finite element software FER/Impact are given to illustrate the efficiency and accuracy of the resulting methods.

In soft particle materials such as metallic powders the particles can undergo large deformations without rupture. The large elastic or plastic deformations of the particles are expected to strongly affect the mechanical properties of these materials compared to hard particle materials more often considered in research on granular materials. Herein, two numerical approaches are proposed for the simulation of soft granular systems: (i) an implicit formulation of the Material Point Method (MPM) combined with the Contact Dynamics (CD) method to deal with contact interactions, and (i) Bonded Particle Model (BPM), in which each deformable particle is modeled as an aggregate of rigid primary particles using the CD method. These two approaches allow us to simulate the compaction of an assembly of elastic or plastic particles. By analyzing the uniaxial compaction of 2D soft particle packings, we investigate the effects of particle shape change on the stress-strain relationship and volume change behavior as well as the evolution of the microstructure.

International audience; We study the physics of adhesion and the contact mechanics at the nanoscale with a peeling experiment of a carbon nanotube on a flat substrate. Using an interferometric atomic force microscope and an extended force modulation protocol, we investigate the frequency response of the stiffness of the nano-contact from DC to 20 kHz. We show that this dynamic stiffness is only weakly frequency dependent, increasing by a factor 2 when the frequency grows by 3 orders of magnitude. Such behavior may be the signature of amorphous relaxations during the mechanical solicitation at the nano-scale.

Proceedings of the 1st International Conference on the Material Point Method (MPM 2017); International audience; Soft particle materials are composed of discrete particles that can undergo large deformations without rupture. Most food products, many powders, colloidal pastes, vesicles and biological cells are soft particle systems. In order to model such materials, we present an efficient numerical approach combining an implicit formulation of the Material Point Method (MPM) and Contact Dynamics (CD) method. The MPM deals with bulk variables of an individual particle by discretizing it as a collection of material points, whereas the CD allows for the treatment of frictional contacts between particles. This model is applied for the simulation of the uniaxial compression of 2D soft-particle packings. The compaction is a nonlinear process in which new contacts are formed between particles and the contact areas increase. The change of particle shapes allows these materials to reach high packing fraction. We find that the contact specific surface, the orientation anisotropy and the aspect ratio of particles increase as a function of the packing fraction but at different rates. We also evidence the effect of friction, which favors strong stress chains and thus the elongation of particles, leading to larger values of the orientation anisotropy and the aspect ratio at a given level of packing fraction as compared to a frictionless particle packing.

International audience; This paper concerns modeling of soft granular materials in which the grains are highly deformable. In order to simulate these materials, an approach based on an implicit formulation of the Material Point Method in the context of the finite strain theory, allowing for large deformations of grains, coupled with the Contact Dynamics method for the treatment of unilateral frictional contacts between grains, is proposed. In this context, the Mooney-Rivlin constitutive relationship is applied with two different set of elastic parameters. Considering these two material behaviors, a uniaxial compression of 2D soft granular packings is analyzed. The stress-strain relation and the evolution of the packing fraction as well as of the connectivity of the grains are discussed.

