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
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
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