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Revision of Poroelasticity, or diffusion in elastic solids from Fri, 2009-05-01 07:59

Zhigang Suo's picture

A sponge is an elastic solid with connected pores. When immersed in water, the sponge absorbs water. When a saturated sponge is squeezed, water will come out. More generally, the subject is known as diffusion in elastic solids, or elasticity of fluid-infiltrated porous solids, or poroelasticity. The theory has been applied to diverse phenomena. Here are a few examples.

Consolidation of soils. A soil is a composite of solid particles and fluids (mainly water). Particles in the soil are more or less bound together and constitute an elastic skeleton. The interstices of the skeleton are filled with water. When a load is applied to the soil, water will flow out gradually, so that the soil will deform over some time. This process is known as consolidation.

  • M.A. Biot, General theory of three-dimensional consolidation, Journal of Applied Physics 12, 155-164 (1941).
  • J. Bear, Dynamics of fluids in porous media. Dover reprint, 1988.
  • E. Detournay and A.H.-D. Cheng, Fundamentals of Poroelasticity, Chap. 5 in Comprehensive Rock Engineering: Principles, Practice and Projects, Vol. II, Analysis and Design Method, ed. C. Fairhurst, Pergamon, 113-171, 1993.
  • J.R. Rice, Elasticity of fluid-infiltrated porous solids, notes for teaching on hydrology and environmental geomechanics.
  • J.R. Rice and M.P. Cleary, Some basic stress-diffusion solutions for fluid-saturated elastic porous media with compressible constituents. Reviews of Geophysics and Space Physics 14, 227-241 (1976).
  • H. F. Wang, Theory of linear poroelasticity. Princeton University Press, 2000.

Swelling of gels. A gel is a composite of a network of crosslinked molecules, and a solvent consisting of all other molecules that permeate in the interstices of the network, but are not linked to the network. The network is elastic, while the solvent can migrate through the interstices of the network. The elasticity of the network and migration of the solvent are coupled: the network swells where the solvent accumulates, and the solvent migrates in response to the deformation of the network. The gel is called a hydrogel when the solvent is water, or an aerogel when the solvent is a gas.

  • J. Dolbow, E. Fried, H. Ji, Chemically induced swelling of hydrogels. Journal of the Mechanics and Physics of Solids 52, 51-84 (2004).
  • A. Sidorenko, T. Krupenkin, A. Taylor, P. Fratzl, and J. Aizenberg, Reversible switching of hydrogel-actuated nanostructures into complex micropatterns. Science 315, 487-490 (2007).

Fluid migration in tissues. Nearly all living tissues are porous and elastic, with fluid migrating in the pores inside the tissues to transport nutrients and wastes.

Diffusion in crystals. Metals and ceramics are often in the form of alloys, consisting of dissimilar atoms. Some atoms diffuse much faster than other atoms, so that the slow diffusers may serve the role of an elastic network. For example, some materials can absorb and release large amounts of hydrogen, making them candidates for hydrogen storage technology.

  • F.C. Larche and J.W. Cahn, The interactions of composition and stress in crystalline solids, Acta Metallurgica 33, 331-357 (1985).
  • P.W. Voorhees and W.C. Johnson, The thermodynamics of elastically stressed crystals, Solid State Physics 59, 1-201 (2004).

However, for most alloys, diffusion is coupled with inelastic deformation, so that the theory of diffusion in elastic crystals is not applicable. See discussions in

These notes will focus on diffusion in elastic solids. Historically, the theory coupling diffusion and elasticity has caused a great deal of confusion. It might be helpful if we start with elementary ideas.

  • Migration of matter in an elastic solid
  • Thermodynamics of a fluid of single species of molecules
  • Chemical potential of an incompressible liquid
  • Chemical potential of an ideal gas
  • Equilibrating a liquid and a vapor of the same species of molecules
  • Humidity
  • Equilibrate a gel with a weight and a moist environment
  • A homogeneous field of stress and water concentration
  • Alternative free-energy functions
  • Inhomogeneous, equilibrium field
  • Invariance under rigid-body rotation
  • Isotropic material
  • Diffusion in a rigid network
  • Fluid infiltrating a rigid network
  • Thermodynamics of nonequilibrium processes
  • Nonlinear poroelasticity
  • Summary of equations
  • Linear poroelasticity
  • Stress in a thin film due to change of the humidity in the environment
  • Stress induced by drying
  • Analysis of a soil test (Biot, 1941)
  • A stationary long crack
  • A crack extending at a constant velocity

Return to the main page of ES 241 Advanced Elasticity.

Comments

MichelleLOyen's picture

Zhigang, I have added a link to some additional nice references on poroelasticity on my own blog page

Zhigang Suo's picture

Michelle:

Thank you so much for this useful site, and for many other discussions that you have posted on this subject. As you know, I'm teaching this section in my Advanced Elasticity course now. I wrote these notes on poroelasticity to teach myself the subject, and hope the notes will also be useful to the students in the class.

This is the first time I'm learning poroelasticity. Fascinating subject! In the opening section I listed a few areas of applications (e.g., soils, hydrogels, tissues, solid solutions), with references that I have looked at. I have had some experience with the last topic, which has helped me in reading the literature on other subjects.

Biot's idea of fluid pressure is a good one for large pores, such as pores in rocks and soils. However, for hydrogels, when the "pores" are really the interstices between the network of molecules, fluid pressure is a confusing idea. In particular, even when the relative humidity in the environment is below 100%, there will be lots of water molecules inside a hydrogel, because molecules in the gel love to bind with water molecules.

The right concept to use, as people have recognized, is the chemical potential of water molecules. Chemical potential readily recovers Biot's formulation: For an incompressible fluid,

chemical potential = pressure x (volume per molecule).

Now a question for you. In tissue mechanics, what are recent and emerging applications of poroelasticity?

MichelleLOyen's picture

Another interesting topic in which diffusion through pores is really important is in biology.  Mostly within the biophysics community, the transport of small molecules through pores in cell membranes and in filtration applications such as the kidney.  There is a nice treatment of this subject in the text "Intermediate Physics for Medicine and Biology" by Russell Hobbie.  It will be interesting to compare this approach with the others.

 

Henry Tan's picture

Another interesting topic for poroelasticity is in the impact behaviour of cellular materials.

