The present paper proposes an extension of the classical discrete element method used to study third body flows. Based on the concept of the tribological triplet proposed by Godet and Berthier, the aim of this work is to enrich description, by accounting for the deformation of the first body and investigating its influence on third-body rheology. To achieve this, a novel hybrid approach that combines continuous and discontinuous descriptions is used. To illustrate the advantage of such modeling, comparisons with the classical approach, which considers the first body as rigid, are performed in terms of macroscopic friction coefficient and velocity and stress profiles.

References

References
1.
Godet
,
M.
, 1984, “
The Third-Body Approach: A Mechanical View of Wear
,”
Wear
,
100
, pp.
437
452
.
2.
Berthier
,
Y.
, 1990, “
Experimental Evidence for Friction and Wear Modelling
,”
Wear
,
139
, pp.
77
92
.
3.
Weinzapfel
,
N.
, and
Sadeghi
,
F.
, 2009, “
A Discrete Element Approach for Modeling Cage Flexibility in Ball Bearing Dynamics Simulations
,”
ASME J. Tribol.
,
131
, p.
021102
.
4.
Massi
,
F.
,
Giannini
,
G.
, and
Baillet
,
L.
, 2006, “
Brake Squeal as Dynamic Instability: An Experimental Investigation
”,
J. Acoust. Soc. Am.
,
120
(
3
), pp.
1388
1399
.
5.
Berthier
,
Y.
,
Vincent
,
L.
, and
Godet
,
M.
, 1988, “
Velocity Accommodation in Fretting
,”
Wear
,
125
(
1–2
), pp.
25
38
.
6.
Berthier
,
Y.
, 2005,
Wear - Materials, Mechanisms and Practice
,
John Wiley & Sons, Ltd.
, Chap. 12.
7.
Sawyer
,
W.
, and
Tichy
,
J.
, 2001, “
Lubrication With Granular Flow: Continuum Theory, Particle Simulations, Comparison With Experiment
,”
ASME J. Tribol.
,
123
, pp.
777
784
.
8.
Higgs
III,
C. F.
, and
Tichy
,
J.
, 2004, “
Granular Flow Lubrication: Continuum Modeling of Shear Behaviour
,”
ASME J. Tribol.
,
126
, pp.
499
509
.
9.
Yu
,
C.-M.
,
Craig
,
K.
, and
Tichy
,
J.
, 1994, “
Granular Collision Lubrication
,”
J. Rheol.
,
38
(
4
), pp.
921
936
.
10.
Hou
,
K.
,
Kalousek
,
J.
, and
Magel
,
E.
, 1997, “
Rheological Model of Solid Layer in Rolling Contact
,”
Wear
,
211
, pp.
134
140
.
11.
Zhou
,
L.
, and
Khonsari
,
M.
, 2000, “
Flow Characteristics of a Powder Lubricant Sheared Between Parallel Plates
,”
ASME J. Tribol.
,
122
(
1
), pp.
147
155
.
12.
Elrod
,
H.
, and
Brewe
,
D.
, 1991, “
Numerical Experiments With Flows of Elongated Granules
,”
Tribol. S.
,
21
, pp.
219
226
.
13.
Lubrecht
,
A.
, and
Berthier
,
Y.
, 1995, “
Granular Lubrication; a Simple Model and Trends
,”
Tribol. S.
,
30
, pp.
53
62
.
14.
Ghaouti
,
A.
,
Chaze
,
M.
,
Dubujet
,
P.
, and
Sidoroff
,
F.
, 1996, “
Particulate and Granular Simulation of the Third Body Behaviour
,”
Tribol. S.
,
31
, pp.
355
365
.
15.
Seve
,
B.
,
Iordanoff
,
I.
, and
Berthier
,
Y.
, 2001, “
A Discrete Solid Third Body Model: Influence of the Inter Granular Forces on the Macroscopic Behaviour
,”
Tribol. S.
,
39
, pp.
361
368
.
16.
Iordanoff
,
I.
,
Berthier
,
Y.
,
Descartes
,
S.
, and
Heshmat
,
H.
, 2002, “
A Review of Recent Approaches for Modeling Third Bodies
,”
ASME J. Tribol.
,
124
, pp.
725
735
.
17.
Fillot
,
N.
