234
Views
59
CrossRef citations to date
0
Altmetric
Original Articles

Mixed and Penalty Finite Element Models for the Nonlinear Behavior of Biphasic Soft Tissues in Finite Deformation: Part I — Alternate Formulations

&
Pages 25-46 | Received 04 Jan 1997, Published online: 31 Mar 2010

Keep up to date with the latest research on this topic with citation updates for this article.

Read on this site (5)

Hongqiang Guo & Robert L. Spilker. (2014) An augmented Lagrangian finite element formulation for 3D contact of biphasic tissues. Computer Methods in Biomechanics and Biomedical Engineering 17:11, pages 1206-1216.
Read now
Taiseung Yang & Robert L. Spilker. (2007) A Study of preconditioned Krylov subspace methods with reordering for linear systems from a biphasic v–p finite element formulation. Computer Methods in Biomechanics and Biomedical Engineering 10:1, pages 13-24.
Read now
Samer M. Adeeb, Ezzeldin Y. Sayed Ahmed, John Matyas, David A. Hart, Cyril B. Frank & Nigel G. Shrive. (2004) Congruency Effects on Load Bearing in Diarthrodial Joints. Computer Methods in Biomechanics and Biomedical Engineering 7:3, pages 147-157.
Read now
E. A. MEROI, A. N. NATALI & B. A. SCHREFLER. (1999) A Porous Media Approach to Finite Deformation Behaviour in Soft Tissues. Computer Methods in Biomechanics and Biomedical Engineering 2:3, pages 157-170.
Read now
EDGARDS. ALMEIDA & ROBERTL. SPILKER. (1997) Mixed and Penalty Finite Element Models for the Nonlinear Behavior of Biphasic Soft Tissues in Finite Deformation: Part II — Nonlinear Examples. Computer Methods in Biomechanics and Biomedical Engineering 1:2, pages 151-170.
Read now

Articles from other publishers (54)