Rui Huang's picture

I did not know the connection between poroelasticity and diffusion. I also thought that diffusion in solids is conceptually different from flow in porous media like soil. A lot more to learn! Thanks again for the note, Zhigang.

The last two examples are particularly interesting to me. I remember discussing with George Scherer of Princeton University a few years ago about fracture of concrete due to diffusion or migration of water as well as other chemical species (don't remember what exactly). That discussion however led to nowhere. Another failing effort more recently was about porous low-k dielectrics in Cu interconnects. When my colleague, Paul Ho, asked me about any fracture mechanics solutions for porous materials, I had no clue, mainly because I have no confidence in applying linear elastic fracture mechanics for a sharp crack to porous materials. I wonder if anyone has worked out any mechanics for this industry-relevant topic.

RH

Li Han's picture

This is actually an ongoing project in our lab(Vlassak group at Harvard). To model the fracture of porous materials, porosity, pore size distribution, pore geometry are all key factors to consider, and are also nontrivial tasks to accomplish. It will be truly appreciated if someone can offer some constructive comments.  

Li Han

Henry Tan's picture

An introductory level handout provide by James R. Rice formulates the equations describing coupled processes of elastic deformation and pore fluid diffusion in fluid-infiltrated elastic solids.

Mogadalai Gururajan's picture

Dear Prof. Suo:

Thank you very much for the very interesting notes. Here are some more papers discussing diffusion in solid solutions.

  1. A paper by Morton E Gurtin, which, using his microforce balance concept, extends the Cahn-Hilliard equation (which is a generalised diffusion equation ) to allow for deformation. Such a model is ideal for the numerical study of evolution of microstructures in the presence of elastic stresses.
  2. Such a numerical study of diffusion in solid solutions in the presence of elastic stresses and defects (dislocations, voids, cracks etc) has been pioneered by Khachaturyan and his co-workers.

And, on a historical note, the problem of absorption of fluid in a solid (and the resulting equilibration) is discussed by Gibbs in his On the equilibrium of heterogeneous substances; however, since Gibbs was not aware of solid-state diffusion, diffusion in crystals is not discussed. In fact, the story of the acceptance of solid state diffusion by metallurgists is an interesting one -- I will try and do a post about it in my blog sometime!

Zhigang Suo's picture

Dear Guru:

Thank you so much for your note. Following it, I looked at Gibbs's collected papers on my shelf, and found the relevant sections:

  • Page 184. The conditions of internal and external equilibrium for solids in contact with fields with regard to all possible states of strain of the solids
  • Page 201. Fundamental equations for solids
  • Page 215 Concerning solids which absorb fluids

I'm astonished that my notes on poroelasticity has followed his approach exactly, including the exclusive use of deformation gradient and nominal stress. Gibbs's formulation was in terms of finite deformation.

Although I have looked at his long paper many times, I don't believe that I had read these particular sections before. His approach must have permeated in our blood no matter we read him or not.

More interestingly, Biot's 1941 paper, which is widely regarded as the founding paper of the theory of poroelasticity, contained no reference to Gibbs's work. Of course, Biot went beyond equilibrium, and added a kinetic law, Darcy's law, to the theory. Still, many people have long regarded that most intriguing part of Biot's formulation is the reciprocal relation. The latter was clearly identified in Gibbs's paper.

Incidentally, Biot's 1941 paper has also been identified, by Shaofan Li, as one of the most cited papers in our field. If a great mechanician and a Timoshenko Medalist like Biot inadvertently rediscovered a result of others in his most influential work, we should all be happy if we can do anything original at all. We should all remind ourselves of this perspective in moments of despair.

Thank you again, Guru, for the detective work of these remarkable papers. It has been fun.

P.S. For those who have not read Gibbs, as I remarked elsewhere, an excellent place to start is his two short papers. Guru has also pointed out that you can read and download Gibbs's collected works for free at Google Book.

Dear Zhigang:

    It would be interesting for folks in applied mechanics to check PubMed (http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?CMD=search&DB=pubmed) and type in mow vc cartilage.  You will find poroelastic or mixture theory in cartilage biomechanics since early 1980s....

 

Best reagrds,

 

Ed 

MichelleLOyen's picture

Dear Ed,

last I had heard, there were still some open discussions about the Mow et al. "biphasic" approach, which was more or less independently developed within the biomechanics community, and to what extent and in what conditions it was the same as poroelasticity. Is there a definitive word on this?

Regardless, an even more active poroelasticity and biomechanics crowd in recent years has been within the bone community; for anyone new to the subject I recommend the review

Cowin SC, Bone poroelasticity, J. Biomech. 32, 217-38 (1999).

The review covers basic poroelastic equations as well as the application of the model to bone at two different length-scales of porosity. I know of no similarly comprehensive review for cartilage or spinal disc, but if anyone knows of one I'd love to see a complimentary reference posted here.

Dear Michelle: 

The biphasic theory has been extended in cartilage mechanics to "triphasic" including electric charges.

 

1: Lux Lu X, Miller C, Chen FH, Edward Guo X, Mow VC.
The generalized triphasic correspondence principle for simultaneous
determination of the mechanical properties and proteoglycan content of articular
cartilage by indentation.
J Biomech. 2007 Jan 11; [Epub ahead of print]
PMID: 17222852 [PubMed - as supplied by publisher]

2: Wan LQ, Miller C, Guo XE, Mow VC.
Fixed electrical charges and mobile ions affect the measurable
mechano-electrochemical properties of charged-hydrated biological tissues: the
articular cartilage paradigm.
Mech Chem Biosyst. 2004 Mar;1(1):81-99.
PMID: 16783948 [PubMed - indexed for MEDLINE]

3: Likhitpanichkul M, Guo XE, Mow VC.
The effect of matrix tension-compression nonlinearity and fixed negative
charges on chondrocyte responses in cartilage.
Mol Cell Biomech. 2005 Dec;2(4):191-204.
PMID: 16705865 [PubMed - indexed for MEDLINE]

4: Huang CY, Stankiewicz A, Ateshian GA, Mow VC.
Anisotropy, inhomogeneity, and tension-compression nonlinearity of human
glenohumeral cartilage in finite deformation.
J Biomech. 2005 Apr;38(4):799-809.
PMID: 15713301 [PubMed - indexed for MEDLINE]

