Abstract
This study formulates and implements a finite element contact algorithm for solid-fluid (biphasic) mixtures, accommodating both finite deformation and sliding. The finite element source code is made available to the general public. The algorithm uses a penalty method regularized with an augmented Lagrangian method to enforce the continuity of contact traction and normal component of fluid flux across the contact interface. The formulation addresses the need to automatically enforce free-draining conditions outside of the contact interface. The accuracy of the implementation is verified using contact problems, for which exact solutions are obtained by alternative analyses. Illustrations are also provided that demonstrate large deformations and sliding under configurations relevant to biomechanical applications such as articular contact. This study addresses an important computational need in the biomechanics of porous-permeable soft tissues. Placing the source code in the public domain provides a useful resource to the biomechanics community.
Issue Section:
Research Papers
References
1.
Donzelli
, P.
S.
, and Spilker
, R.
L.
, 1998,
“A Contact Finite Element Formulation for Biological Soft
Hydrated Tissues
,” Comput. Methods Appl. Mech.
Eng.
0045-7825, 153
(1–2
), pp.
63
–79
.2.
Mow
, V.
C.
, Kuei
, S.
C.
, Lai
, W.
M.
, and Armstrong
,
C. G.
, 1980,
“Biphasic Creep and Stress Relaxation of Articular Cartilage
in Compression: Theory and Experiments
,” J. Biomech.
Eng.
0148-0731, 102
(1
), pp.
73
–84
.3.
Yang
,
T.
, and
Spilker
, R.
L.
, 2007,
“A Lagrange Multiplier Mixed Finite Element Formulation for
Three-Dimensional Contact of Biphasic Tissues
,” J.
Biomech. Eng.
0148-0731, 129
(3
), pp.
457
–471
.4.
Chen
,
X.
,
Chen
,
Y.
, and
Hisada
,
T.
,
2005, “Development of a
Finite Element Procedure of Contact Analysis for Articular Cartilage With
Large Deformation Based on the Biphasic Theory
,”
JSME Int. J., Ser. C
1340-8062, 48
(4
), pp.
537
–546
.5.
Federico
,
S.
,
La Rosa
,
G.
,
Herzog
,
W.
, and
Wu
, J. Z.
, 2004,
“Effect of Fluid Boundary Conditions on Joint Contact
Mechanics and Applications to the Modeling of Osteoarthritic
Joints
,” J. Biomech. Eng.
0148-0731, 126
(2
), pp.
220
–225
(Erratum in:
Federico
,
S.
,
La Rosa
,
G.
,
Herzog
,
W.
, and
Wu
, J. Z.
(2005),
J. Biomech. Eng.
0148-0731, 127
(1
), pp.
205
–209
).6.
Warner
, M.
D.
, Taylor
, W.
R.
, and Clift
, S.
E.
, 2001,
“Finite Element Biphasic Indentation of Cartilage: A
Comparison of Experimental Indenter and Physiological Contact
Geometries
,” Proc. Inst. Mech. Eng., Part H: J. Eng.
Med.
0954-4119, 215
(5
), pp.
487
–496
.7.
Wu
, J.
Z.
, Herzog
,
W.
, and
Epstein
,
M.
,
1997, “Evaluation of the
Finite Element Software ABAQUS for Biomechanical Modelling of
Biphasic Tissues
,” J. Biomech.
0021-9290, 31
(2
), pp.
165
–169
.8.
Laursen
, T.
A.
, and Simo
, J.
C.
, 1993,
“Continuum-Based Finite Element Formulation for the Implicit
Solution of Multibody, Large Deformation Frictional Contact
Problems
,” Int. J. Numer. Methods Eng.
0029-5981, 36
(20
), pp.
3451
–3485
.9.
Simo
, J.
C.
, and Laursen
, T.
A.
, 1992,
“Augmented Lagrangian Treatment of Contact Problems Involving
Friction
,” Comput. Struct.
0045-7949, 42
(1
), pp.
97
–116
.10.
Bowen
, R.
M.
, 1980,
“Incompressible Porous Media Models by Use of the Theory of
Mixtures
,” Int. J. Eng. Sci.
0020-7225, 18
(9
), pp.
1129
–1148
.11.
Truesdell
,
C.
, and
Toupin
,
R.
,
1960, The Classical Field
Theories
, Springer
,
Heidelberg
.12.
Ün
,
K.
, and
Spilker
, R.
L.
, 2006,
“A Penetration-Based Finite Element Method for Hyperelastic
3D Biphasic Tissues in Contact. Part II: Finite Element
Simulations
,” J. Biomech. Eng.
0148-0731, 128
(6
), pp.
934
–942
.13.
Bonet
,
J.
, and
Wood
, R.
D.
, 1997,
Nonlinear Continuum Mechanics for Finite Element Analysis
,
Cambridge University Press
,
Cambridge, NY
.14.
Curnier
,
A.
,
Qi-Chang
,
H.
, and
Zysset
,
P.
,
1994, “Conewise Linear
Elastic Materials
,” J. Elast.
0374-3535, 37
(1
), pp.
1
–38
.15.
Ateshian
, G.
A.
, Lai
, W.
M.
, Zhu
, W.
B.
, and Mow
, V.
C.
, 1994,
“An Asymptotic Solution for the Contact of Two Biphasic
Cartilage Layers
,” J. Biomech.
0021-9290, 27
(11
), pp.
1347
–1360
.16.