International audience; Models with impact or dry friction, yielding discontinuous velocities or accelerations, have motivated research for appropriate numerical methods in the community of non-smooth dynamics. In this work, we apply such methods on the grand piano action. This multibody system has two properties of interest in terms of modelling and simulation: it is extremely sensitive to small misadjustements, and its functioning strongly relies on dry friction and stick-slip transitions—known to be crucial for the touch of the pianist. Using numerical methods of non-smooth contact dynamics, the non-smooth character of dry friction was conserved, in contrast to classical approaches based on regularization which additionally impose the somewhat arbitrary choice of a regularizing parameter. The use of such numerical method resulted in computations about a few hundred times faster than those reported in recent literature. For the first time, the presented predictions of the piano action's simulations are forces (in particular, the reaction force of the key on the pianist's finger), instead of displacements which filter out most of the dynamical subtleties of the mechanism. The comparisons between measured and simulated forces in response to a given motion are successful, which constitutes an excellent validation of the model, from the dynamical and the haptic points of view. Altogether, numerical methods for non-smooth contact dynamics applied to a non-smooth model of the piano action proved to be both accurate and efficient, opening doors to industrial and haptic applications of sensitive multibody systems for which dry friction is essential.Simulation-based videos Simulations of a keystroke: Your browser does not support the video tag. Comparisons between simulations and experiments: Your browser does not support the video tag. Experimental and educational videos High-speed captures of the piano key mechanism (Left: piano keystroke. Right: forte keystroke.) [A. Thorin and X. Boutillon, LMS@École polytechnique / CEA LIST] Your browser does not support the video tag. Your browser does not support the video tag. Explanations on how the mechanism works [A. Thorin based on O. Remez's drawing] Your browser does not support the video tag. Tracking of the kinematics using J. Diener's implementation of KLT tracking algorithms: Your browser does not support the video tag.

International audience; Soft-grain materials such as clays and other colloidal pastes share the common feature of being composed of grains that can undergo large deformations without rupture. For the simulation of such materials, we present two alternative methods: (1) an implicit formulation of the material point method (MPM), in which each grain is discretized as a collection of material points, and (2) the bonded particle model (BPM), in which each soft grain is modeled as an aggregate of rigid particles using the contact dynamics method. In the MPM, a linear elastic behavior is used for the grains. In order to allow the aggregates in the BPM to deform without breaking, we use long-range center-to-center attraction forces between the primary particles belonging to each grain together with steric repulsion at their contact points. We show that these interactions lead to a plastic behavior of the grains. Using both methods, we analyze the uniaxial compaction of 2D soft granular packings. This process is nonlinear and involves both grain rearrangements and large deformations. High packing fractions beyond the jamming state are reached as a result of grain shape change for both methods. We discuss the stress-strain and volume change behavior as well as the evolution of the connectivity of the grains. Similar textures are observed at large deformations although the BPM requires higher stress than the MPM to reach the same level of packing fraction.

International audience; Abrasive water-jet manufacturing process can shape a lot of materials ranging from metals to glasses. It has a lot of advantages, as its low cutting forces, but remains quite difficult to control. Indeed, the process is leaded by the abrasive particle trajectories which depends on the water static pressure and many other parameters. The impact pressure on the work-piece is commonly modeled by a two Gaussian fit sum which are representative of the particles velocity distribution and the granulometry respectively. Today no studies based on discrete elements take into account the mixing chamber and the focal canon which are the two main steps of the abrasive water-jet tool constitution. In this preliminary work we propose to model the flow through the focal canon until the target impact by an original numeric granular approach. The Non-Smooth Contact Dynamics is an efficient method on a large range of simulation domains. In our case, we consider the water phase and the abrasive phase as two collections of distinct polydisperse elements. The masses are corrected and the contact interaction laws are adjusted to account for an equivalent fluid which similar mechanical properties. These two phases are mixed in a chamber and focalised through the canon, knowing water static pressure and abrasive mass rate. After the canon end the abrasive water-jet evolves in air and thus decelerates by friction. The tool-fluid adapts its geometric configuration from this kinetic energy decrease and impacts a target plane located at a known distance from the canon. Such a model is built on some classic process parameters as the water static pressure, the abrasive mass rate or the work-piece vs. canon distance, but it also naturally takes into account finer mechanical parameters as the abrasive granulometry or friction dissipation. Simulations gives interesting results of impact pressure distribution on the target work-piece with dynamic data of all the collection particles. More generally, this work final aim is to link elemental particle damage studies with a macroscopic wear prediction law.

