This contribution outlines a computational framework for the analysis of flexible multibody dynamics contact problems. The framework combines a flexible body formalism, specifically, the absolute nodal coordinate formulation (ANCF), with a discrete continuous contact force model to address many-body dynamics problems, i.e., problems with hundreds of thousands of rigid and deformable bodies. Since the computational effort associated with these problems is significant, the analytical framework is implemented to leverage the computational power available on today's commodity graphical processing unit (GPU) cards. The framework developed is validated against commercial and research finite element software. The robustness and efficiency of this approach is demonstrated through numerical simulations. The resulting simulation capability is shown to result in 2 orders of magnitude shorter simulation times for systems with a large number of flexible beams that might typically be encountered in hair or polymer simulations.

References

References
1.
Belytschko
,
T.
,
Liu
,
W.
, and
Moran
,
B.
,
2000
,
Nonlinear Finite Elements for Continua and Structures
, Vol.
36
,
Wiley
,
New York
.
2.
Shabana
,
A. A.
,
2008
,
Computational Continuum Mechanics
,
Cambridge University Press
,
New York
.
3.
Wriggers
,
P.
,
2006
,
Computational Contact Mechanics
,
Springer-Verlag
,
Berlin
.
4.
McDevitt
,
T. W.
, and
Laursen
,
T. A.
,
2000
, “
A Mortar-Finite Element Formulation for Frictional Contact Problems
,”
Int. J. Numer. Methods Eng.
,
48
, pp.
1525
1547
.10.1002/1097-0207(20000810)48:10<1525::AID-NME953>3.0.CO;2-Y
5.
Kikuchi
,
N.
, and
Oden
,
J. T.
,
1988
,
Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods
, Vol.
8
,
SIAM
,
Philadelphia, PA
.
6.
Khude
,
N.
,
Melanz
,
D.
,
Stanciulescu
,
I.
,
Jayakumar
,
P.
, and
Negrut
,
D.
,
2013
, “
A Comparison of Penalty and Lagrangean Methods for Handling Frictional Contact in Flexible Multi-Body Systems Undergoing Finite Deformations
,” (in press).
7.
Hughes
,
T.
,
Taylor
,
R.
, and
Kanoknukulchai
,
W.
,
1977
, “
A Finite Element Method for Large Displacement Contact and Impact Problems
,”
Formulations and Computational Algorithms in FE Analysis
,
MIT Press
,
Boston, MA
, pp.
468
495
.
8.
Puso
,
M. A.
, and
Laursen
,
T. A.
,
2004
, “
A Mortar Segment-To-Segment Frictional Contact Method for Large Deformations
,”
Comput. Methods Appl. Mech. Eng.
193
, pp.
4891
4913
.10.1016/j.cma.2004.06.001
9.
Cundall
,
P.
, and
Strack
,
O.
,
1979
, “
A Discrete Element Model for Granular Assemblies
,”
Geotechnique
,
29
, pp.
47
65
.10.1680/geot.1979.29.1.47
10.
Taylor
,
R. L.
,
2010
, “
A Finite Element Analysis Program, Version 8.3
,” http:www.ce.Berkeley.edu/∼rlt/feap
11.
Shabana
,
A.
, and
Yakoub
,
R.
,
2001
, “
Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Theory
,”
J. Mech. Des.
,
123
, pp.
606
613
.10.1115/1.1410100
12.
Schwab
,
A.
, and
Meijaard
,
J.
,
2005
, “
Comparison of Three-Dimensional Flexible Beam Elements for Dynamic Analysis: Finite Element Method and Absolute Nodal Coordinate Formulation
,”
Proceedings of the ASME 2005 IDETC/CIE
,
Orlando, Florida
,
Nov. 5–11
, pp.
24
28
.
13.
Gerstmayr
,
J.
, and
Shabana
,
A.
,
2006
, “
Analysis of Thin Beams and Cables Using the Absolute Nodal Co-Ordinate Formulation
,”
Nonlinear Dyn.
,
45
, pp.