Hou
, J.
S.
, Holmes
, M.
H.
, Lai
, W.
M.
, and Mow
, V.
C.
, 1989,
“Boundary Conditions at the Cartilage-Synovial Fluid
Interface for Joint Lubrication and Theoretical
Verifications
,” J. Biomech. Eng.
0148-0731, 111
(1
), pp.
78
–87
.17.
Ateshian
, G.
A.
, 2009,
“The Role of Interstitial Fluid Pressurization in Articular
Cartilage Lubrication
,” J. Biomech.
0021-9290, 42
(9
), pp.
1163
–1176
.18.
El-Abbasi
,
N.
, and
Bathe
, K.
-J.
,
2001, “Stability and
Patch Test Performance of Contact Discretizations and a New Solution
Algorithm
,” Comput. Struct.
0045-7949, 79
(16
), pp.
1473
–1486
.19.
Ateshian
, G.
A.
, 2007,
“On the Theory of Reactive Mixtures for Modeling Biological
Growth
,” Biomech. Model. Mechanobiol.
1617-7959, 6
(6
), pp.
423
–445
.20.
Holmes
, M.
H.
, and Mow
, V.
C.
, 1990,
“The Nonlinear Characteristics of Soft Gels and Hydrated
Connective Tissues in Ultrafiltration
,” J.
Biomech.
0021-9290, 23
(11
), pp.
1145
–1156
.21.
Ateshian
, G.
A.
, Warden
, W.
H.
, Kim
, J.
J.
, Grelsamer
, R.
P.
, and Mow
, V.
C.
, 1997,
“Finite Deformation Biphasic Material Properties of Bovine
Articular Cartilage From Confined Compression Experiments
,”
J. Biomech.
0021-9290, 30
(11–12
), pp.
1157
–1164
.22.
Mak
, A.
F.
, Lai
, W.
M.
, and Mow
, V.
C.
, 1987,
“Biphasic Indentation of Articular Cartilage—I. Theoretical
Analysis
,” J. Biomech.
0021-9290, 20
(7
), pp.
703
–714
.23.
Ateshian
, G.
A.
, Ellis
, B.
J.
, and Weiss
, J.
A.
, 2007,
“Equivalence Between Short-Time Biphasic and Incompressible
Elastic Material Responses
,” J. Biomech.
Eng.
0148-0731, 129
(3
), pp.
405
–412
.24.
Ateshian
, G.
A.
, and Wang
,
H.
,
1995, “A Theoretical
Solution for the Frictionless Rolling Contact of Cylindrical Biphasic
Articular Cartilage Layers
,” J. Biomech.
0021-9290, 28
(11
), pp.
1341
–1355
.25.
Li
, L.
P.
, and Herzog
,
W.
,
2006, “Arthroscopic
Evaluation of Cartilage Degeneration Using Indentation Testing—Influence of
Indenter Geometry
,” Clin. Biomech. (Bristol,
Avon)
0268-0033, 21
(4
), pp.
420
–426
.26.
Li
, L.
P.
, Cheung
, J.
T.
, and Herzog
,
W.
,
2009, “Three-Dimensional
Fibril-Reinforced Finite Element Model of Articular
Cartilage
,” Med. Biol. Eng. Comput.
0140-0118, 47
(6
), pp.
607
–615
.27.
Ferguson
, S.
J.
, Bryant
, J.
T.
, Ganz
,
R.
, and
Ito
,
K.
,
2000, “The Influence of
the Acetabular Labrum on Hip Joint Cartilage Consolidation: A Poroelastic
Finite Element Model
,” J. Biomech.
0021-9290, 33
(8
), pp.
953
–960
.28.
Ferguson
, S.
J.
, Bryant
, J.
T.
, Ganz
,
R.
, and
Ito
,
K.
,
2000, “The Acetabular
Labrum Seal: A Poroelastic Finite Element Model
,”
Clin. Biomech. (Bristol, Avon)
0268-0033, 15
(6
), pp.
463
–468
.29.
Vadher
, S.
P.
, Nayeb-Hashemi
,
H.
,
Canavan
, P.
K.
, and Warner
, G.
M.
, 2006,
“Finite Element Modeling Following Partial Meniscectomy:
Effect of Various Size of Resection
,” Conf. Proc.
IEEE End. Med. Biol. Soc.
0018-9219, 1
, pp.
2098
–2101
.30.
Dunbar
, W.
L.
, Jr.,
Un
,
K.
,
Donzelli
, P.
S.
, and Spilker
, R.
L.
, 2001,
“An Evaluation of Three-Dimensional Diarthrodial Joint
Contact Using Penetration Data and the Finite Element
Method
,” J. Biomech. Eng.
0148-0731, 123
(4
), pp.
333
–340
.31.
Un
,
K.
, and
Spilker
, R.
L.
, 2006,
“A Penetration-Based Finite Element Method for Hyperelastic
3D Biphasic Tissues in Contact: Part 1—Derivation of Contact Boundary
Conditions
,” J. Biomech. Eng.
0148-0731, 128
(1
), pp.
124
–130
.32.
Maker
, B.
N.
, 1995,
“NIKE3D: A Nonlinear, Implicit, Three-Dimensional Finite
Element Code for Solid and Structural Mechanics
,”
Lawrence Livermore Lab
Technical Report No.
UCRL-MA-105268.Copyright © 2010
by American Society of Mechanical Engineers
You do not currently have access to this content.