This thesis deals with the study of mechanical wave propagation in dry or wet granular media, with the aim of relating the phenomena at the microscopic scale (particles dynamics, interaction potentials between grains, rheology of the interstitial fluid) to the features at the macroscopic scale (dispersion relation, wave speed and attenuation in the long wavelength approximation). The systems under study are either large one-dimensional granular media, as the analogs of the paths of the most compressed grains (the force chains) in real granular packings, or the real granular media themselves. In a first place, we study experimentally the wave transmission through alignments of dry centimetric spheres, which we model via the Hertz potential. We show that the elasto-frictional coupling between the grains and a substrate (the spheres’ support) induces an on-site elastic potential, which in turn induces a band gap at zero frequency in the transfer function. In a second place, we show that the presence of an infinitesimal amount of viscous fluid at the contact between every particle induces an elasto-hydrodynamic (EHD) interaction. The later affects the attenuation of waves in addition to a significant increase of the wave speed, which in this case both non-trivially depend on the elasticity of the particles, on the viscosity of the fluid and on the frequency. In a third place, we check the reliability of our analysis to describe ultrasonic wave propagation in real granular materials such as dry or wet sand; our particles are here millimetric spheres. In the dry configuration, our results are consistent with an effective medium theory (EMT) which relies on the Hertz-Mindlin interaction in the long wavelength approximation. In the wet configuration, the EMT model combined with an EHD mechanism fairly reproduces our preliminary observations., Cette thèse porte sur l’étude de la propagation d’ondes mécaniques dans des milieux granulaires secs ou mouillés, avec pour objectif de relier les phénomènes de l’échelle microscopique (dynamique des grains, potentiels d’interactions entre particules, rhéologie du fluide interstitiel) aux propriétés de l’échelle macroscopique (relation de dispersion, vitesse et atténuation des ondes dans l’approximation des grandes longueurs d’ondes). Les systèmes étudiés sont soit des milieux granulaires unidimensionnels de grande taille, analogues des chemins de plus forts contacts entre particules (les chaînes de force) dans les empilements de grains réels, soit les milieux granulaires réels eux-mêmes. Dans un premier temps, nous étudions expérimentalement la transmission d’ondes au travers d’un alignement de sphères centimétriques sèches, que nous modélisons via le potentiel de Hertz. Nous montrons que le couplage élastofrictionnel entre les grains et un substrat (le support des sphères) engendre un potentiel élastique local, qui induit à son tour une bande interdite a fréquence nulle dans la fonction de transfert. Dans un deuxième temps, nous montrons que la présence d'une quantité infime de fluide visqueux au contact entre chaque particule induit une interaction élasto-hydrodynamique (EHD). Ce dernier induit une modification de l’atténuation des ondes et une augmentation très significative de la vitesse de propagation, qui dans ce cas dépendent de manière non-triviale de l’élasticité des particules, de la viscosité du fluide et de la fréquence. Dans un troisième temps, nous vérifions la fiabilité de notre analyse pour décrire la propagation d'ondes ultrasonores dans des milieux granulaires réels, tel que le sable mouillé ou non ; les particules sont ici des sphères millimétriques. Dans le cas sec, nos résultats sont en accord avec un modèle connu de milieux effectifs (EMT) qui relève de l’interaction de Hertz-Mindlin dans l'approximation des grandes longueurs d'ondes. Dans le cas mouille, le modèle EMT combiné à un mécanisme EHD reproduit de manière acceptable nos observations préliminaires.

International audience; Periodic solutions of autonomous and conservative second-order dynamical systems of finite dimension n undergoing a single unilateral contact condition are investigated in continuous time. The unilateral constraint is complemented with a purely elastic impact law conserving total energy. The dynamics is linear away from impacts. It is proven that the phase-space is primarily populated by one-dimensional continua of periodic solutions, generating an invariant manifold which can be understood as a nonsmooth mode of vibration in the context of vibration analysis. Additionally, it is shown that nonsmooth modes of vibration can be calculated by solving only $k-1$ equations where $k$ is the number of impacts per period. Results are illustrated on a mass-spring chain whose last mass undergoes a contact condition with an obstacle.

