Finite deformation of soft tissue:​ analysis of a mixture model in uni-axial compression

Holmes, M. H.

Affiliations

¹Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, N.Y. 12180

Abstract

The dynamic finite deformational behavior of a biphasic model for soft hydrated tissue is examined. In the case of uni-axial confined compression the displacement and stress fields are derived for steady-state permeation, creep, and stressrelaxation. It is shown how to use the results of this analysis to obtain the constitutive relations, as well as the associated material parameters, from the corresponding experiments. It is also shown that the solutions from the theory go much farther, giving a detailed account of the deformation and iteraction of the fluid and solid phases in the tissue.

Links

DOI: 10.1115/1.3138633

PubMed: 3795885

WoS: A1986E975600016

History

Received: 1986-01-23

Revised: 1986-08-14

Cited Works (10)

Year	Entry
1980	Bowen RM. Incompressible porous media models by use of the theory of mixtures. Int J Eng Sci. 1980;18(9):1129-1148.
1968	Maroudas A, Bullough P, Swanson SAV, Freeman MAR. The permeability of articular cartilage. J Bone Joint Surg. February 1968;50B(1):166-177.
1985	Holmes MH, Lai WM, Mow VC. Singular perturbation analysis of the nonlinear, flow-dependent compressive stress relaxation behavior of articular cartilage. J Biomech Eng. August 1985;107(3):206-218.
1985	Kwan MK-W. A Finite Deformation Theory for Nonlinearly Permeable Cartilage and Other Soft Hydrated Connective Tissues and Rheological Study of Cartilage Proteoglycans [PhD thesis]. Troy, NY: Rensselaer Polytechnic Institute; December 1985.
1980	Mow VC, Kuei SC, Lai WM, Armstrong CG. Biphasic creep and stress relaxation of articular cartilage in compression: theory and experiments. J Biomech Eng. February 1980;102(1):73-84.
1984	Myers ER, Lai WM, Mow VC. A continuum theory and an experiment for the ion-induced swelling behavior of articular cartilage. J Biomech Eng. May 1984;106(2):151-158.
1985	Eisenberg SR, Grodzinsky AJ. Swelling of articular cartilage and other connective tissues: electromechanochemical forces. J Orthop Res. 1985;3(2):148-159.
1980	Lai WM, Mow VC. Drag-induced compression of articular cartilage during a permeation experiment. Biorheology. 1980;17(1-2):111-123.
1976	Mansour JM, Mow VC. The permeability of articular cartilage under compressive strain and at high pressures. J Bone Joint Surg. June 1976;58A(4):509-516.
1962	McCutchen CW. The frictional properties of animal joints. Wear. January–February 1962;5(1):1-17.

Cited By (48)