5: Gu WY, Sun DN, Lai WM, Mow VC.
Analysis of the dynamic permeation experiment with implication to cartilaginous
tissue engineering.
J Biomech Eng. 2004 Aug;126(4):485-91.
PMID: 15543866 [PubMed - indexed for MEDLINE]

6: Zheng YP, Shi J, Qin L, Patil SG, Mow VC, Zhou KY.
Dynamic depth-dependent osmotic swelling and solute diffusion in articular
cartilage monitored using real-time ultrasound.
Ultrasound Med Biol. 2004 Jun;30(6):841-9.
PMID: 15219963 [PubMed - indexed for MEDLINE]

7: Sun DD, Guo XE, Likhitpanichkul M, Lai WM, Mow VC.
The influence of the fixed negative charges on mechanical and electrical
behaviors of articular cartilage under unconfined compression.
J Biomech Eng. 2004 Feb;126(1):6-16.
PMID: 15171124 [PubMed - indexed for MEDLINE]

8: Lu XL, Sun DD, Guo XE, Chen FH, Lai WM, Mow VC.
Indentation determined mechanoelectrochemical properties and fixed charge
density of articular cartilage.
Ann Biomed Eng. 2004 Mar;32(3):370-9.
PMID: 15095811 [PubMed - indexed for MEDLINE]

9: Buckwalter JA, Martin JA, Olmstead M, Athanasiou KA, Rosenwasser MP, Mow VC.

Osteochondral repair of primate knee femoral and patellar articular surfaces:
implications for preventing post-traumatic osteoarthritis.
Iowa Orthop J. 2003;23:66-74.
PMID: 14575253 [PubMed - indexed for MEDLINE]

10: Cohen ZA, Mow VC, Henry JH, Levine WN, Ateshian GA.
Templates of the cartilage layers of the patellofemoral joint and their use in
the assessment of osteoarthritic cartilage damage.
Osteoarthritis Cartilage. 2003 Aug;11(8):569-79.
PMID: 12880579 [PubMed - indexed for MEDLINE]

11: Koff MF, Ugwonali OF, Strauch RJ, Rosenwasser MP, Ateshian GA, Mow VC.
Sequential wear patterns of the articular cartilage of the thumb
carpometacarpal joint in osteoarthritis.
J Hand Surg [Am]. 2003 Jul;28(4):597-604.
PMID: 12877846 [PubMed - indexed for MEDLINE]

12: Huang CY, Soltz MA, Kopacz M, Mow VC, Ateshian GA.
Experimental verification of the roles of intrinsic matrix viscoelasticity and
tension-compression nonlinearity in the biphasic response of cartilage.
J Biomech Eng. 2003 Feb;125(1):84-93.
PMID: 12661200 [PubMed - indexed for MEDLINE]

13: Cohen ZA, Henry JH, McCarthy DM, Mow VC, Ateshian GA.
Computer simulations of patellofemoral joint surgery. Patient-specific models
for tuberosity transfer.
Am J Sports Med. 2003 Jan-Feb;31(1):87-98.
PMID: 12531764 [PubMed - indexed for MEDLINE]

14: Mow VC, Guo XE.
Mechano-electrochemical properties of articular cartilage: their
inhomogeneities and anisotropies.
Annu Rev Biomed Eng. 2002;4:175-209. Epub 2002 Mar 22. Review.
PMID: 12117756 [PubMed - indexed for MEDLINE]

15: Lai WM, Sun DD, Ateshian GA, Guo XE, Mow VC.
Electrical signals for chondrocytes in cartilage.
Biorheology. 2002;39(1-2):39-45.
PMID: 12082265 [PubMed - indexed for MEDLINE]

16: Wang CC, Guo XE, Sun D, Mow VC, Ateshian GA, Hung CT.
The functional environment of chondrocytes within cartilage subjected to
compressive loading: a theoretical and experimental approach.
Biorheology. 2002;39(1-2):11-25.
PMID: 12082263 [PubMed - indexed for MEDLINE]

17: Huang CY, Mow VC, Ateshian GA.
The role of flow-independent viscoelasticity in the biphasic tensile and
compressive responses of articular cartilage.
J Biomech Eng. 2001 Oct;123(5):410-7.
PMID: 11601725 [PubMed - indexed for MEDLINE]

18: Cohen ZA, Roglic H, Grelsamer RP, Henry JH, Levine WN, Mow VC, Ateshian GA.

Patellofemoral stresses during open and closed kinetic chain exercises. An
analysis using computer simulation.
Am J Sports Med. 2001 Jul-Aug;29(4):480-7.
PMID: 11476390 [PubMed - indexed for MEDLINE]

19: Wang CC, Hung CT, Mow VC.
An analysis of the effects of depth-dependent aggregate modulus on articular
cartilage stress-relaxation behavior in compression.
J Biomech. 2001 Jan;34(1):75-84.
PMID: 11425083 [PubMed - indexed for MEDLINE]

20: Ahmad CS, Cohen ZA, Levine WN, Ateshian GA, Mow VC.
Biomechanical and topographic considerations for autologous osteochondral
grafting in the knee.
Am J Sports Med. 2001 Mar-Apr;29(2):201-6.
PMID: 11292046 [PubMed - indexed for MEDLINE]

21: Kelkar R, Wang VM, Flatow EL, Newton PM, Ateshian GA, Bigliani LU, Pawluk
RJ, Mow VC.
Glenohumeral mechanics: a study of articular geometry, contact, and kinematics.
J Shoulder Elbow Surg. 2001 Jan-Feb;10(1):73-84.
PMID: 11182740 [PubMed - indexed for MEDLINE]

22: Rivers PA, Rosenwasser MP, Mow VC, Pawluk RJ, Strauch RJ, Sugalski MT,
Ateshian GA.
Osteoarthritic changes in the biochemical composition of thumb carpometacarpal
joint cartilage and correlation with biomechanical properties.
J Hand Surg [Am]. 2000 Sep;25(5):889-98.
PMID: 11040304 [PubMed - indexed for MEDLINE]

23: Lai WM, Mow VC, Sun DD, Ateshian GA.
On the electric potentials inside a charged soft hydrated biological tissue:
streaming potential versus diffusion potential.
J Biomech Eng. 2000 Aug;122(4):336-46.
PMID: 11036556 [PubMed - indexed for MEDLINE]