Bruno Klahr, José Luís Medeiros Thiesen, Otávio Teixeira Pinto, Thiago André Carniel & Eduardo Alberto Fancello. (2022) An investigation of coupled solution algorithms for finite‐strain poroviscoelasticity applied to soft biological tissues. International Journal for Numerical Methods in Engineering 123:9, pages 2112-2141.
Crossref
David M. Pierce. (2021) Multi-phase, large-strain constitutive models of cartilage for finite element analyses in 3-D. Archive of Applied Mechanics 92:2, pages 513-528.
Crossref
Jay J. Shim, Steve A. Maas, Jeffrey A. Weiss & Gerard A. Ateshian. (2021) Finite Element Implementation of Biphasic-Fluid Structure Interactions in febio . Journal of Biomechanical Engineering 143:9.
Crossref
M. Kerem Ün & Ahmet Çalık. (2019) Estimation of depth-dependent material properties of biphasic soft tissues through finite element optimization and sensitivity analysis. Medical Engineering & Physics 74, pages 73-81.
Crossref
M. Kerem ÜN. (2019) Sonlu Elemanlar Yöntemi ve Hassasiyet Analizi ile İki Fazlı Yumuşak Dokuların Malzeme Özelliklerinin TayiniDetermination of Material Properties of Biphasic Tissues Using Finite Element Method and Sensitivity Analysis. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi 34:1, pages 201-210.
Crossref
. 2018. Multiscale Biomechanics. Multiscale Biomechanics 511 554 .
Peter A. Wijeratne, John H. Hipwell, David J. Hawkes, Triantafyllos Stylianopoulos & Vasileios Vavourakis. (2017) Multiscale biphasic modelling of peritumoural collagen microstructure: The effect of tumour growth on permeability and fluid flow. PLOS ONE 12:9, pages e0184511.
Crossref
Steve A. MaasGerard A. Ateshian & Jeffrey A. Weiss. (2017) FEBio: History and Advances. Annual Review of Biomedical Engineering 19:1, pages 279-299.
Crossref
Michelle Hine Armstrong, Adrián Buganza Tepole, Ellen Kuhl, Bruce R. Simon & Jonathan P. Vande Geest. (2016) A Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growth. PLOS ONE 11:4, pages e0152806.
Crossref
Hongqiang Guo, Mitul Shah & Robert L Spilker. (2014) A finite element implementation for biphasic contact of hydrated porous media under finite deformation and sliding. Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 228:3, pages 225-236.
Crossref
J.L. Harper, B.R. Simon & J.P. Vande Geest. (2014) A one-dimensional mixed porohyperelastic transport swelling finite element model with growth. Journal of the Mechanical Behavior of Biomedical Materials 29, pages 663-675.
Crossref
Gerard A. Ateshian, Steve Maas & Jeffrey A. Weiss. (2013) Multiphasic Finite Element Framework for Modeling Hydrated Mixtures With Multiple Neutral and Charged Solutes. Journal of Biomechanical Engineering 135:11.
Crossref
Hongqiang Guo, Suzanne A. Maher & Robert L. Spilker. (2013) Biphasic finite element contact analysis of the knee joint using an augmented Lagrangian method. Medical Engineering & Physics 35:9, pages 1313-1320.
Crossref
Hamid Khodaei, Salar Mostofizadeh, Karin Brolin, Håkan Johansson & Jonas Östh. (2013) Simulation of active skeletal muscle tissue with a transversely isotropic viscohyperelastic continuum material model. Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 227:5, pages 571-580.
Crossref
Beth WinkelsteinReza Shirazi, Scott Hazelwood, Robert Sah & Stephen Klisch. 2012. Orthopaedic Biomechanics. Orthopaedic Biomechanics 383 418 .
Hongqiang Guo, Jeffrey C. Nickel, Laura R. Iwasaki & Robert L. Spilker. (2012) An Augmented Lagrangian Method for Sliding Contact of Soft Tissue. Journal of Biomechanical Engineering 134:8.
Crossref
Joshua H. Smith, Kathleen A. Starkweather & José Jaime García. (2011) Implications of Transvascular Fluid Exchange in Nonlinear, Biphasic Analyses of Flow-Controlled Infusion in Brain. Bulletin of Mathematical Biology 74:4, pages 881-907.
Crossref
Stanislav Polzer, T Gasser, Bernd Markert, Jiri Bursa & Pavel Skacel. (2012) Impact of poroelasticity of intraluminal thrombus on wall stress of abdominal aortic aneurysms. BioMedical Engineering OnLine 11:1, pages 62.
