In transient vehicle maneuvers, structural tire deformation due to the large load transfer causes abrupt change in normal contact pressure and slip distribution over the contact patch, and it has a dominant effect on characterizing the transient braking and cornering forces including the history-dependent friction-induced hysteresis effect. To account for the dynamic coupling of structural tire deformations and the transient tire friction behavior, a physics-based flexible tire model is developed using the laminated composite shell element based on the absolute nodal coordinate formulation and the distributed parameter LuGre tire friction model. In particular, a numerical procedure to integrate the distributed parameter LuGre tire friction model into the finite-element based spatial flexible tire model is proposed. To this end, the spatially discretized form of the LuGre tire friction model is derived and integrated into the finite-element tire model such that change in the normal contact pressure and slip distributions over the contact patch predicted by the deformable tire model enters into the spatially discretized LuGre tire friction model to predict the transient shear contact stress distribution. By doing so, the structural tire deformation and the LuGre tire friction force model are dynamically coupled in the final form of the equations, and these equations are integrated simultaneously forward in time at every time step. The tire model developed is experimentally validated and several numerical examples for hard braking and cornering simulation are presented to demonstrate capabilities of the physics-based flexible tire model developed in this study.

References

References
1.
Clark
,
S. K.
, ed.,
1981
, “
Mechanics of Pneumatic Tires
,”
NHTSA
, Washington, DC, Technical Report No.
US DOT HS805 952
.
2.
Lee
,
C. R.
,
Kim
,
J. W.
,
Hallquist
,
J. O.
,
Zhang
,
Y.
, and
Farahani
,
A. D.
,
1997
, “
Validation of a FEA Tire Model for Vehicle Dynamic Analysis and Full Vehicle Real Time Proving Ground Simulations
,”
SAE
Technical Paper No. 971100.
3.
Koishi
,
M.
,
Kabe
,
K.
, and
Shiratori
,
M.
,
1998
, “
Tire Cornering Simulation Using an Explicit Finite Element Analysis Code
,”
Tire Sci. Technol.
,
26
(
2
), pp.
109
119
.
4.
Gruber
,
P.
,
Sharp
,
R. S.
, and
Crocombe
,
A. D.
,
2012
, “
Normal and Shear Forces in the Contact Patch of a Braked Racing Tyre—Part 1: Results From a Finite-Element Model
,”
Veh. Syst. Dyn.
,
50
(
2
), pp.
323
337
.
5.
Tanner
,
J. A.
,
1996
, “
Computational Methods for Frictional Contact With Applications to the Space Shuttle Orbiter Nose-Gear Tire
,”
NASA Technical Report No. 3573
, pp.
1
52
.
6.
Gipser
,
M.
,
2005
, “
FTire: A Physically Based Application-Oriented Tyre Model for Use With Detailed MBS and Finite-Element Suspension Models
,”
Veh. Syst. Dyn.
,
43
(
Suppl. 1
), pp.
76
91
.
7.
Gallrein
,
A.
, and
Baecker
,
M.
,
2007
, “
CDTire: A Tire Model for Comfort and Durability Applications
,”
Veh. Syst. Dyn.
,
45
(Suppl.
1
), pp.
69
77
.
8.
Oertel
,
C.
, and
Fandre
,
A.
,
1999
, “
Ride Comfort Simulations and Step Towards Life Time Calculations: RMOD-K and ADAMS
,”
International ADAMS Conference
,
Berlin, Germany
, pp.
1
17
.
9.
Roller
,
M.
,
Betsch
,
P.
,
Gallrein
,
A.
, and
Linn
,
J.
,
2014
, “
On the Use of Geometrically Exact Shells for Dynamic Tyre Simulation
,”
Multibody Dynamics, Computational Methods in Applied Sciences
, Vol.
35
,
Z.
Terze
, ed.,
Springer-Verlag
,
New York
, pp.
205
236
.
10.
Roller
,
M.
,
Betsch
,
P.
,
Gallrein
,
A.
, and
Linn
,
J.