International audience; This article is devoted to the study of the conservation and the dissi-pation properties of the mechanical energy of several time–integration methods dedicated to the elasto–dynamics with unilateral contact. Given that the direct application of the standard schemes as the Newmark schemes or the generalized– α schemes leads to energy blow-up, we study two schemes dedicated to the time–integration of nonsmooth systems with contact: the Moreau–Jean scheme and the nonsmooth generalized–α scheme. The energy conservation and dissi-pation properties of the Moreau–Jean is firstly shown. In a second step, the nonsmooth generalized–α scheme is studied by adapting the previous works of Krenk and Høgsberg in the context of unilateral contact. Finally, the known properties of the Newmark and the Hilber–Hughes–Taylor (HHT) scheme in the unconstrained case are extended without any further assumptions to the case with contact.

International audience; Whether you are walking on a concrete floor, standing on a carpet, or sitting on a soft chair, your entire body continuously controls the posture and the contact forces that are produced by acting on rigid and compliant surfaces. Sometimes, like when reaching for a distant object or standing inside a moving bus that suddenly brakes, humans plan intentionally new contacts to preserve their balance and avoid falling. For humanoid robots to act in unstructured natural environments as humans do, contacts and physical interactions are necessary and unavoidable. This special issue of the Autonomous Robots journal aims at presenting the advances in whole-body control of real robots, focusing on control and learning techniques applied to estimation, control and adaptation of whole-body dynamics movement and contact forces that go beyond basic balancing abilities.

International audience; We present a three-dimensional numerical method for the simulation of particle crushing in 3D. This model is capable of producing irregular angular fragments upon particle fragmentation while conserving the total volume. The particle is modeled as a cluster of rigid polyhedral cells generated by a Voronoi tessellation. The cells are bonded along their faces by a cohesive Tresca law with independent tensile and shear strengths and simulated by the contact dynamics method. Using this model, we analyze the mechanical response of a single particle subjected to diametral compression for varying number of cells, their degree of disorder, and intercell tensile and shear strength. In particular, we identify the functional dependence of particle strength on the intercell strengths. We find that two different regimes can be distinguished depending on whether intercell shear strength is below or above its tensile strength. In both regimes, we observe a power-law dependence of particle strength on both intercell strengths but with different exponents. The strong effect of intercell shear strength on the particle strength reflects an interlocking effect between cells. In fact, even at low tensile strength, the particle global strength can still considerably increase with intercell shear strength. We finally show that the Weibull statistics describes well the particlestrength variability.

International audience; We analyze the shear strength and microstructure of binary granular mixtures consisting of disks and elongated particles by varying systematically both the mixture ratio and degree of homogeneity (from homogeneous to fully segregated). The contact dynamics method is used for numerical simulations with rigid particles interacting by frictional contacts. A counterintuitive finding of this work is that the shear strength, packing fraction, and, at the microscopic scale, the fabric, force, and friction anisotropies of the contact network are all nearly independent of the degree of homogeneity. In other words, homogeneous mixtures have the same strength properties as segregated packings of the two particle shapes. In contrast, the shear strength increases with the proportion of elongated particles correlatively with the increase of the corresponding force and fabric anisotropies. By a detailed analysis of the contact network topology, we show that various contact types contribute differently to force transmission and friction mobilization.

International audience; A method of a floating frame of reference that performs splitting of a deformable solid into rigid and deforming parts is presented within the context of non-smooth contact dynamics. The decomposition is made in such a way that the deforming part of the velocity field does not contribute either to the motion of the center of mass or the rotational motion. The corresponding numerical method that computes both rigid and deforming motions is presented and extended to multi-body dynamics simulation allowing non-smooth contact interactions, such as impacts and friction. Numerical experiments, where the method is compared with a more traditionally used Total Lagrangian method, justify its preference as a more efficient tool for the simulation of assemblies of stiff and massive objects.