Crossref
Hongqiang Guo & Robert L. Spilker. (2011) Biphasic Finite Element Modeling of Hydrated Soft Tissue Contact Using an Augmented Lagrangian Method. Journal of Biomechanical Engineering 133:11.
Crossref
Franck J. Vernerey & Mehdi Farsad. (2011) A constrained mixture approach to mechano-sensing and force generation in contractile cells. Journal of the Mechanical Behavior of Biomedical Materials 4:8, pages 1683-1699.
Crossref
John R. Owen & Jennifer S. Wayne. (2010) Contact models of repaired articular surfaces: influence of loading conditions and the superficial tangential zone. Biomechanics and Modeling in Mechanobiology 10:4, pages 461-471.
Crossref
Jonathan P. Vande Geest, B. R. Simon, Paul H. Rigby & Tyler P. Newberg. (2011) Coupled Porohyperelastic Mass Transport (PHEXPT) Finite Element Models for Soft Tissues Using ABAQUS. Journal of Biomechanical Engineering 133:4.
Crossref
Hongqiang Guo & Robert Spilker. (2011) An augmented Lagrange finite element implementation for 2D axisymmetric contact of biphasic tissues. An augmented Lagrange finite element implementation for 2D axisymmetric contact of biphasic tissues.
Gerard A. Ateshian & Jeffrey A. Weiss. (2010) Anisotropic Hydraulic Permeability Under Finite Deformation. Journal of Biomechanical Engineering 132:11.
Crossref
Joshua H. Smith & José Jaime García. (2009) A nonlinear biphasic model of flow-controlled infusion in brain: Fluid transport and tissue deformation analyses. Journal of Biomechanics 42:13, pages 2017-2025.
Crossref
J. A. Teixeira de Freitas & M. Toma. (2009) Hybrid‐Trefftz stress elements for incompressible biphasic media. International Journal for Numerical Methods in Engineering 79:2, pages 205-238.
Crossref
Gerard A. Ateshian. (2009) The role of interstitial fluid pressurization in articular cartilage lubrication. Journal of Biomechanics 42:9, pages 1163-1176.
Crossref
R. L. Spilker, J. C. Nickel & L. R. Iwasaki. (2009) A Biphasic Finite Element Model of In Vitro Plowing Tests of the Temporomandibular Joint Disc. Annals of Biomedical Engineering 37:6, pages 1152-1164.
Crossref
José Jaime García & Joshua H. Smith. (2008) A Biphasic Hyperelastic Model for the Analysis of Fluid and Mass Transport in Brain Tissue. Annals of Biomedical Engineering 37:2, pages 375-386.
Crossref
Marie E. Rognes, M.-Carme Calderer & Catherine A. Micek. (2009) Modelling of and Mixed Finite Element Methods for Gels in Biomedical Applications. SIAM Journal on Applied Mathematics 70:4, pages 1305-1329.
Crossref
Taiseung Yang & Robert L. Spilker. (2007) A Lagrange Multiplier Mixed Finite Element Formulation for Three-Dimensional Contact of Biphasic Tissues. Journal of Biomechanical Engineering 129:3, pages 457-471.
Crossref
Gerard A. Ateshian, Benjamin J. Ellis & Jeffrey A. Weiss. (2007) Equivalence Between Short-Time Biphasic and Incompressible Elastic Material Responses. Journal of Biomechanical Engineering 129:3, pages 405-412.
Crossref
Mansoor A. Haider & Farshid Guilak. (2007) Application of a three-dimensional poroelastic BEM to modeling the biphasic mechanics of cell–matrix interactions in articular cartilage. Computer Methods in Applied Mechanics and Engineering 196:31-32, pages 2999-3010.
Crossref
José Jaime García & Daniel Humberto Cortés. (2007) A biphasic viscohyperelastic fibril-reinforced model for articular cartilage: Formulation and comparison with experimental data. Journal of Biomechanics 40:8, pages 1737-1744.
Crossref
G. A. Ateshian, K. D. Costa & C. T. Hung. (2006) A Theoretical Analysis of Water Transport Through Chondrocytes. Biomechanics and Modeling in Mechanobiology 6:1-2, pages 91-101.
Crossref
Kerem Ün & Robert L. Spilker. (2006) A Penetration-Based Finite Element Method for Hyperelastic 3D Biphasic Tissues in Contact. Part II: Finite Element Simulations. Journal of Biomechanical Engineering 128:6, pages 934-942.