,
2015
, “
An Enhanced Tire Model for Dynamic Simulation Based on Geometrically Exact Shells
,”
ECCOMAS
Thematic Conference on Multibody Dynamics
,
Barcelona, Spain
, June 29–July 2, pp.
1260
1271
.
11.
Yamashita
,
H.
,
Matsutani
,
Y.
, and
Sugiyama
,
H.
,
2015
, “
Longitudinal Tire Dynamics Model for Transient Braking Analysis: ANCF-LuGre Tire Model
,”
ASME J. Comput. Nonlinear Dyn.
,
10
(
3
), p.
031003
.
12.
Sugiyama
,
H.
,
Yamashita
,
H.
, and
Jayakumar
,
P.
,
2014
, “
Right on Tracks—An Integrated Tire Model for Ground Vehicle Simulation
,”
Tire Technol. Int.
,
67
, pp.
52
55
.
13.
Sugiyama
,
H.
, and
Suda
,
Y.
,
2009
, “
Nonlinear Elastic Ring Tyre Model Using the Absolute Nodal Coordinate Formulation
,”
Proc. Inst. Mech. Eng., Part K
,
223
(
3
), pp.
211
219
.
14.
Shabana
,
A. A.
,
2005
,
Dynamics of Multibody Systems
,
Cambridge University Press
,
New York
.
15.
Gerstmayr
,
J.
,
Sugiyama
,
H.
, and
Mikkola
,
A.
,
2013
, “
Review on the Absolute Nodal Coordinate Formulation for Large Deformation Analysis of Multibody Systems
,”
ASME J. Comput. Nonlinear Dyn.
,
8
(
3
), p.
031016
.
16.
Hauptmann
,
R.
,
Doll
,
S.
,
Harnau
,
M.
, and
Schweizerhof
,
K.
,
1998
, “
A Systematic Development of ‘Solid-Shell’ Element Formulations for Linear and Non-Linear Analyses Employing Only Displacement Degrees of Freedom
,”
Int. J. Numer. Methods Eng.
,
42
(
1
), pp.
49
69
.
17.
Hauptmann
,
R.
,
Doll
,
S.
,
Harnau
,
M.
, and
Schweizerhof
,
K.
,
2001
, “
Solid-Shell Elements With Linear and Quadratic Shape Functions at Large Deformations With Nearly Incompressible Materials
,”
Comput. Struct.
,
79
(
18
), pp.
1671
1685
.
18.
Vu-Quoc
,
L.
, and
Tan
,
X. G.
,
2003
, “
Optimal Solid Shells for Non-Linear Analyses of Multilayer Composites: I Statics
,”
Comput. Methods Appl. Mech. Eng.
,
192
(
9–10
), pp.
975
1016
.
19.
Vu-Quoc
,
L.
, and
Tan
,
X. G.
,
2003
, “
Optimal Solid Shells for Nonlinear Analyses of Multilayer Composites—Part II: Dynamics
,”
Comput. Methods Appl. Mech. Eng.
,
192
(
9–10
), pp.
1017
1059
.
20.
Simo
,
J. C.
,
Rifai
,
M. S.
, and
Fox
,
D. D.
,
1990
, “
On a Stress Resultant Geometrically Exact Shell Model—Part IV: Variable Thickness Shells With Through-the-Thickness Stretching
,”
Int. J. Numer. Methods Eng.
,
81
(
1
), pp.
91
126
.
21.
Betsch
,
P.
, and
Stein
,
E.
,
1995
, “
An Assumed Strain Approach Avoiding Artificial Thickness Straining for a Non-Linear 4-Node Shell Element
,”
Commun. Numer. Methods Eng.
,
11
(
11
), pp.
899
909
.
22.
Betsch
,
P.
, and
Stein
,
E.
,
1996
, “
A Nonlinear Extensible 4-Node Shell Element Based on Continuum Theory and Assumed Strain Interpolations
,”
J. Nonlinear Sci.
,
6
(
2
), pp.
169
199
.
23.
Sugiyama
,
H.