24: Guilak F, Mow VC.
The mechanical environment of the chondrocyte: a biphasic finite element model
of cell-matrix interactions in articular cartilage.
J Biomech. 2000 Dec;33(12):1663-73.
PMID: 11006391 [PubMed - indexed for MEDLINE]

25: Roh MS, Strauch RJ, Xu L, Rosenwasser MP, Pawluk RJ, Mow VC.
Thenar insertion of abductor pollicis longus accessory tendons and thumb
carpometacarpal osteoarthritis.
J Hand Surg [Am]. 2000 May;25(3):458-63.
PMID: 10811749 [PubMed - indexed for MEDLINE]

26: Gu WY, Mao XG, Foster RJ, Weidenbaum M, Mow VC, Rawlins BA.
The anisotropic hydraulic permeability of human lumbar anulus fibrosus.
Influence of age, degeneration, direction, and water content.
Spine. 1999 Dec 1;24(23):2449-55.
PMID: 10626306 [PubMed - indexed for MEDLINE]

27: Hung CT, Henshaw DR, Wang CC, Mauck RL, Raia F, Palmer G, Chao PH, Mow VC,
Ratcliffe A, Valhmu WB.
Mitogen-activated protein kinase signaling in bovine articular chondrocytes in
response to fluid flow does not require calcium mobilization.
J Biomech. 2000 Jan;33(1):73-80.
PMID: 10609520 [PubMed - indexed for MEDLINE]

28: Gu WY, Mao XG, Rawlins BA, Iatridis JC, Foster RJ, Sun DN, Weidenbaum M,
Mow VC.
Streaming potential of human lumbar anulus fibrosus is anisotropic and affected
by disc degeneration.
J Biomech. 1999 Nov;32(11):1177-82.
PMID: 10541067 [PubMed - indexed for MEDLINE]

29: Iatridis JC, Kumar S, Foster RJ, Weidenbaum M, Mow VC.
Shear mechanical properties of human lumbar annulus fibrosus.
J Orthop Res. 1999 Sep;17(5):732-7.
PMID: 10569484 [PubMed - indexed for MEDLINE]

30: Mow VC, Wang CC.
Some bioengineering considerations for tissue engineering of articular
cartilage.
Clin Orthop Relat Res. 1999 Oct;(367 Suppl):S204-23.
PMID: 10546648 [PubMed - indexed for MEDLINE]

31: Donzelli PS, Spilker RL, Ateshian GA, Mow VC.
Contact analysis of biphasic transversely isotropic cartilage layers and
correlations with tissue failure.
J Biomech. 1999 Oct;32(10):1037-47.
PMID: 10476842 [PubMed - indexed for MEDLINE]

32: Cohen B, Lai WM, Mow VC.
A transversely isotropic biphasic model for unconfined compression of growth
plate and chondroepiphysis.
J Biomech Eng. 1998 Aug;120(4):491-6.
PMID: 10412420 [PubMed - indexed for MEDLINE]

33: Setton LA, Tohyama H, Mow VC.
Swelling and curling behaviors of articular cartilage.
J Biomech Eng. 1998 Jun;120(3):355-61.
PMID: 10412403 [PubMed - indexed for MEDLINE]

34: Mow VC, Wang CC, Hung CT.
The extracellular matrix, interstitial fluid and ions as a mechanical signal
transducer in articular cartilage.
Osteoarthritis Cartilage. 1999 Jan;7(1):41-58. Review.
PMID: 10367014 [PubMed - indexed for MEDLINE]

35: Setton LA, Elliott DM, Mow VC.
Altered mechanics of cartilage with osteoarthritis: human osteoarthritis and an
experimental model of joint degeneration.
Osteoarthritis Cartilage. 1999 Jan;7(1):2-14. Review.
PMID: 10367011 [PubMed - indexed for MEDLINE]

36: Lai WM, Gu WY, Mow VC.
On the conditional equivalence of chemical loading and mechanical loading on
articular cartilage.
J Biomech. 1998 Dec;31(12):1181-5.
PMID: 9882052 [PubMed - indexed for MEDLINE]

37: Cohen NP, Foster RJ, Mow VC.
Composition and dynamics of articular cartilage: structure, function, and
maintaining healthy state.
J Orthop Sports Phys Ther. 1998 Oct;28(4):203-15. Review.
PMID: 9785256 [PubMed - indexed for MEDLINE]

38: 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. 1998 Jun;31(6):535-44.
PMID: 9755038 [PubMed - indexed for MEDLINE]

39: Bachrach NM, Mow VC, Guilak F.
Incompressibility of the solid matrix of articular cartilage under high
hydrostatic pressures.
J Biomech. 1998 May;31(5):445-51.
PMID: 9727342 [PubMed - indexed for MEDLINE]

40: Valhmu WB, Stazzone EJ, Bachrach NM, Saed-Nejad F, Fischer SG, Mow VC,
Ratcliffe A.
Load-controlled compression of articular cartilage induces a transient
stimulation of aggrecan gene expression.
Arch Biochem Biophys. 1998 May 1;353(1):29-36.
PMID: 9578597 [PubMed - indexed for MEDLINE]

41: Xu L, Strauch RJ, Ateshian GA, Pawluk RJ, Mow VC, Rosenwasser MP.
Topography of the osteoarthritic thumb carpometacarpal joint and its variations
with regard to gender, age, site, and osteoarthritic stage.
J Hand Surg [Am]. 1998 May;23(3):454-64.
PMID: 9620186 [PubMed - indexed for MEDLINE]

42: Froimson MI, Ratcliffe A, Gardner TR, Mow VC.
Differences in patellofemoral joint cartilage material properties and their
significance to the etiology of cartilage surface fibrillation.
Osteoarthritis Cartilage. 1997 Nov;5(6):377-86.
PMID: 9536286 [PubMed - indexed for MEDLINE]

43: Ateshian GA, Warden WH, Kim JJ, Grelsamer RP, Mow VC.
Finite deformation biphasic material properties of bovine articular cartilage
from confined compression experiments.
J Biomech. 1997 Nov-Dec;30(11-12):1157-64.
PMID: 9456384 [PubMed - indexed for MEDLINE]

