Development of a finite element contact analysis algorithm for charged-hydrated soft tissues with large sliding

International Journal for Numerical Methods in Engineering

Volumn 78, Issue 4, 2009, Pages 483-504

  Chen, Xian ^a   Sunagawa, Kenji ^b   Hisada, Toshiaki ^c  

^a KYUSHU UNIVERSITY   (Japan)

^b KYUSHU UNIVERSITY   (Japan)

^c UNIVERSITY OF TOKYO   (Japan)

Author keywords

Cartilage; Charged hydrated soft tissue; Contact problem; Finite element methods; Patch test

Indexed keywords

ARTICULAR CARTILAGES; BIOLOGICAL SOFT TISSUES; CHARGED-HYDRATED SOFT TISSUE; CONTACT ANALYSIS; CONTACT BOUNDARIES; CONTACT PATCHES; CONTACT PHENOMENON; CONTACT PRESSURES; CONTACT PROBLEM; CONTACT SURFACES; CONTINUOUS DISTRIBUTIONS; DEGREES OF FREEDOMS; ELECTROCHEMICAL POTENTIALS; FINITE ELEMENT METHODS; FINITE-ELEMENT ANALYSIS; FLUID FLOWS; INTERSTITIAL FLUIDS; LAGRANGE MULTIPLIER APPROACHES; LARGE DEFORMATIONS; LARGE SLIDING; MOLAR FLOWS; NUMERICAL EXAMPLES; ONE PASS; OVER CONSTRAINTS; PATCH TEST;

CARTILAGE; FINITE ELEMENT METHOD; HISTOLOGY; HYDRATES; HYDRATION; LIGAMENTS;

LAGRANGE MULTIPLIERS;

EID: 64049092719     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2497     Document Type: Article

References (43)