,
Escalona
,
J. L.
, and
Shabana
,
A. A.
,
2003
, “
Formulation of Three-Dimensional Joint Constraints Using the Absolute Nodal Coordinates
,”
Nonlinear Dyn.
,
31
(
2
), pp.
167
195
.
24.
Sugiyama
,
H.
, and
Yamashita
,
H.
,
2011
, “
Spatial Joint Constraints for the Absolute Nodal Coordinate Formulation Using the Non-Generalized Intermediate Coordinates
,”
Multibody Syst. Dyn.
,
26
(
1
), pp.
15
36
.
25.
Kim
,
S.
,
Nikravesh
,
P. E.
, and
Gim
,
G.
,
2008
, “
A Two-Dimensional Tire Model on Uneven Roads for Vehicle Dynamic Simulation
,”
Veh. Syst. Dyn.
,
46
(
10
), pp.
913
930
.
26.
Shabana
,
A. A.
, and
Yakoub
,
R. Y.
,
2001
, “
Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Theory
,”
ASME J. Mech. Des.
,
123
(
4
), pp.
606
613
.
27.
Mikkola
,
A. M.
, and
Shabana
,
A. A.
,
2003
, “
A Non-Incremental Finite Element Procedure for the Analysis of Large Deformation of Plates and Shells in Mechanical System Applications
,”
Multibody Syst. Dyn.
,
9
(
3
), pp.
283
309
.
28.
Romero
,
I.
,
2008
, “
A Comparison of Finite Elements for Nonlinear Beams: The Absolute Nodal Coordinate and Geometrically Exact Formulations
,”
Multibody Syst. Dyn.
,
20
(
1
), pp.
51
68
.
29.
Bauchau
,
O. A.
,
Han
,
S. L.
,
Mikkola
,
A.
,
Matikainen
,
M. K.
, and
Gruber
,
P.
,
2015
, “
Experimental Validation of Flexible Multibody Dynamics Beam Formulations
,”
Multibody Syst. Dyn.
,
34
(
4
), pp.
373
389
.
30.
Kerkkänen
,
K. S.
,
Sopanen
,
J. T.
, and
Mikkola
,
A. M.
,
2005
, “
A Linear Beam Finite Element Based on the Absolute Nodal Coordinate Formulation
,”
ASME J. Mech. Des.
,
127
(
4
), pp.
621
630
.
31.
Garcia-Vallejo
,
D.
,
Mikkola
,
A. M.
, and
Escalona
,
J. L.
,
2007
, “
A New Locking-Free Shear Deformable Finite Element Based on Absolute Nodal Coordinates
,”
Nonlinear Dyn.
,
50
(
1
), pp.
249
264
.
32.
Nachbagauer
,
K.
,
Pechstein
,
S. A.
,
Irschik
,
H.
, and
Gerstmayr
,
J.
,
2011
, “
A New Locking Free Formulation for Planar, Shear Deformable, Linear and Quadratic Beam Finite Elements Based on the Absolute Nodal Coordinate Formulation
,”
Multibody Syst. Dyn.
,
26
(
3
), pp.
245
263
.
33.
Nachbagauer
,
K.
,
Gruber
,
P.
, and
Gerstmayr
,
J.
,
2013
, “
Structural and Continuum Mechanics Approaches for a 3D Shear Deformable ANCF Beam Finite Element: Application to Static and Linearized Dynamic Examples
,”
ASME J. Comput. Nonlinear Dyn.
,
8
(
2
), p.
021004
.
34.
Nachbagauer
,
K.
, and
Gerstmayr
,
J.
,
2014
, “
Structural and Continuum Mechanics Approaches for a 3D Shear Deformable ANCF Beam Finite Element: Application to Buckling and Nonlinear Dynamic Examples
,”
ASME J. Comput. Nonlinear Dyn.
,
9
(
1
), p.
011013
.
35.
Dmitrochenko
,
O.
,
Matikainen
,
M.
, and
Mikkola
,
A.
,
2012
, “
The Simplest 3-and 4-Noded Fully Parameterized ANCF Plate Elements
,”
ASME
Paper No. DETC2012-70524.
36.
Olshevskiy
,
A.