Whenever relative motion between two system components occurs, through a dry contact interface, vibrations are induced by the frictional contact. The local dynamics at the contact (ruptures and wave generation) couples with the system dynamics, giving origin to vibrations and affecting the macroscopic frictional behavior of the system. In this thesis, in order to develop an overall approach to the investigation of the multi-physic phenomenon, the energy has been pointed out as a coupling physical characteristic among the several phenomena at the different scales. The formulation of a mechanical energy balance is used for distinguishing between two different dissipative terms, i.e. the dissipation by material/system damping and the dissipation at the contact. The energy flows coming from the frictional surfaces, by friction induced vibrations, excites the dynamic response of the system, and vice versa the influence of the system dynamic response on the local energy dissipation at the contact interface affects the related tribological phenomena. The friction-induced vibrations have been analyzed using three different approaches: the finite element approach, to investigate the coupling between the contact and system dynamics by the analysis of the energy flows; the experimental approach to validate the numerical results and observe the influence of phenomena not still included into the numerical model; a lumped parameter model approach to quickly investigate the effects of the system parameters. The numerical analysis by the 2D finite element model allowed investigating the repartition of the energy introduced into the mechanical system between the two dissipative terms (material damping and contact) during both stable and unstable friction-induced vibrations. In particular, it has been shown how the friction-induced vibrations modify the overall capacity of the system to absorb and dissipate energy; an estimation of the power dissipated at the contact, without considering the dynamic behavior of the system (energy flows by friction induced vibrations) can lead to significant error in the quantification of the dissipated energy at the contact, which affects directly several tribological phenomena. The experimental squeal measurements show how the same unstable modes are recovered both experimentally and numerically, validating the use of the 2D transient simulations for the reproduction of the unstable friction-induced vibrations. Once the energy balance formulated, it has been used on the lumped model to approach the instability over-prediction issue characteristic of the complex eigenvalue analysis. By energy considerations, a newer instability index (MAI) has been defined to compare the different unstable modes and to select the mode that becomes effectively unstable during the transient response. The Modal Absorption Index allows quantifying the capability of each mode to exchange energy with the external environment., Chaque fois que se produit un mouvement relatif entre deux systèmes, avec une interface à contact sec, le contact frottant induit des vibrations. La dynamique locale au contact (ruptures et la génération d'ondes) se couple avec la dynamique du système, donnant origine à des vibrations et affectant le comportement frictionnel macroscopique du système. Dans cette thèse, afin de développer une approche globale pour l'investigation des phénomènes multi-physiques, l'énergie a été utilisée comme une caractéristique physique universelle du couplage. La formulation de un bilan énergétique mécanique est utilisé pour identifier deux termes dissipatifs différents, i.e. la dissipation par amortissement matériel/système et la dissipation au contact. Les flux d'énergie, provenant des surfaces en contact et dus aux vibrations induites par frottement, excitent la réponse dynamique du système et, vice versa, l'influence de la réponse dynamique du système sur la dissipation d'énergie locale à l'interface de contact affecte les phénomènes tribologiques connexes. Dans cette thèse, les vibrations induites par le frottement ont été analysées en utilisant: l'approche par éléments finis pour étudier, par l'analyse des flux d'énergie, le couplage entre le contact et la dynamique du système; l'approche expérimentale pour valider les résultats numériques et observer l'influence des phénomènes pas encore inclus dans les modèles numériques; une approche avec une modèle à paramètres concentrés pour évaluer rapidement les effets des paramètres du système. L'analyse numérique par le modèle éléments finis 2D permet une répartition de l’énergie introduite dans le système mécanique entre les deux termes dissipatifs (amortissement matériau et contact), au cours de la réponse transitoire aussi bien en conditions stables qu’instables. En particulier, les vibrations induites par frottement modifient la capacité globale du système à absorber et dissiper l’énergie; une estimation de la puissance dissipée au contact, sans prendre en compte le comportement dynamique du système (flux d’énergie par les vibrations induites par frottement) peut conduire à des erreurs significatives dans la quantification de l’énergie dissipée au contact, ce qui affecte directement plusieurs phénomènes tribologiques. Les mesures expérimentales de crissement montrent comment les mêmes modes instables sont reproduits soit expérimentalement soit numériquement, validant l’utilisation de la simulation 2D transitoires pour l’analyse des vibrations instables induites par le frottement. L’équilibre énergétique a été utilisé sur le modèle à paramétrés concentrés, pour approcher le problème de la surestimation d’instabilité, qui est caractéristique d’une analyse des valeurs propres complexes. Un nouvel indice d’instabilité (MAI) a été défini, par des considérations énergétiques, pour comparer les différents modes instables et pour sélectionner le mode qui devient effectivement instable pendant le crissement.