109
130
.10.1007/s11071-006-1856-1
14.
Sopanen
,
J. T.
, and
Mikkola
,
A. M.
,
2003
, “
Description of Elastic Forces in Absolute Nodal Coordinate Formulation
,”
Nonlinear Dyn.
,
34
, pp.
53
74
.10.1023/B:NODY.0000014552.68786.bc
15.
Hussein
,
B.
,
Sugiyama
,
H.
, and
Shabana
,
A.
,
2007
, “
Coupled Deformation Modes in the Large Deformation Finite-Element Analysis: Problem Definition
,”
J. Comput. Nonlinear Dyn.
,
2
, pp.
146
154
.10.1115/1.2447353
16.
Sugiyama
,
H.
, and
Suda
,
Y.
,
2007
, “
A Curved Beam Element in the Analysis of Flexible Multi-Body Systems Using the Absolute Nodal Coordinates
,”
Proc. Inst. Mech. Eng.
, Part K,
221
, pp.
219
231
.10.1243/1464419JMBD86
17.
Sugiyama
,
H.
,
Koyama
,
H.
, and
Yamashita
,
H.
,
2010
, “
Gradient Deficient Curved Beam Element Using the Absolute Nodal Coordinate Formulation
,”
J. Comput. Nonlinear Dyn.
,
5
, p.
021001
.10.1115/1.4000793
18.
Delannay
,
R.
,
Louge
,
M.
,
Richard
,
P.
,
Taberlet
,
N.
, and
Valance
,
A.
,
2007
, “
Towards a Theoretical Picture of Dense Granular Flows Down Inclines
,”
Nature Mater.
,
6
, pp.
99
108
.10.1038/nmat1813
19.
Haug
,
E. J.
,
Wu
,
S. C.
, and
Yang
,
S. M.
,
1986
, “
Dynamics of Mechanical Systems With Coulomb Friction, Stiction, Impact, and Constraint Addition-Deletion-I
,”
Mech. Mach. Theory
,
21
, pp.
401
406
.10.1016/0094-114X(86)90088-1
20.
Khulief
,
Y. A.
, and
Shabana
,
A. A.
,
1987
, “
A Continuous Force Model for the Impact Analysis of Flexible Multibody Systems
,”
Mech. Mach. Theory
,
22
, pp.
213
224
.10.1016/0094-114X(87)90004-8
21.
Lankarani
,
H. M.
, and
Nikravesh
,
P. E.
,
1990
, “
A Contact Force Model With Hysteresis Damping for Impact Analysis of Multibody Systems
,”
J. Mech. Des.
,
112
, pp.
369
376
.10.1115/1.2912617
22.
Hunt
,
K. H.
, and
Crossley
,
F. R. E.
,
1975
, “
Coefficient of Restitution Interpreted as Damping in Vibroimpact
,”
J. Appl. Mech.
,
42
, pp.
440
445
.10.1115/1.3423596
23.
Johnson
,
K. L.
,
1987
,
Contact Mechanics
,
Cambridge University
,
Cambridge, UK
.
24.
Timoshenko
,
S.
, and
Goodier
,
J.
,
1970
,
Theory of Elasticity
,
McGraw-Hill
,
New York
, p.
2
.
25.
Gonthier
,
Y.
,
McPhee
,
J.
, and
Lange
,
C.
,
2007
, “
On the Implementation of Coulomb Friction in a Volumetric-Based Model for Contact Dynamics
,”
Proceedings of the ASME 2007 IDETC/CIE
,
Las Vegas, NV
,
Sept. 4–7
.
26.
Cundall
,
P.
,
1971
, “
A Computer Model for Simulating Progressive, Large-Scale Movements in Blocky Rock Systems
,”
Proceedings of the Symposium of the International Society for Rock Mechanics
.
27.
Rapaport
,
D.
,
2002
, “
Simulational Studies of Axial Granular Segregation in a Rotating Cylinder
,”
Physical Review E
,
65
, p.
61306
.10.1103/PhysRevE.65.061306
28.
Rapaport
,
D.