44: Iatridis JC, Setton LA, Weidenbaum M, Mow VC.
The viscoelastic behavior of the non-degenerate human lumbar nucleus pulposus
in shear.
J Biomech. 1997 Oct;30(10):1005-13.
PMID: 9391867 [PubMed - indexed for MEDLINE]

45: Kwak SD, Colman WW, Ateshian GA, Grelsamer RP, Henry JH, Mow VC.
Anatomy of the human patellofemoral joint articular cartilage: surface
curvature analysis.
J Orthop Res. 1997 May;15(3):468-72.
PMID: 9246097 [PubMed - indexed for MEDLINE]

46: Newton PM, Mow VC, Gardner TR, Buckwalter JA, Albright JP.
Winner of the 1996 Cabaud Award. The effect of lifelong exercise on canine
articular cartilage.
Am J Sports Med. 1997 May-Jun;25(3):282-7.
PMID: 9167804 [PubMed - indexed for MEDLINE]

47: Iatridis JC, Setton LA, Weidenbaum M, Mow VC.
Alterations in the mechanical behavior of the human lumbar nucleus pulposus
with degeneration and aging.
J Orthop Res. 1997 Mar;15(2):318-22.
PMID: 9167638 [PubMed - indexed for MEDLINE]

48: Setton LA, Mow VC, Muller FJ, Pita JC, Howell DS.
Mechanical behavior and biochemical composition of canine knee cartilage
following periods of joint disuse and disuse with remobilization.
Osteoarthritis Cartilage. 1997 Jan;5(1):1-16.
PMID: 9010874 [PubMed - indexed for MEDLINE]

49: Gu WY, Lai WM, Mow VC.
A triphasic analysis of negative osmotic flows through charged hydrated soft
tissues.
J Biomech. 1997 Jan;30(1):71-8.
PMID: 8970927 [PubMed - indexed for MEDLINE]

50: Zhu W, Iatridis JC, Hlibczuk V, Ratcliffe A, Mow VC.
Determination of collagen-proteoglycan interactions in vitro.
J Biomech. 1996 Jun;29(6):773-83.
PMID: 9147974 [PubMed - indexed for MEDLINE]

51: Iatridis JC, Weidenbaum M, Setton LA, Mow VC.
Is the nucleus pulposus a solid or a fluid? Mechanical behaviors of the nucleus
pulposus of the human intervertebral disc.
Spine. 1996 May 15;21(10):1174-84. Review.
PMID: 8727192 [PubMed - indexed for MEDLINE]

52: Ebara S, Iatridis JC, Setton LA, Foster RJ, Mow VC, Weidenbaum M.
Tensile properties of nondegenerate human lumbar anulus fibrosus.
Spine. 1996 Feb 15;21(4):452-61.
PMID: 8658249 [PubMed - indexed for MEDLINE]

53: Acaroglu ER, Iatridis JC, Setton LA, Foster RJ, Mow VC, Weidenbaum M.
Degeneration and aging affect the tensile behavior of human lumbar anulus
fibrosus.
Spine. 1995 Dec 15;20(24):2690-701.
PMID: 8747247 [PubMed - indexed for MEDLINE]

54: 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.
J Biomech. 1995 Dec;28(12):1561-9.
PMID: 8666595 [PubMed - indexed for MEDLINE]

55: Setton LA, Mow VC, Howell DS.
Mechanical behavior of articular cartilage in shear is altered by transection
of the anterior cruciate ligament.
J Orthop Res. 1995 Jul;13(4):473-82.
PMID: 7674064 [PubMed - indexed for MEDLINE]

56: Ateshian GA, Ark JW, Rosenwasser MP, Pawluk RJ, Soslowsky LJ, Mow VC.
Contact areas in the thumb carpometacarpal joint.
J Orthop Res. 1995 May;13(3):450-8.
PMID: 7602407 [PubMed - indexed for MEDLINE]

57: Guilak F, Ratcliffe A, Mow VC.
Chondrocyte deformation and local tissue strain in articular cartilage: a
confocal microscopy study.
J Orthop Res. 1995 May;13(3):410-21.
PMID: 7602402 [PubMed - indexed for MEDLINE]

58: Grumbles RM, Howell DS, Howard GA, Roos BA, Setton LA, Mow VC, Ratcliffe A,
Muller FJ, Altman RD.
Cartilage metalloproteases in disuse atrophy.
J Rheumatol Suppl. 1995 Feb;43:146-8.
PMID: 7538586 [PubMed - indexed for MEDLINE]

59: Ateshian GA, Lai WM, Zhu WB, Mow VC.
An asymptotic solution for the contact of two biphasic cartilage layers.
J Biomech. 1994 Nov;27(11):1347-60.
PMID: 7798285 [PubMed - indexed for MEDLINE]

60: Zhu W, Chern KY, Mow VC.
Anisotropic viscoelastic shear properties of bovine meniscus.
Clin Orthop Relat Res. 1994 Sep;(306):34-45.
PMID: 8070209 [PubMed - indexed for MEDLINE]

61: Buckwalter JA, Mow VC, Ratcliffe A.
Restoration of Injured or Degenerated Articular Cartilage.
J Am Acad Orthop Surg. 1994 Jul;2(4):192-201.
PMID: 10709009 [PubMed - as supplied by publisher]

62: Muller FJ, Setton LA, Manicourt DH, Mow VC, Howell DS, Pita JC.
Centrifugal and biochemical comparison of proteoglycan aggregates from
articular cartilage in experimental joint disuse and joint instability.
J Orthop Res. 1994 Jul;12(4):498-508.
PMID: 8064480 [PubMed - indexed for MEDLINE]

63: Guilak F, Ratcliffe A, Lane N, Rosenwasser MP, Mow VC.
Mechanical and biochemical changes in the superficial zone of articular
cartilage in canine experimental osteoarthritis.
J Orthop Res. 1994 Jul;12(4):474-84.
PMID: 8064478 [PubMed - indexed for MEDLINE]

64: Setton LA, Mow VC, Muller FJ, Pita JC, Howell DS.
Mechanical properties of canine articular cartilage are significantly altered
following transection of the anterior cruciate ligament.
J Orthop Res. 1994 Jul;12(4):451-63.
PMID: 8064477 [PubMed - indexed for MEDLINE]

