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

Renouf, Mathieu; Dubois, Frédéric; Alart, Pierre

doi:10.1016/j.cam.2003.05.019

Cited by 108 publications

(77 citation statements)

References 3 publications

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“…In fact the number of solutions is infinite and the algorithms have to reach one solution that we hope to be representative of the global behavior of the medium. A first study concerning the parallel treatment of the Gauss Seidel type method shows that the macroscopic features of the granular medium are preserved even if different deformation paths are followed when several processors are used [38]. More generally the Gauss Seidel type algorithms revealed to be efficient for granular problems [20,30], they converge even if the matrix is singular [12], but the optimization techniques are recommended in this case as long as the function stays lower bounded, which may be proved.…”

Section: Structural and Granular Type Frictionless Problemsmentioning

confidence: 99%

“…This method is intrinsically sequential and we tried a simple multi-threading technique which consists in splitting the contact loop into several threads dedicated to different processors. This approach was tested and analyzed in [38]: the performance of the solver is weakly perturbed. But Gauss Seidel algorithms are not the most efficient methods to solve large linear systems.…”

Section: Introductionmentioning

confidence: 99%

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

Renouf¹,

Alart²

2005

Computer Methods in Applied Mechanics and Engineering

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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

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Section: Structural and Granular Type Frictionless Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Renouf¹,

Alart²

2005

Computer Methods in Applied Mechanics and Engineering

Self Cite

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“…Various strategies may be applied when handling this problem [25,7,26], either privileging the global or the local levels. For instance, one may use the first three equations to obtain…”

Section: Methodsmentioning

confidence: 99%

Modelling ballast behaviour under dynamic loading. Part 1: A 2D polygonal discrete element method approach

Saussine

Cholet

Gautier

et al. 2006

Computer Methods in Applied Mechanics and Engineering

132

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Discrete element simulation provides some insight into the alteration of railway ballast after repeated train passings. The present Part 1 is devoted to a 2D model of this granular layer interposed between the deformable ground and the rail sleeper, to which a large number of loading cycles is applied. Ballast grains are modelled as indeformable polygonal solids. A detailed account of the application to this frictional dynamical problem of the Non-Smooth Contact Dynamics numerical method is given. Validation is obtained through comparison with physical experiments performed on assemblies of prismatic mineral grains. Numerical results on the settlement of a track submitted to 20,000 loading cycles or more are presented.

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“…In the first one, the emphasis is put on considering dynamical systems with relatively simple sets of unilateral constraints and the main objective is to develop a better understanding on fundamental issues related to the dynamic response, stability and bifurcation of non-smooth systems (e.g., [5][6][7][8][9][10][11][12][13][14][15]). On the other hand, a parallel and equally intensive effort is also underway, where the attention is focused on developing accurate and efficient numerical methodologies for capturing the response of models involving more complex sets of multiple unilateral constraints, by employing set-valued force law theory (e.g., [16][17][18][19][20][21][22][23]). …”

Section: Introductionmentioning

confidence: 99%

“…Moreover, most of the earlier studies devoted to systems with multiple contacts were related mainly to dynamics of granular materials or rigid and flexible blocks or metal forming (e.g., [20][21][22][23]) and not to classical structural dynamics applications.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of finite element structural models with multiple unilateral constraints

Theodosiou¹,

Natsiavas²

2009

International Journal of Non-Linear Mechanics

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Fast and accurate simulation of mechanical structures with complex geometry requires application of the finite element method. Τhis leads frequently to models with a relatively large number of degrees of freedom, which may also possess nonlinear properties. Things become more complicated for systems involving unilateral contact and friction. In classical structural dynamics approaches, such constraints are usually modeled by special contact elements. The characteristics of these elements must be selected in a delicate way, but even so the success of these methods can not be guaranteed. This study presents a numerical methodology, which is suitable for determining dynamic response of large scale finite element models of mechanical systems with multiple unilateral constraints. The method developed is based on a proper combination of results from two classes of direct integration methodologies. The first one includes standard methods employed in determining dynamic response of structural models possessing smooth nonlinearities. The second class of methods includes specialized methodologies that simulate response of dynamical systems with unilateral constraints. The validity and effectiveness of the methodology developed is illustrated by numerical results.

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

Cited by 108 publications

References 3 publications

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

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

Modelling ballast behaviour under dynamic loading. Part 1: A 2D polygonal discrete element method approach

Dynamics of finite element structural models with multiple unilateral constraints

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