On inconsistency in frictional granular systems

International audienceNumerical simulation of granular systems is often based on a discrete element method. The nonsmooth contact dynamics approach can be used to solve a broad range of granular problems, especially involving rigid bodies. However, difficulties could be encountered and hamper successful completion of some simulations. The slow convergence of the nonsmooth solver may sometimes be attributed to an ill-conditioned system, but the convergence may also fail. The prime aim of the present study was to identify situations that hamper the consistency of the mathematical problem to solve. Some simple granular systems were investigated in detail while reviewing and applying the related theoretical results. A practical alternative is briefly analyzed and tested

Conjugate gradient type algorithms for frictional multi-contact problems: applications to granular materials

International audienceThis paper presents gradient type algorithms to solve frictional multi contact problems written as quasi optimization problems. A single loop scheme formally close to the classical conjugate gradient method is proposed with some adap tations of the iterate corrections and gradient projections. Since the convergence is difficult to prove, various tests in the field of granular media are performed with comparison with the non linear Gauss Seidel scheme

From discrete to continuous numerical identification of a geomaterial with an internal length

International audienceA geomaterial called TexSol and composed of sand and wires was investigated by numerical experiments in order to determine its geometrical and mechanical parameters, such as tortuousness of the wire, anisotropy and characteristic length. This stage is essential for studying a material with an obvious non-local behavior. Investigations by discrete elements highlighted that the characteristic length was dependant on the loading level. These simulations provided access to variables that standard physical experiments cannot provide. Some parameters of a continuous model of TexSol were identified through discrete numerical experiments using a classic procedure. The other parameters were determined by finite element method updating

A parallel version of the non smooth contact dynamics algorithm applied to the simulation of granular media

AbstractThe NSCD method has shown its efficiency in the simulation of granular media. Since the number of particles and contact increases, the shape of the discrete elements becomes more complicated and the simulated problems becomes more complex, the numerical tools need to be improved in order to preserve reasonable elapsed CPU time. In this paper we present a parallelization approach of the NSCD algorithm and we investigate its influence on the numerical behaviour of the method. We illustrate the efficiency on an example made of hard disks: a free surface compaction

Numerical investigations of fault propagation and forced-fold using a non smooth discrete element method

Geophysical problems as forced-fold evolution and fault propagation induce large deformations and many localisation. The continuum mechanics does not seem the more appropriate for their description and it appears more interesting to represent the media as initially discontinuous. To face both phenomena, a non smooth Discrete Element Method is used. Geophysical structures are considered as collection of rigid disks which interact by cohesive frictional contact laws. Numerical geophysical formations are correlated to mechanical properties of structures through observation and mechanical analysis.Les problèmes géophysiques tels que l’évolution des plis et la propagation de failles induisent de grandes déformations et de nombreuses localisations. Il apparaît donc difficile de décrire le problème avec les outils de la mécanique des milieux continus, et il est donc preferable de représenter la structure comme initialement divisée. Ces deux phénomènes sont étudiés via une approche non régulière par éléments discrets. Les structures géologiques sont considérées comme des collections de particules dont les interactions répondent à des lois de contact cohésif frottant. Les observations des structures géophysiques numériques sont corrélées aux propriétés des structures au travers d’une analyse mécanique

A domain decomposition strategy for nonclassical frictional multi-contact problems

International audienceIn this paper we present a numerical strategy to be solve large scale frictional contact problems by domain decomposition methods which are adapted to parallel computers. The motivation is given by the study of the mechanical behavior of rolling shutters composed by many hinged slats. The numerical treatment of such nonclassical contact problems leads to very large strongly nonlinear, nonsymmetric and ill-conditioned systems. Domain decomposition methods are a good alternative to overcome the difficulties of classical sequential solutions. We present a nonlinear strategy adapted to problems, called “multi-contact” problems

Is it reasonable to split sand grains before gluing them together?

Colloque en l'honneur de Michel Jean à l'occasion de son 70° anniversaireInternational audienceThis lecture is connected with a pioneering work of . Jean and P. Breitkopf on the use of the parallel computing for the granular dynamics [1]. The chosen parallel strategy is similar to a Domain Decomposition Method (DDM), even if the substructuring procedure is more modestly called a "box method" and does not refer explicitly to a DDM. The Domain Decomposition methods in the context of multiprocessor computations, are well established from theoretical and practical standpoints when dealing with a linear system derived from a discretization of a continuous problem [4]

From indetermination to inconsistency: how to avoid it

International audienceFor illustrating the limits of the NSCD approach we focus our attention on dense granular systems that are strongly confined. In order to respect the “elegant rusticity” of the Moreau’s approach we restrict the analysis to a collection of rigid bodies without considering global or local deformations of the grains. Some simple examples highlight the issue of inconsistencies, i.e. some configurations for which no solution exists, as well as indeterminacies, i.e. configurations that lead to non-uniqueness of solutions. We recover here the Painlevé paradox underlined at the beginning of the twentieth century. The non existence of solutions is the more important challenge we have to face. We can first identify the situations leading to this non existence among them the granular systems submitted to moving walls. If such a case may not be avoided another response consists in changing the Coulomb friction law. The NSCD approach is well adapted to inelastic shocks that predominate in granular media. However J.J. Moreau introduced the concept of formal velocity to account for an elastic restitution. This concept is richer than a restitution coefficient (Newton or Poisson type) involving a binary shock; this permits to deal with multicontact situations without introducing either deformable grains or elastic-plastic contact laws. However this does not allow to reproduce shock propagation as it occurs for instance in the famous Newton’s cradle. Is it then possible to propose an algorithmic solution in the NSCD framework

Contribution a la resolution numerique des inclusions differentielles

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