65: Skaggs DL, Weidenbaum M, Iatridis JC, Ratcliffe A, Mow VC.
Regional variation in tensile properties and biochemical composition of the
human lumbar anulus fibrosus.
Spine. 1994 Jun 15;19(12):1310-9.
PMID: 8066509 [PubMed - indexed for MEDLINE]

66: Guilak F, Meyer BC, Ratcliffe A, Mow VC.
The effects of matrix compression on proteoglycan metabolism in articular
cartilage explants.
Osteoarthritis Cartilage. 1994 Jun;2(2):91-101.
PMID: 11548233 [PubMed - indexed for MEDLINE]

67: Zhu W, Mow VC, Rosenberg LC, Tang LH.
Determination of kinetic changes of aggrecan-hyaluronan interactions in
solution from its rheological properties.
J Biomech. 1994 May;27(5):571-9.
PMID: 8027091 [PubMed - indexed for MEDLINE]

68: Best BA, Guilak F, Setton LA, Zhu W, Saed-Nejad F, Ratcliffe A, Weidenbaum
M, Mow VC.
Compressive mechanical properties of the human anulus fibrosus and their
relationship to biochemical composition.
Spine. 1994 Jan 15;19(2):212-21.
PMID: 8153833 [PubMed - indexed for MEDLINE]

69: Ateshian GA, Kwak SD, Soslowsky LJ, Mow VC.
A stereophotogrammetric method for determining in situ contact areas in
diarthrodial joints, and a comparison with other methods.
J Biomech. 1994 Jan;27(1):111-24.
PMID: 7508940 [PubMed - indexed for MEDLINE]

70: Lai WM, Mow VC, Zhu W.
Constitutive modeling of articular cartilage and biomacromolecular solutions.
J Biomech Eng. 1993 Nov;115(4B):474-80. Review. No abstract available.
PMID: 8302028 [PubMed - indexed for MEDLINE]

71: Mow VC, Ateshian GA, Spilker RL.
Biomechanics of diarthrodial joints: a review of twenty years of progress.
J Biomech Eng. 1993 Nov;115(4B):460-7. Review.
PMID: 8302026 [PubMed - indexed for MEDLINE]

72: Zhu W, Mow VC, Koob TJ, Eyre DR.
Viscoelastic shear properties of articular cartilage and the effects of
glycosidase treatments.
J Orthop Res. 1993 Nov;11(6):771-81.
PMID: 8283321 [PubMed - indexed for MEDLINE]

73: Gu WY, Lai WM, Mow VC.
Transport of fluid and ions through a porous-permeable charged-hydrated tissue,
and streaming potential data on normal bovine articular cartilage.
J Biomech. 1993 Jun;26(6):709-23.
PMID: 8514815 [PubMed - indexed for MEDLINE]

74: Setton LA, Zhu W, Mow VC.
The biphasic poroviscoelastic behavior of articular cartilage: role of the
surface zone in governing the compressive behavior.
J Biomech. 1993 Apr-May;26(4-5):581-92.
PMID: 8478359 [PubMed - indexed for MEDLINE]

75: Ratcliffe A, Azzo W, Saed-Nejad F, Lane N, Rosenwasser MP, Mow VC.
In vivo effects of naproxen on composition, proteoglycan metabolism, and matrix
metalloproteinase activities in canine articular cartilage.
J Orthop Res. 1993 Mar;11(2):163-71.
PMID: 8483029 [PubMed - indexed for MEDLINE]

76: Setton LA, Mow VC, Muller FJ, Pita JC, Howell DS.
Altered structure-function relationships for articular cartilage in human
osteoarthritis and an experimental canine model.
Agents Actions Suppl. 1993;39:27-48. Review.
PMID: 8456641 [PubMed - indexed for MEDLINE]

77: Ratcliffe A, Rosenwasser MP, Mahmud F, Glazer PA, Saed-Nejad F, Lane N, Mow
VC.
The in vivo effects of naproxen on canine experimental osteoarthritic articular
cartilage: composition, metalloproteinase activities and metabolism.
Agents Actions Suppl. 1993;39:207-11.
PMID: 8456630 [PubMed - indexed for MEDLINE]

78: Soslowsky LJ, Flatow EL, Bigliani LU, Mow VC.
Articular geometry of the glenohumeral joint.
Clin Orthop Relat Res. 1992 Dec;(285):181-90.
PMID: 1446435 [PubMed - indexed for MEDLINE]

79: Spilker RL, Donzelli PS, Mow VC.
A transversely isotropic biphasic finite element model of the meniscus.
J Biomech. 1992 Sep;25(9):1027-45.
PMID: 1517263 [PubMed - indexed for MEDLINE]

80: Weidenbaum M, Foster RJ, Best BA, Saed-Nejad F, Nickoloff E, Newhouse J,
Ratcliffe A, Mow VC.
Correlating magnetic resonance imaging with the biochemical content of the
normal human intervertebral disc.
J Orthop Res. 1992 Jul;10(4):552-61.
PMID: 1613629 [PubMed - indexed for MEDLINE]

81: Soslowsky LJ, Flatow EL, Bigliani LU, Pawluk RJ, Ateshian GA, Mow VC.
Quantitation of in situ contact areas at the glenohumeral joint: a
biomechanical study.
J Orthop Res. 1992 Jul;10(4):524-34.
PMID: 1613626 [PubMed - indexed for MEDLINE]

82: Ateshian GA, Rosenwasser MP, Mow VC.
Curvature characteristics and congruence of the thumb carpometacarpal joint:
differences between female and male joints.
J Biomech. 1992 Jun;25(6):591-607.
PMID: 1517255 [PubMed - indexed for MEDLINE]

83: Spilker RL, Suh JK, Mow VC.
A finite element analysis of the indentation stress-relaxation response of
linear biphasic articular cartilage.
J Biomech Eng. 1992 May;114(2):191-201.
PMID: 1602762 [PubMed - indexed for MEDLINE]

84: Hou JS, Mow VC, Lai WM, Holmes MH.
An analysis of the squeeze-film lubrication mechanism for articular cartilage.
J Biomech. 1992 Mar;25(3):247-59.
PMID: 1564060 [PubMed - indexed for MEDLINE]