,
Iordanoff
,
I.
, and
Berthier
,
Y.
, 2004, “
A Granular Dynamic Model for the Degradation of Material
,”
ASME J. Tribol.
,
126
(
3
), pp.
606
614
.
18.
Renouf
,
M.
,
Saulot
,
A.
, and
Berthier
,
Y.
, 2006, “
Third Body Flow During a Wheel-Rail Interaction
,”
Proc. 3rd European Conference on Computational Mechanics Solids
,
C. A. M. S.
et al.
, eds., Lisboa, Portugal, CD-ROM.
19.
Kabir
,
A.
,
Jasti
,
V.
,
Higgs
III,
C. F.
, and
Lovell
,
M.
, 2008, “
An Evaluation of the Explicit Finite-Element Method Approach for Modelling Dense Flows of Discrete Grains in a Couette Shear Cell
,”
I. Mech. E
,
222
, pp.
715
723
.
20.
Moreau
,
J. J.
, 1994, “
Some Numerical Methods in Multibody Dynamics: Application to Granular Materials
,”
Eur. J. Mech. A Solids
,
13
(4-suppl.), pp.
93
114
.
21.
Jean
,
M.
, 1999, “
The Non Smooth Contact Dynamics Method
,”
Comput. Meth. Appl. Math. Engrg.
,
177
, pp.
235
257
.
22.
Saussine
,
G.
,
Cholet
,
C.
,
Dubois
,
F.
,
Bohatier
,
C.
,
Gautier
,
P.
, and
Moreau
,
J. J.
, 2006, “
Modelling Ballast Behaviour Under Dynamic Loading. Part 1: A 2D Polygonal Discrete Element Method Approach
,”
Comput. Meth. Appl. Mech. Engrg.
,
195
(
19–22
), pp.
2841
2859
.
23.
Acary
,
V.
, and
Jean
,
M.
, 2000, “
Numerical Modeling of Three Dimensional Divided Structures by the Non Smooth Contact Dynamics Method: Application to Masonry Structure
,”
Proc. 5th International Conference on Computational Structures Technology
,
B.
Topping
, ed., Civil-Comp Press, pp.
211
222
.
24.
Chevoir
,
F.
,
Roux
,
J.-N.
,
da Cruz
,
F.
,
Rognon
,
P.
, and
Koval
, Jr.,
G.
, 2009, “
Friction Law in Dense Granular Flows
,”
Powder Tech.
,
190
(
1–2
), pp.
264
268
.
25.
Iordanoff
,
I.
,
Sève
,
B.
, and
Berthier
,
Y.
, 2002, “
Solid Third Body Analysis Using a Discrete Approach: Influence of Adhesion and Particle Size on the Macroscopic Behavior of the Contact
,”
ASME J. Tribol.
,
124
, pp.
530
538
.
26.
Richard
,
D.
,
Iordanoff
,
I.
,
Berthier
,
Y.
,
Renouf
,
M.
, and
Fillot
,
N.
, 2007, “
Friction Coefficient as a Macroscopic View of Local Dissipation
,”
ASME J. Tribol.
,
129
(
4
),
p.
031404
.
27.
Iordanoff
,
I.
,
Fillot
,
N.
, and
Berthier
,
Y.
, 2005, “
Numerical Study of a Thin Layer of Cohesive Particles Under Plane Shearing
,”
Powder Tech.
,
159
(
1
), pp.
46
54
.
28.
Radjai
,
F.
,
Jean
,
M.
,
Moreau
,
J.-J.
, and
Roux
,
S.
, 1996, “
Force Distributions in Dense Two-Dimensional Granular Systems
,”
Phys. Rev. Lett.
,
77
(
2
), pp.
264
277
.
29.
Richard
,
D.
,
Iordanoff
,
I.
,
Renouf
,
M.
, and
Berthier
,
Y.
, 2008, “
Thermal Study of the Dry Sliding Contact With Third-Body Presence
,”
ASME J. Tribol.
,
130
(
3
), p.
031404
.
30.
Renouf
,
M.
,
Cao
,
H.-P.
, and
Nhu
,
V.-H.
, 2011, “
Multiphysical Modeling of Third-Body Rheology
,”
Tribol. Inter.
,
44
(
4
), pp.
417
425
.
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