International audience; We introduce a novel numerical approach for the simulation of soft particles interacting via frictional contacts. This approach is based on an implicit formulation of the Material Point Method, allowing for large particle deformations, combined with the Contact Dynamics method for the treatment of unilateral frictional contacts between particles. This approach is both precise due to the treatment of contacts with no regularization and artificial damping parameters, and robust due to implicit time integration of both bulk degrees of freedom and relative contact velocities at the nodes representing the contact points. By construction, our algorithm is capable of handling arbitrary particle shapes and deformations. We illustrate this approach by two simple 2D examples: a Hertz contact and a rolling particle on an inclined plane. We also investigate the compaction of a packing of circular particles up to a solid fraction well above the jamming limit of hard particles. We find that, for the same level of deformation, the solid fraction in a packing of frictional particles is above that of a packing of frictionless particles as a result of larger particle shape change.

International audience; We propose an original formulation to describe the motion of a rolling object in contact with a flat surface, and propose a complete application of this model to generate optimal walk of a humanoid system. We derive an analytic formulation of the contact equations which does not require any numerical approximation. We then show how the model performs when applied to the simulation of bipedal locomotion: by replacing polyhedral models of the feet by ellipsoidal ones, the numerical algorithms run faster and provide higher quality results. Furthermore, as any convex shape may be approximated locally by an ellipsoid, the scope of the model goes beyond locomotion simulation.

International audience; The aim of this work is to improve the safety and control robustness of robots interacting physically with humans by enhancing their contact perception. More specifically in the abdominal area, respiratory motions are clearly influencing the contact dynamics but have not yet been accounted for in the estimation of the contact impedance. We propose here a combined mechanical-respiratory model of impedance along with its on-line identification. Numerical and practical experiments with living subjects validate the identification process and show the relevance in accuracy of accounting for the respiratory beats.

Volume 7B: Structures and DynamicsConference Sponsors: International Gas Turbine InstituteISBN: 978-0-7918-5677-2; International audience; Abradable materials are widely used as a coating within compressor and turbine stages of modern aircraft engines in order to reduce operating blade-tip/casing clearances and thus maximize the engine energy efficiency. However, recent investigations revealed that the interaction between a blade and these materials may threaten blades structural integrity. Consequently, there is a need for a better understanding of the physical phenomena at play and for an accurate modelling of the interaction in order to predict hazardous events. The cornerstone of related numerical investigations lies in the modelling of the abradable coating removal due to the blade/abradable coating interaction and the associated contact forces along the contact interface. In this context, this article presents a macroscopic model for abradable coating removal accounting for key wear mechanisms including adhesive wear, abrasive wear, micro-rupture wear and machining wear. It is coupled with an in-house numerical strategy for the modelling of full 3D blade/abradable coating interactions within turbomachines and applied to an aircraft engine. Numerical results are compared with respect to existing models and available experimental data. The applicability of the proposed model for 3D interaction simulations is underlined as well as the consistency of the obtained results with experimental observations.