,
Dmitrochenko
,
O.
,
Dai
,
M. D.
, and
Kim
,
C.-W.
,
2015
, “
The Simplest 3-, 6- and 8-Noded Fully-Parameterized ANCF Plate Elements Using Only Transverse Slopes
,”
Multibody Syst. Dyn.
,
34
(
1
), pp.
23
51
.
37.
Yamashita
,
H.
,
Valkeapää
,
A.
,
Jayakumar
,
P.
, and
Sugiyama
,
H.
,
2015
, “
Continuum Mechanics Based Bi-Linear Shear Deformable Shell Element Using Absolute Nodal Coordinate Formulation
,”
ASME J. Comput. Nonlinear Dyn.
,
10
(
5
), p.
051012
.
38.
Valkeapää
,
A.
,
Yamashita
,
H.
,
Jayakumar
,
P.
, and
Sugiyama
,
H.
,
2015
, “
On the Use of Elastic Middle Surface Approach in the Large Deformation Analysis of Moderately Thick Shell Structures Using Absolute Nodal Coordinate Formulation
,”
Nonlinear Dyn.
,
80
(
3
), pp.
1133
1146
.
39.
Dvorkin
,
E. N.
, and
Bathe
,
K. J.
,
1984
, “
A Continuum Mechanics Based Four-Node Shell Element for General Non-Linear Analysis
,”
Eng. Comput.
,
1
(
1
), pp.
77
88
.
40.
Bathe
,
K. J.
, and
Dvorkin
,
E. N.
,
1985
, “
A Four-Node Plate Bending Element Based on Mindlin/Reissner Plate Theory and a Mixed Interpolation
,”
Int. J. Numer. Methods Eng.
,
21
(
2
), pp.
367
383
.
41.
Simo
,
J. C.
, and
Rifai
,
M. S.
,
1990
, “
A Class of Mixed Assumed Strain Methods and the Method of Incompatible Modes
,”
Int. J. Numer. Methods Eng.
,
29
(
8
), pp.
1595
1638
.
42.
Andelfinger
,
U.
, and
Ramm
,
E.
,
1993
, “
EAS-Elements for Two-Dimensional, Three-Dimensional, Plate and Shell Structures and Their Equivalence to HR-Elements
,”
Int. J. Numer. Methods Eng.
,
36
(
8
), pp.
1311
1337
.
43.
Jones
,
R. M.
,
1999
,
Mechanics of Composite Materials
,
Taylor and Francis
,
New York
.
44.
Noor
,
A. K.
, and
Burton
,
W. S.
,
1989
, “
Assessment of Shear Deformation Theories for Multilayered Composite Plates
,”
ASME Appl. Mech. Rev.
,
42
(
1
), pp.
1
13
.
45.
Noor
,
A. K.
, and
Burton
,
W. S.
,
1990
, “
Assessment of Computational Models for Multilayered Composite Shells
,”
ASME Appl. Mech. Rev.
,
43
(
4
), pp.
67
97
.
46.
Canudas-de-Wit
,
C.
,
Tsiotras
,
P.
,
Velenis
,
E.
,
Basset
,
M.
, and
Gissinger
,
G.
,
2003
, “
Dynamic Friction Models for Road/Tire Longitudinal Interaction
,”
Veh. Syst. Dyn.
,
39
(
3
), pp.
189
226
.
47.
Deur
,
J.
,
Asgari
,
J.
, and
Hrovat
,
D.
,
2004
, “
A 3D Brush-Type Dynamic Tire Friction Model
,”
Veh. Syst. Dyn.
,
42
(
3
), pp.
133
173
.
48.
Bathe
,
K. J.
,
1996
,
Finite Element Procedures
,
Prentice Hall
,
Englewood Cliffs, NJ
.
49.
Hilber
,
H. M.
,
Hughes
,
T. J. R.
, and
Taylor
,
R. L.
,
1977
, “
Improved Numerical Dissipation for Time Integration Algorithms in Structural Dynamics
,”
Earthquake Eng. Struct. Dyn.
,
5
(
3
), pp.
265
284
.
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