Year	Entry
1990	Mow VC, Hou JS, Owens JM, Ratcliffe A. Biphasic and quasilinear viscoelastic theories for hydrated soft tissues. In: Mow VC, Ratcliffe A, Woo SL-Y, eds. Biomechanics of Diarthrodial Joints. Vol 1. New York, NY: Springer-Verlag; 1990:215-260.
1990	Frank EH, Grodzinsky AJ, Phillips SL, Grimshaw PE. Physicochemical and bioelectrical determinants of cartilage material properties. In: Mow VC, Ratcliffe A, Woo SL-Y, eds. Biomechanics of Diarthrodial Joints. Vol 1. New York, NY: Springer-Verlag; 1990:261-282.
1990	Spilker RL, Suh J-K, Vermilyea ME, Maxian TA. Alternate hybrid, mixed, and penalty finite element formulations for the biphasic model of soft hydrated tissues. In: Mow VC, Ratcliffe A, Woo SL-Y, eds. Biomechanics of Diarthrodial Joints. Vol 1. New York, NY: Springer-Verlag; 1990:401-435.
1990	Hou JS, Holmes MH, Lai WM, Mow VC. Squeeze film lubrication for articular cartilage with synovial fluid. In: Mow VC, Ratcliffe A, Woo SL-Y, eds. Biomechanics of Diarthrodial Joints. Vol 2. New York, NY: Springer-Verlag; 1990:347-367.
1993	Fung YC. Biomechanics: Mechanical Properties of Living Tissues. 2nd ed. New York, NY: Springer-Verlag; 1993.
1998	Lizee E, Robin S, Song E, Bertholon N, Le Coz J-Y, Besnault B, Lavaste F. Development of a 3D finite element model of the human body. In: Proceedings of the 42nd Stapp Car Crash Conference. November 2-4, 1998; Tempa, AZ. Warrendale, PA: Society of Automotive Engineers:115-137. SAE 983152.
1992	Simon BR. Multiphase poroelastic finite element models for soft tissue structures. Appl Mech Rev. June 1992;45(6):191-218.
1991	Suh J-K, Spilker RL, Holmes MH. A penalty finite element analysis for nonlinear mechanics of biphasic hydrated soft tissue under large deformation. Int J Num Meth Eng. November 1991;32(7):1411-1439.
1990	Holmes MH, Mow VC. The nonlinear characteristics of soft gels and hydrated connective tissues in ultrafiltration. J Biomech. 1990;23(11):1145-1156.
1992	Spilker RL, Donzelli PS, Mow VC. A transversely isotropic biphasic finite element model of the meniscus. J Biomech. September 1992;25(9):1027-1045.
1995	Suh J-K, Li Z, Woo SL-Y. Dynamic behavior of a biphasic cartilage model under cyclic compressive loading. J Biomech. April 1995;28(4):357-364.
1996	Argoubi M, Shirazi-Adl A. Poroelastic creep response analysis of a lumbar motion segment in compression. J Biomech. October 1996;29(10):1331-1339.
1997	Ateshian GA, Warden W, Kim JJ, Grelsamer RP, Mow VC. Finite deformation biphasic material properties of bovine articular cartilage from confined compression experiments. J Biomech. November–December 1997;30:1157.
1998	Iatridis JC, Setton LA, Foster RJ, Rawlins BA, Weidenbaum M, Mow VC. Degeneration affects the anisotropic and nonlinear behaviors of human anulus fibrosus in compression. J Biomech. June 1998;31(6):535-544.
2004	Ferguson SJ, Ito K, Nolte L-P. Fluid flow and convective transport of solutes within the intervertebral disc. J Biomech. February 2004;37(2):213-221.
2007	Cheng S, Bilston LE. Unconfined compression of white matter. J Biomech. 2007;40(2):117-124.
1990	Spilker RL, Suh J-K, Mow VC. Effects of friction on the unconfined compressive response of articular cartilage: a finite element analysis. J Biomech Eng. May 1990;112(2):138-146.
1992	Spilker RL, Suh J-K, Mow VC. A finite element analysis of the indentation stress-relaxation response of linear biphasic articular cartilage. J Biomech Eng. May 1992;114(2):191-201.
1994	Suh J-K, Spilker RL. Indentation analysis of biphasic articular cartilage: nonlinear phenomena under finite deformation. J Biomech Eng. February 1994;116(1):1-9.
1995	Drost MR, Willems P, Snijders H, Huyghe JM, Janssen JD, Huson A. Confined compression of canine annulus fibrosus under chemical and mechanical loading. J Biomech Eng. November 1995;117(4):390-396.
1998	Suh J-K, Bai S. Finite element formulation of biphasic poroviscoelastic model for articular cartilage. J Biomech Eng. April 1998;120(2):195-201.
2000	Klisch SM, Lotz JC. A special theory of biphasic mixtures and experimental results for human annulus fibrosus tested in confined compression. J Biomech Eng. April 2000;122(2):180-188.
1999	Chen C-T, Burton-Wurster N, Lust G, Bank RA, Tekoppele JM. Compositional and metabolic changes in damaged cartilage are peak-stress, stress-rate, and loading-duration dependent. J Orthop Res. November 1999;17(6):870-879.