1. Maroudas A. In Physico-Chemical Properties of Articular Cartilage: Adult Articular Cartilage, Freeman MAR (ed.). Pitman Medical: London, 1979.
2. Eisenberg SR, Grodzinsky AJ. The kinetics of chemically-induced nonequilibrium swelling of articular-cartilage and corneal stroma. Journal of Biomechanical Engineering - Transactions of the ASME 1987; 109(1):79-89.
3. Frank EH, Grodzinsky AJ. Cartilage electromechanics. 1. Electrokinetic transduction and the effects of electrolyte Ph and ionic-strength. Journal of Biomechanics 1987; 20(6):615-627.
4. Lanir Y. Biorheology and fluid flux in swelling tissues. 1. Bicomponent theory for small deformations, including concentration effects. Biorheology 1987; 24(2):173-187.
5. Maroudas A, Bannon C. Measurement of swelling pressure in cartilage and comparison with the osmotic-pressure of constituent proteoglycans. Biorheology 1981; 18(3-6):619-632.
6. Myers ER, Lai WM, Mow VC. A continuum theory and an experiment for the ion-induced swelling behavior of articular-cartilage. Journal of Biomechanical Engineering - Transactions of the ASME 1984; 106(2):151-158.
7. Parsons JR, Black J. Mechanical-behavior of articular cartilage - quantitative changes with alteration of ionic environment. Journal of Biomechanics 1979; 12(10):765-773.
8. Frank EH, Grodzinsky AJ. Cartilage electromechanics. 2. A continuum model of cartilage electrokinetics and correlation with experiments. Journal of Biomechanics 1987; 20(6):629-639.
9. Lai WM, Hou JS, Mow VC. A triphasic theory for the swelling and deformation behaviors of articular-cartilage. Journal of Biomechanical Engineering - Transactions of the ASME 1991; 113(3):245-258.
10. Huyghe JM, Janssen JD. Quadriphasic mechanics of swelling incompressible porous media. International Journal of Engineering Science 1997; 35(8):793-802.
11. Gu WY, Lai WM, Mow VC. A mixture theory for charged-hydrated soft tissues containing multi-electrolytes: passive transport and swelling behaviors. Journal of Biomechanical Engineering - Transactions of the ASME 1998; 120(2):169-180.
12. Chen Y, Chen X, Hisada T. Non-linear finite element analysis of mechanical electrochemical phenomena in hydrated soft tissues based on triphasic theory. International Journal for Numerical Methods in Engineering 2006; 65(2):147-173.
13. Sun DN, Gu WY, Guo XE, Lai WM, Mow VC. A mixed finite element formulation of triphasic mechano-electrochemical theory for charged, hydrated biological soft tissues. International Journal for Numerical Methods in Engineering 1999; 45(10):1375-1402.
14. van Loon R, Huyghe JM, Wijlaars MW, Baaijens FPT. 3D FE implementation of an incompressible quadriphasic mixture model. International Journal for Numerical Methods in Engineering 2003; 57(9):1243-1258.
15. Ateshian GA. A theoretical formulation for boundary friction in articular cartilage. Journal of Biomechanical Engineering - Transactions of the ASME 1997; 119(1):81-86.
16. Ateshian GA, Lai WM, Zhu WB, Mow VC. An asymptotic solution for the contact of 2 biphasic cartilage layers. Journal of Biomechanics 1994; 27(11):1347-1360.
17. Ateshian GA, Wang H. A theoretical solution for the frictionless rolling contact of cylindrical biphasic articular cartilage layers - reply. Journal of Biomechanics 1997; 30(1):99-99.
18. Ateshian GA, Wang HQ. A theoretical solution for the frictionless rolling-contact of cylindrical biphasic articular-cartilage layers. Journal of Biomechanics 1995; 28(11):1341-1355.
19. Ateshian GA, Wang HQ, Lai WM. The role of interstitial fluid pressurization and surface porosities on the boundary friction of articular cartilage. Journal of Tribology - Transactions of the ASME 1998; 120(2):241-248.
20. Federico S, La Rosa G, Herzog W, Wu JZ. Effect of fluid boundary conditions on joint contact mechanics and applications to the modeling of osteoarthritic joints. Journal of Biomechanical Engineering - Transactions of the ASME 2004; 126(2):220-225.
21. Hlavacek M. A note on an asymptotic solution for the contact of two biphasic cartilage layers in a loaded synovial joint at rest. Journal of Biomechanics 1999; 32(9):987-991.
22. Kelkar R, Ateshian GA. Contact creep of biphasic cartilage layers. Journal of Applied Mechanics - Transactions of the ASME 1999; 66(1):137-145.
23. Wu JZ, Herzog W. On the pressure gradient boundary condition for the contact of two biphasic cartilage layers. Journal of Biomechanics 2000; 33(10):1331-1332.
24. Wu JZ, Herzog W, Epstein M. An improved solution for the contact of two biphasic cartilage layers. Journal of Biomechanics 1997; 30(4):371-375.
25. Wu JZ, Herzog W, Epstein M. Articular joint mechanics with biphasic cartilage layers under dynamic loading. Journal of Biomechanical Engineering - Transactions of the ASME 1998; 120(1):77-84.
26. Wu JZ, Herzog W, Ronsky J. Modeling axi-symmetrical joint contact with biphasic cartilage layers - an asymptotic solution. Journal of Biomechanics 1996; 29(10):1263-1281.
27. Donzelli PS, Spilker RL. A contact finite element formulation for biological soft hydrated tissues. Computer Methods in Applied Mechanics and Engineering 1998; 153(1-2):63-79.
28. Donzelli PS, Spilker RL, Ateshian GA, Mow VC. Contact analysis of biphasic transversely isotropic cartilage layers and correlations with tissue failure. Journal of Biomechanics 1999; 32(10):1037-1047.
29. Dunbar WL, Un K, Donzelli PS, Spilker RL. An evaluation of three-dimensional diarthrodial joint contact using penetration data and the finite element method. Journal of Biomechanical Engineering - Transactions of the ASME 2001; 123(4):333-340.
30. Han SK, Federico S, Epstein M, Herzog W. An articular cartilage contact model based on real surface geometry. Journal of Biomechanics 2005; 38(1):179-184.
31. Krishnan R, Park S, Eckstein F, Ateshian GA. Inhomogeneous cartilage properties enhance superficial interstitial fluid support and frictional properties, but do not provide a homogeneous state of stress. Journal of Biomechanical Engineering - Transactions of the ASME 2003; 125(5):569-577.
32. Wu JZ, Herzog W, Epstein M. Evaluation of the finite element software ABAQUS for biomechanical modelling of biphasic tissues. Journal of Biomechanics 1998; 31(2):165-169.
33. Yang T, Spilker RL. A Lagrange multiplier mixed finite element formulation for three-dimensional contact of biphasic tissues. Journal of Biomechanical Engineering - Transactions of the ASME 2007; 129(3):457-471.
34. Pawaskar SS, Jin ZM, Fisher J. Modelling of fluid support inside articular cartilage during sliding. Proceedings of the Institution of Mechanical Engineers Part J-Journal of Engineering Tribology 2007; 221(13):165-174.
35. Chen X, Chen Y, Hisada T. Development of a finite element procedure of contact analysis for articular cartilage with large deformation based on the biphasic theory. JSME International Journal Series C-Mechanical Systems Machine Elements and Manufacturing 2005; 48(4):537-546.
36. Setton LA, Tohyama H, Mow VC. Swelling and curling behaviors of articular cartilage. Journal of Biomechanical Engineering - Transactions of the ASME 1998; 120(3):355-361.
37. Bachrach NM, Valhmu WB, Stazzone E, Ratcliffe A, Lai WM, Mow VC. Changes in proteoglycan synthesis of chondrocytes in articular cartilage are associated with the time-dependent changes in their mechanical environment. Journal of Biomechanics 1995; 28(12):1561-1569.
38. Huyghe JM, Janssen CF, van Donkelaar CC, Lanir Y. Measuring principles of frictional coefficients in cartilaginous tissues and its substitutes. Biorheology 2002; 39(1-2):47-53.
39. Ateshian GA, Soltz MA, Mauck RL, Basalo IM, Hung CT, Lai WM. The role of osmotic pressure and tension-compression nonlinearity in the frictional response of articular cartilage. Transport in Porous Media 2003; 50(1-2):5-33.
40. Hou JS, Holmes MH, Lai WM, Mow VC. Boundary-conditions at the cartilage-synovial fluid interface for joint lubrication and theoretical verifications. Journal of Biomechanical Engineering - Transactions of the ASME 1989; 111(1):78-87.
41. El-Abbasi N, Bathe KJ. Stability and patch test performance of contact discretizations and a new solution algorithm. Computers and Structures 2001; 79(16):1473-1486.
42. Chen X, Hisada T. Development of a finite element contact analysis algorithm to pass the patch test. JSME International Journal Series A - Solid Mechanics and Materials Engineering 2006; 49(4):483-491.
43. Mow VC, Ateshian GA, Lai WM, Gu WY. Effects of fixed charges on the stress-relaxation behavior of hydrated soft tissues in a confined compression problem. International Journal of Solids and Structures 1998; 35(34-35):4945-4962.