,
2007
, “
Radial and Axial Segregation of Granular Matter in a Rotating Cylinder: A Simulation Study
,”
Phys. Rev. E
,
75
, p.
031301
.10.1103/PhysRevE.75.031301
29.
Silbert
,
L.
,
Erta
,
D.
,
Grest
,
G.
,
Halsey
,
T.
,
Levine
,
D.
, and
Plimpton
,
S.
,
2001
, “
Granular Flow Down an Inclined Plane: Bagnold Scaling and Rheology
,”
Phys. Rev. E
,
64
, p.
051302
.10.1103/PhysRevE.64.051302
30.
Landry
,
J.
,
Grest
,
G.
,
Silbert
,
L.
, and
Plimpton
,
S.
,
2003
, “
Confined Granular Packings: Structure, Stress, and Forces
,”
Phys. Rev. E
,
67
, p.
041303
.10.1103/PhysRevE.67.041303
31.
Pfeiffer
,
F.
, and
Glocker
,
C.
,
1996
,
Multibody Dynamics With Unilateral Contacts
,
Wiley
,
New York
.
32.
Pang
,
J. S.
, and
Stewart
,
D. E.
,
2008
, “
Differential Variational Inequalities
,”
Mathematical Program.
,
113
, pp.
345
424
.10.1007/s10107-006-0052-x
33.
Moreau
,
J. J.
,
1983
, “
Standard Inelastic Shocks and the Dynamics of Unilateral Constraints: CISM Courses and Lectures
,”
Unilateral Problems in Structural Analysis
, Vol.
288
,
G. D.
Piero
and
F.
Macieri
, eds.,
Springer
,
New York
,
1983
, pp.
173
221
.
34.
Lotstedt
,
P.
,
1982
, “
Mechanical Systems of Rigid Bodies Subject to Unilateral Constraints
,”
SIAM J. Appl. Math.
,
42
, pp.
281
296
.10.1137/0142022
35.
Monteiro-Marques
,
M.
,
1993
,
Differential Inclusions in Nonsmooth Mechanical Problems: Shocks and Dry Friction, Progress in Nonlinear Differential Equations and Their Applications
, Vol.
9
,
Springer
,
New York
.
36.
Baraff
,
D.
,
1993
, “
Issues in Computing Contact Forces for Non-Penetrating Rigid Bodies
,”
Algorithmica
,
10
, pp.
292
352
.10.1007/BF01891843
37.
Pang
,
J. S.
, and
Trinkle
,
J. C.
,
1996
, “
Complementarity Formulations and Existence of Solutions of Dynamic Multi-Rigid-Body Contact Problems With Coulomb Friction
,”
Math. Program.
,
73
, pp.
199
226
.10.1007/BF02592103
38.
Trinkle
,
J.
,
Pang
,
J. S.
,
Sudarsky
,
S.
, and
Lo
,
G.
,
1997
, “
On Dynamic Multi-Rigid-Body Contact Problems With Coulomb Friction
,”
Z. Angew. Math. Mech.
,
77
, pp.
267
279
.10.1002/zamm.19970770411
39.
Stewart
,
D. E.
, and
Trinkle
,
J. C.
,
1996
, “
An Implicit Time-Stepping Scheme for Rigid-Body Dynamics With Inelastic Collisions and Coulomb Friction
,”
Int. J. Numer. Methods Eng.
,
39
, pp.
2673
2691
.10.1002/(SICI)1097-0207(19960815)39:15<2673::AID-NME972>3.0.CO;2-I
40.
Anitescu
,
M.
, and
Potra
,
F. A.
,
1997
, “
Formulating Dynamic Multi-Rigid-Body Contact Problems With Friction as Solvable Linear Complementarity Problems
,”
Nonlinear Dyn.
,
14
, pp.
231
247
.10.1023/A:1008292328909
41.
Anitescu
,
M.
,
Potra
,
F. A.
, and
Stewart
,
D. E.
,
1999
, “
Time-Stepping for Three-Dimensional Rigid Body Dynamics
,”
Comput. Methods Appl. Mech. Eng.