85: Mow VC, Ratcliffe A, Poole AR.
Cartilage and diarthrodial joints as paradigms for hierarchical materials and
structures.
Biomaterials. 1992;13(2):67-97. Review.
PMID: 1550898 [PubMed - indexed for MEDLINE]

86: Lai WM, Hou JS, Mow VC.
A triphasic theory for the swelling and deformation behaviors of articular
cartilage.
J Biomech Eng. 1991 Aug;113(3):245-58.
PMID: 1921350 [PubMed - indexed for MEDLINE]

87: Athanasiou KA, Rosenwasser MP, Buckwalter JA, Malinin TI, Mow VC.
Interspecies comparisons of in situ intrinsic mechanical properties of distal
femoral cartilage.
J Orthop Res. 1991 May;9(3):330-40.
PMID: 2010837 [PubMed - indexed for MEDLINE]

88: Mow VC, Ratcliffe A, Rosenwasser MP, Buckwalter JA.
Experimental studies on repair of large osteochondral defects at a high weight
bearing area of the knee joint: a tissue engineering study.
J Biomech Eng. 1991 May;113(2):198-207.
PMID: 1875694 [PubMed - indexed for MEDLINE]

89: Ateshian GA, Soslowsky LJ, Mow VC.
Quantitation of articular surface topography and cartilage thickness in knee
joints using stereophotogrammetry.
J Biomech. 1991;24(8):761-76.
PMID: 1918099 [PubMed - indexed for MEDLINE]

90: Zhu W, Lai WM, Mow VC.
The density and strength of proteoglycan-proteoglycan interaction sites in
concentrated solutions.
J Biomech. 1991;24(11):1007-18.
PMID: 1761579 [PubMed - indexed for MEDLINE]

91: Spilker RL, Suh JK, Mow VC.
Effects of friction on the unconfined compressive response of articular
cartilage: a finite element analysis.
J Biomech Eng. 1990 May;112(2):138-46.
PMID: 2345443 [PubMed - indexed for MEDLINE]

92: Schmidt MB, Mow VC, Chun LE, Eyre DR.
Effects of proteoglycan extraction on the tensile behavior of articular
cartilage.
J Orthop Res. 1990 May;8(3):353-63.
PMID: 2324854 [PubMed - indexed for MEDLINE]

93: Fithian DC, Kelly MA, Mow VC.
Material properties and structure-function relationships in the menisci.
Clin Orthop Relat Res. 1990 Mar;(252):19-31. Review.
PMID: 2406069 [PubMed - indexed for MEDLINE]

94: Kwan MK, Lai WM, Mow VC.
A finite deformation theory for cartilage and other soft hydrated connective
tissues--I. Equilibrium results.
J Biomech. 1990;23(2):145-55.
PMID: 2312519 [PubMed - indexed for MEDLINE]

95: Holmes MH, Mow VC.
The nonlinear characteristics of soft gels and hydrated connective tissues in
ultrafiltration.
J Biomech. 1990;23(11):1145-56.
PMID: 2277049 [PubMed - indexed for MEDLINE]

96: Mow VC, Zhu W, Lai WM, Hardingham TE, Hughes C, Muir H.
The influence of link protein stabilization on the viscometric properties of
proteoglycan aggregate solutions.
Biochim Biophys Acta. 1989 Aug 18;992(2):201-8.
PMID: 2758065 [PubMed - indexed for MEDLINE]

97: Hou JS, Holmes MH, Lai WM, Mow VC.
Boundary conditions at the cartilage-synovial fluid interface for joint
lubrication and theoretical verifications.
J Biomech Eng. 1989 Feb;111(1):78-87.
PMID: 2747237 [PubMed - indexed for MEDLINE]

98: Muller FJ, Pita JC, Manicourt DH, Malinin TI, Schoonbeck JM, Mow VC.
Centrifugal characterization of proteoglycans from various depth layers and
weight-bearing areas of normal and abnormal human articular cartilage.
J Orthop Res. 1989;7(3):326-34.
PMID: 2703925 [PubMed - indexed for MEDLINE]

99: Proctor CS, Schmidt MB, Whipple RR, Kelly MA, Mow VC.
Material properties of the normal medial bovine meniscus.
J Orthop Res. 1989;7(6):771-82. Review.
PMID: 2677284 [PubMed - indexed for MEDLINE]

100: Mow VC, Gibbs MC, Lai WM, Zhu WB, Athanasiou KA.
Biphasic indentation of articular cartilage--II. A numerical algorithm and an
experimental study.
J Biomech. 1989;22(8-9):853-61.
PMID: 2613721 [PubMed - indexed for MEDLINE]

101: Arnoczky SP, McDevitt CA, Schmidt MB, Mow VC, Warren RF.
The effect of cryopreservation on canine menisci: a biochemical, morphologic,
and biomechanical evaluation.
J Orthop Res. 1988;6(1):1-12.
PMID: 3334728 [PubMed - indexed for MEDLINE]

102: Hardingham TE, Muir H, Kwan MK, Lai WM, Mow VC.
Viscoelastic properties of proteoglycan solutions with varying proportions
present as aggregates.
J Orthop Res. 1987;5(1):36-46.
PMID: 3819910 [PubMed - indexed for MEDLINE]

103: Mak AF, Lai WM, Mow VC.
Biphasic indentation of articular cartilage--I. Theoretical analysis.
J Biomech. 1987;20(7):703-14.
PMID: 3654668 [PubMed - indexed for MEDLINE]

104: Akizuki S, Mow VC, Muller F, Pita JC, Howell DS.
Tensile properties of human knee joint cartilage. II. Correlations between
weight bearing and tissue pathology and the kinetics of swelling.
J Orthop Res. 1987;5(2):173-86.
PMID: 3572588 [PubMed - indexed for MEDLINE]

105: Akizuki S, Mow VC, Muller F, Pita JC, Howell DS, Manicourt DH.
Tensile properties of human knee joint cartilage: I. Influence of ionic
conditions, weight bearing, and fibrillation on the tensile modulus.
J Orthop Res. 1986;4(4):379-92.
PMID: 3783297 [PubMed - indexed for MEDLINE]

106: Holmes MH, Lai WM, Mow VC.
Singular perturbation analysis of the nonlinear, flow-dependent compressive
stress relaxation behavior of articular cartilage.
J Biomech Eng. 1985 Aug;107(3):206-18.
PMID: 4046561 [PubMed - indexed for MEDLINE]

