A domain decomposition method for granular dynamics using discrete elements and application to railway ballast

The paper is devoted to the development of a non overlapping domain decomposition method suited to granular dynamics. The formulation and the efficiency of such a method are well established for structural mechanics. In order to extend this approach to granular systems a so-called primal splitting of the domain is chosen because it is a less intrusive method for software development. Once the interface problem is defined and the solver is slightly enriched with some extra numerical parameters, the method is tested on railway ballast simulations for improving the maintenance of railway tracks.

[1]  Pierre Alart,et al.  A parallel version of the non smooth contact dynamics algorithm applied to the simulation of granular media , 2004 .

[2]  C. Farhat,et al.  A numerically scalable domain decomposition method for the solution of frictionless contact problems , 2001 .

[3]  Pierre-Etienne Gautier,et al.  Modelling ballast behaviour under dynamic loading. Part 1: A 2D polygonal discrete element method approach , 2006 .

[4]  Bruce Hendrickson,et al.  Parallel strategies for crash and impact simulations , 1998 .

[5]  G. Saussine,et al.  Quasistatic rheology, force transmission and fabric properties of a packing of irregular polyhedral particles , 2008, 0805.0178.

[6]  P. Cundall,et al.  A discrete numerical model for granular assemblies , 1979 .

[7]  Michel Saint Jean,et al.  The non-smooth contact dynamics method , 1999 .

[8]  Clark R. Dohrmann,et al.  Convergence of a balancing domain decomposition by constraints and energy minimization , 2002, Numer. Linear Algebra Appl..

[9]  V. Richefeu,et al.  Short-time dynamics of a packing of polyhedral grains under horizontal vibrations , 2007, The European physical journal. E, Soft matter.

[10]  P. Alart,et al.  A mixed formulation for frictional contact problems prone to Newton like solution methods , 1991 .

[11]  J. Moreau,et al.  FACING THE PLURALITY OF SOLUTIONS IN NONSMOOTH MECHANICS , 2006 .

[12]  G. Midi,et al.  On dense granular flows , 2003, The European physical journal. E, Soft matter.

[13]  Tony F. Chan,et al.  On the Relationship between Overlapping and Nonoverlapping Domain Decomposition Methods , 1992, SIAM J. Matrix Anal. Appl..

[14]  David Dureisseix,et al.  A micro–macro and parallel computational strategy for highly heterogeneous structures , 2001 .

[15]  Algirdas Maknickas,et al.  Parallel discrete element simulation of poly-dispersed granular material , 2010, Adv. Eng. Softw..

[16]  J. Moreau.  Numerical aspects of the sweeping process , 1999 .

[17]  Pierre Alart,et al.  Mixed versus impulse-oriented domain decomposition method for granular dynamics , 2009 .

[18]  E. Azema,et al.  Etude numérique de milieux granulaires à grains polyédriques : rhéologie quasi-statique, dynamique vibratoire et application au procédé de bourrage du ballast. , 2007 .

[19]  Pierre Alart,et al.  A scalable multiscale LATIN method adapted to nonsmooth discrete media , 2008 .

[20]  F. Magoules.  Mesh Partitioning Techniques and Domain Decomposition Methods , 2008 .

[21]  Dawei Zhao,et al.  A fast contact detection algorithm for 3-D discrete element method , 2004 .

[22]  I. G. BONNER CLAPPISON.  Editor , 1960, The Electric Power Engineering Handbook - Five Volume Set.

[23]  Yoshiyuki Shirakawa,et al.  Cell optimization for fast contact detection in the discrete element method algorithm , 2007 .

[24]  J. J.,et al.  Numerical aspects of the sweeping process , 1999 .

[25]  Pierre Alart,et al.  Domain decomposition approach for non-smooth discrete problems, example of a tensegrity structure , 2007 .

[26]  R. Luciano,et al.  Stress-penalty method for unilateral contact problems: mathematical formulation and computational aspects , 1994 .

[27]  D. Rixen,et al.  FETI‐DP: a dual–primal unified FETI method—part I: A faster alternative to the two‐level FETI method , 2001 .

[28]  Barbara Chapman,et al.  Using OpenMP: Portable Shared Memory Parallel Programming (Scientific and Engineering Computation) , 2007 .

[29]  Pierre Alart,et al.  A Multilevel Domain Decomposition Solver Suited to Nonsmooth Mechanical Problems , 2009 .

[30]  F. Dubois,et al.  The non smooth contact dynamic method: recent LMGC90 software developments and application , 2006 .

[31]  Bruno C. Hancock,et al.  An implementation of granular dynamics for simulating frictional elastic particles based on the DL_POLY code , 2005, Comput. Phys. Commun..

[32]  J. S.,et al.  Theory of Friction , 1872, Nature.

[33]  F. Jourdan,et al.  A Gauss-Seidel like algorithm to solve frictional contact problems , 1998 .

[34]  David Dureisseix,et al.  Numerical experimentations of parallel strategies in structural non-linear analysis , 1996 .