,
177
: pp.
183
197
.10.1016/S0045-7825(98)00380-6
42.
Stewart
,
D. E.
,
2000
, “
Rigid-Body Dynamics With Friction and Impact
,”
SIAM Rev.
,
42
, pp.
3
39
.10.1137/S0036144599360110
43.
Heyn
,
T.
,
Mazhar
,
H.
,
Tasora
,
A.
,
Anitescu
,
M.
, and
Negrut
,
D.
,
2009
, “
A Parallel Algorithm for Solving Complex Multibody Problems With Stream Processors
,”
Proceedings of the ECCOMAS Multibody Dynamics
,
Warsaw, Poland
.
44.
Tasora
,
A.
, and
Anitescu
,
M.
,
2011
, “
A Matrix-Free Cone Complementarity Approach for Solving Large-Scale, Nonsmooth, Rigid Body Dynamics
,”
Comput. Methods Appl. Mech. Eng.
,
200
, pp.
439
453
.10.1016/j.cma.2010.06.030
45.
Heyn
,
T.
,
Tasora
,
A.
,
Anitescu
,
M.
, and
Negrut
,
D.
,
2009
, “
A Parallel Algorithm for Solving Complex Multibody Problems With Stream Processors
,”
Int. J. Comput. Vision Biomech.
,
4
, pp.
1517
1532
.10.1115/DETC2009-86478
46.
Boos
,
J.
, and
McPhee
,
J.
,
2010
, “
Volumetric Contact Models and Experimental Validation
,”
Proceedings of the 1st Joint International Conference on Multibody System Dynamics
,
Lappeenranta, Finland
.
47.
Hertz
,
H.
,
1881
, “
On the Contact of Elastic Solids
,”
J. Reine Angew. Math
,
92
, pp.
156
171
.
48.
Goldsmith
,
W.
,
2001
,
Impact: The Theory and Physical Behaviour of Colliding Solids
,
Dover
,
New York
.
49.
Gonthier
,
Y.
,
McPhee
,
J.
,
Lange
,
C.
, and
Piedboeuf
,
J.
,
2004
, “
A Regularized Contact Model With Asymmetric Damping and Dwell-Time Dependent Friction
,”
Multibody Syst. Dyn.
11
, pp.
209
233
.10.1023/B:MUBO.0000029392.21648.bc
50.
Roy
,
A.
,
Carretero
,
J. A.
,
Buckham
,
B. J.
, and
Nicoll
,
R. S.
,
2009
, “
Continuous Collision Detection of Cubic-Spline-Based Tethers in ROV Simulations
,”
J. Offshore Mech. Arct. Eng.
,
131
, p.
041102
.10.1115/1.3124128
51.
SBEL
,
2011
, “
Simulation-Based Engineering Lab
,”
Department of Mechanical Engineering, University of Wisconsin
,
Madison, WI
, Retrieved Sept. 20, 2011, http://sbel.wisc.edu/Animations/#51
52.
Yang
,
B.
,
Laursen
,
T. A.
, and
Meng
,
X.
,
2005
, “
Two Dimensional Mortar Contact Methods for Large Deformation Frictional Sliding
,”
Int. J. Numer. Methods Eng.
,
62
, pp.
1183
1225
.10.1002/nme.1222
53.
NVIDIA
,
2011
, “
Compute Unified Device Architecture Programming Guide 4.0
http://developer.download.nvidia.com/compute/cuda/4_0/toolkit/docs/NVIDIA_CUDA_ProgrammingGuide_4.0.pdf
54.
Mazhar
,
H.
,
Heyn
,
T.
, and
Negrut
,
D.
,
2011
, “
A Scalable Parallel Method for Large Collision Detection Problems
,”
Multibody Syst. Dyn.
,
26
, pp.
37
55
.10.1007/s11044-011-9246-y
55.
Erwin
,
C.
,
2010
, “
Physics Simulation Forum
,” Retrieved Jan. 15, 2010, http://www.bulletphysics.com/Bullet/wordpress/
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