Crossref
A. Pérez del Palomar & M. Doblaré. (2006) On the numerical simulation of the mechanical behaviour of articular cartilage. International Journal for Numerical Methods in Engineering 67:9, pages 1244-1271.
Crossref
Stephen M. Klisch. (2006) A Bimodular Theory for Finite Deformations: Comparison of Orthotropic Second-order and Exponential Stress Constitutive Equations for Articular Cartilage. Biomechanics and Modeling in Mechanobiology 5:2-3, pages 90-101.
Crossref
J. R. Owen & J. S. Wayne. (2006) Influence of a Superficial Tangential Zone Over Repairing Cartilage Defects: Implications for Tissue Engineering. Biomechanics and Modeling in Mechanobiology 5:2-3, pages 102-110.
Crossref
A. Pérez del Palomar & M. Doblaré. (2006) 3D Finite Element Simulation of the Opening Movement of the Mandible in Healthy and Pathologic Situations. Journal of Biomechanical Engineering 128:2, pages 242-249.
Crossref
José Jaime García & Daniel Humberto Cortés. (2006) A nonlinear biphasic viscohyperelastic model for articular cartilage. Journal of Biomechanics 39:16, pages 2991-2998.
Crossref
A. Pérez del Palomar & M. Doblaré. (2006) The effect of collagen reinforcement in the behaviour of the temporomandibular joint disc. Journal of Biomechanics 39:6, pages 1075-1085.
Crossref
KAROL MILLER, ZEIKE TAYLOR & WIESLAW L. NOWINSKI. (2011) TOWARDS COMPUTING BRAIN DEFORMATIONS FOR DIAGNOSIS, PROGNOSIS AND NEUROSURGICAL SIMULATION. Journal of Mechanics in Medicine and Biology 05:01, pages 105-121.
Crossref
Peter S. Donzelli, Luigi M. Gallo, Robert L. Spilker & Sandro Palla. (2004) Biphasic finite element simulation of the TMJ disc from in vivo kinematic and geometric measurements. Journal of Biomechanics 37:11, pages 1787-1791.
Crossref
Bram G. Sengers, Cees W. J. Oomens & Frank P. T. Baaijens. (2004) An Integrated Finite-Element Approach to Mechanics, Transport and Biosynthesis in Tissue Engineering. Journal of Biomechanical Engineering 126:1, pages 82-91.
Crossref
Ramaswamy Krishnan, Seonghun Park, Felix Eckstein & Gerard A. Ateshian. (2003) Inhomogeneous Cartilage Properties Enhance Superficial Interstitial Fluid Support and Frictional Properties, But Do Not Provide a Homogeneous State of Stress. Journal of Biomechanical Engineering 125:5, pages 569-577.
Crossref
Emilio A. Meroi & Bernhard A. Schrefler. (2011) Biomechanical Multiphase Approaches in Soft Tissues. Journal of Mechanics in Medicine and Biology 03:02, pages 197-213.
Crossref
Stephen M. Klisch, Michael A. DiMicco, Anne Hoger & Robert L. Sah. 2003. Functional Tissue Engineering. Functional Tissue Engineering 194 210 .
Robert L. Sah. 2002. The Many Faces of Osteoarthritis. The Many Faces of Osteoarthritis 409 422 .
W. L. Dunbar,Jr.Jr., K. U¨n, P. S. Donzelli & R. L. Spilker. (2001) An Evaluation of Three-Dimensional Diarthrodial Joint Contact Using Penetration Data and the Finite Element Method. Journal of Biomechanical Engineering 123:4, pages 333-340.
Crossref
S.S. Chen, Y.H. Falcovitz, R. Schneiderman, A. Maroudas & R.L. Sah. (2001) Depth-dependent compressive properties of normal aged human femoral head articular cartilage: relationship to fixed charge density. Osteoarthritis and Cartilage 9:6, pages 561-569.
Crossref
William M. Smith. 2001. Wiley Encyclopedia of Electrical and Electronics Engineering. Wiley Encyclopedia of Electrical and Electronics Engineering.
D. N. Sun, W. Y. Gu, X. E. Guo, W. M. Lai & V. C. Mow. (1999) A mixed finite element formulation of triphasic mechano-electrochemical theory for charged, hydrated biological soft tissues. International Journal for Numerical Methods in Engineering 45:10, pages 1375-1402.
Crossref
O. M. G. C. Op den Camp, C. W. J. Oomens, F. E. Veldpaus & J. D. Janssen. (1999) An efficient algorithm to estimate material parameters of biphasic mixtures. International Journal for Numerical Methods in Engineering 45:9, pages 1315-1331.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.