2005	Johannessen W, Elliott DM. Effects of degeneration on the biphasic material properties of human nucleus pulposus in confined compression. Spine. December 15, 2005;30(24):E724-E729.
2022	de Angelis N. Finite Element Analysis of Full Range of Motion Walking and Sitting Down in Patient-Specific Models With Cam Deformities [Master's thesis]. Carleton University; 2022.
1996	Iatridis JC. Biomechanics of the Anulus Fibrosus and Nucleus Pulposus of the Human Lumbar Intervertebral Disc and the Effects of Degeneration [PhD thesis]. Columbia University; 1996.
1997	Wang X. The Frictional Role of Interstitial Fluid Viscosity At the Interface of Deformable Porous Media [PhD thesis]. Columbia University; 1997.
2002	Sun D. Theoretical and Experimental Investigations of the Mechano-Electrochemical Properties of Articular Cartilage, a Charged -Hydrated -Soft, Biological Tissue [PhD thesis]. Columbia University; 2002.
2004	Krishnan R. Role of Interstitial Fluid Pressurization in Articular Cartilage Lubrication [PhD thesis]. Columbia University; 2004.
2006	Basalo Perez-Luna IM. Effects of Enzymatic Degradation and Supplementation of Chrondroitin Sulfate on the Frictional Properties of Articular Cartilage [PhD thesis]. Columbia University; 2006.
2021	Shim JJ. A Multiphasic-Fluid-Structure Interaction Formulation Based on Mixture Theory and Its Finite Element Implementation in FEBio [PhD thesis]. Columbia University; 2021.
2002	Cheung T-mJ. A Finite Element Study of the Effects of Mechanical Loading on the Fluid Flow and Biomechanical Response of the Intervertebral Disc [Master's thesis]. Hong Kong Polytechnic University; September 2002.
2009	Travascio F. Modeling Molecular Transport and Binding Interactions in Intervertebral Disc [PhD thesis]. University of Miami; December 2009.
1998	Garcia JJ. A Transversely Isotropic Hypo-Elastic Biphasic Model of Articular Cartilage Under Impact Loading [PhD thesis]. East Lansing, MI: Michigan State University; 1998.
2012	Bourgeois-Collin L. Évaluation de modèles biphasiques linéaires pour la caractérisation mécanique de la plaque de croissance [Master's thesis]. École polytechnique de Montréal; April 2012.
2014	Tireh Dast M. Biomechanical Response of the Epiphyseal Vertebral Growth Plate Under Static and Cyclic Compression: A Finite Element Study [Master's thesis]. École polytechnique de Montréal; December 2014.
1989	Suh J-K. A Finite Element Formulation for Nonlinear Behavior of Biphasic Hydrated Soft Tissues Under Finite Deformation [PhD thesis]. Troy, NY: Rensselaer Polytechnic Institute; September 1989.
1995	Donzelli PS. A Mixed-Penalty Contact Finite Element Formulation for Biphasic Soft Tissues [PhD thesis]. Troy, NY: Rensselaer Polytechnic Institute; April 1995.
2003	Yang T. A Three-Dimensional Biphasic Finite Element Contact Formulation for Hydrated Soft Tissue [PhD thesis]. Troy, NY: Rensselaer Polytechnic Institute; December 2003.
2003	Han S-K. Articular Cartilage Modeling in the 3-D Patellofemoral Joint Contact [Master's thesis]. Calgary, AB: University of Calgary; June 2003.
2006	Rouhi G. Theoretical Aspects of Bone Remodeling and Resorption Processes [PhD thesis]. Calgary, AB: University of Calgary; March 2006.
2013	Andrews S. Meniscus Structure and Function [PhD thesis]. Calgary, AB: University of Calgary; January 2013.
1999	Klisch SM. A Continuum Mixture Theory With Internal Constraints for Annulus Fibrosus [PhD thesis]. Berkeley, CA: Berkeley, University of California; 1999.
2006	Cheng S. The Role of Brain Tissue Mechanical Properties and Cerebrospinal Fluid Flow in the Biomechanics of the Normal and Hydrocephalic Brain [PhD thesis]. University of New South Wales; 2006.
2006	Johannessen W. Nucleus Pulposus Degeneration and Its Role in Intervertebral Disc Mechanical Function [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 2006.
2013	Henak CR. Cartilage and Labrum Mechanics in the Normal and Pathomorphologic Human Hip [PhD thesis]. University of Utah; August 2013.
2017	Maas S. Development of a Nonlinear Finite Element Code for Computational Biomechanics and Biophysics [PhD thesis]. University of Utah; May 2017.
2021	Guang Y. Understanding a Role for Synovium in Intra-Articular Drug Clearance: A Computational and Experimental Approach [PhD thesis]. St. Louis, MO: Washington University in St. Louis; May 2021.