107: Armstrong CG, Lai WM, Mow VC.
An analysis of the unconfined compression of articular cartilage.
J Biomech Eng. 1984 May;106(2):165-73.
PMID: 6738022 [PubMed - indexed for MEDLINE]

108: Myers ER, Lai WM, Mow VC.
A continuum theory and an experiment for the ion-induced swelling behavior of
articular cartilage.
J Biomech Eng. 1984 May;106(2):151-8.
PMID: 6738020 [PubMed - indexed for MEDLINE]

109: Mow VC, Mak AF, Lai WM, Rosenberg LC, Tang LH.
Viscoelastic properties of proteoglycan subunits and aggregates in varying
solution concentrations.
J Biomech. 1984;17(5):325-38.
PMID: 6736068 [PubMed - indexed for MEDLINE]

110: Kwan MK, Lai WM, Mow VC.
Fundamentals of fluid transport through cartilage in compression.
Ann Biomed Eng. 1984;12(6):537-58.
PMID: 6534222 [PubMed - indexed for MEDLINE]

111: Mow VC, Holmes MH, Lai WM.
Fluid transport and mechanical properties of articular cartilage: a review.
J Biomech. 1984;17(5):377-94. Review.
PMID: 6376512 [PubMed - indexed for MEDLINE]

112: Armstrong CG, Mow VC.
The mechanical properties of articular cartilage.
Bull Hosp Jt Dis Orthop Inst. 1983 Fall;43(2):109-17.
PMID: 6317094 [PubMed - indexed for MEDLINE]

113: Armstrong CG, Mow VC.
Variations in the intrinsic mechanical properties of human articular cartilage
with age, degeneration, and water content.
J Bone Joint Surg Am. 1982 Jan;64(1):88-94.
PMID: 7054208 [PubMed - indexed for MEDLINE]

114: Grodzinsky AJ, Roth V, Myers E, Grossman WD, Mow VC.
The significance of electromechanical and osmotic forces in the nonequilibrium
swelling behavior of articular cartilage in tension.
J Biomech Eng. 1981 Nov;103(4):221-31.
PMID: 7311487 [PubMed - indexed for MEDLINE]

115: Lai WM, Mow VC, Roth V.
Effects of nonlinear strain-dependent permeability and rate of compression on
the stress behavior of articular cartilage.
J Biomech Eng. 1981 May;103(2):61-6.
PMID: 7278183 [PubMed - indexed for MEDLINE]

116: Roth V, Mow VC.
The intrinsic tensile behavior of the matrix of bovine articular cartilage and
its variation with age.
J Bone Joint Surg Am. 1980 Oct;62(7):1102-17.
PMID: 7430196 [PubMed - indexed for MEDLINE]

117: Mow VC, Kuei SC, Lai WM, Armstrong CG.
Biphasic creep and stress relaxation of articular cartilage in compression?
Theory and experiments.
J Biomech Eng. 1980 Feb;102(1):73-84. No abstract available.
PMID: 7382457 [PubMed - indexed for MEDLINE]

118: Lai WM, Mow VC.
Drag-induced compression of articular cartilage during a permeation experiment.
Biorheology. 1980;17(1-2):111-23. No abstract available.
PMID: 7407341 [PubMed - indexed for MEDLINE]

119: Mow VC.
Biphasic rheological properties of cartilage [proceedings]
Bull Hosp Joint Dis. 1977 Oct;38(2):121-4. No abstract available.
PMID: 614864 [PubMed - indexed for MEDLINE]

120: Mow VC, Mansour JM.
The nonlinear interaction between cartilage deformation and interstitial fluid
flow.
J Biomech. 1977;10(1):31-9. No abstract available.
PMID: 845175 [PubMed - indexed for MEDLINE]

121: Mansour JM, Mow VC.
The permeability of articular cartilage under compressive strain and at high
pressures.
J Bone Joint Surg Am. 1976 Jun;58(4):509-16.
PMID: 1270471 [PubMed - indexed for MEDLINE]

122: Torzilli PA, Mow VC.
On the fundamental fluid transport mechanisms through normal and pathological
articular cartilage during function - II. The analysis, solution and
conclusions.
J Biomech. 1976;9(9):587-606. No abstract available.
PMID: 965425 [PubMed - indexed for MEDLINE]

123: Torzilli PA, Mow VC.
On the fundamental fluid transport mechanisms through normal and pathological
articular cartilage during function--I. The formulation.
J Biomech. 1976;9(8):541-52. No abstract available.
PMID: 956198 [PubMed - indexed for MEDLINE]

124: Redler I, Mow VC, Zimny ML, Mansell J.
The ultrastructure and biomechanical significance of the tidemark of articular
cartilage.
Clin Orthop Relat Res. 1975 Oct;(112):357-62.
PMID: 1192647 [PubMed - indexed for MEDLINE]

125: Mow VC, Lai WM, Eisenfeld J, Redler I.
Some surface characteristics of articular cartilage. II. On the stability of
articular surface and a possible biomechanical factor in etiology of
chondrodegeneration.
J Biomech. 1974 Sep;7(5):457-68. No abstract available.
PMID: 4443359 [PubMed - indexed for MEDLINE]

126: Mow VC, Lai WM.
Some surface characteristics of articular cartilage. I. A scanning electron
microscopy study and a theoretical model for the dynamic interaction of synovial
fluid and articular cartilage.
J Biomech. 1974 Sep;7(5):449-56. No abstract available.
PMID: 4443358 [PubMed - indexed for MEDLINE]

127: Katz JL, Mow VC.
Mechanical and structural criteria for orthopaedic implants.
Biomater Med Devices Artif Organs. 1973;1(4):575-634. Review. No abstract
available.
PMID: 4600332 [PubMed - indexed for MEDLINE]

 

Zhigang Suo's picture

Dear Ed:  Thank you so much for providing this list!  For educational purpose, could you please recommend 2 or 3 papers for newcomers to get started to learn the issues and approaches in this area of research?

1) Highlights in the historical development of porous media theory:
toward a consistent macroscopic theory.  de Boer, Reint, Applied
Mechanics Review, 49:201-262, 1996.

2) Mow VC, Kuei SC, Lai WM, Armstrong CG: Biphasic creep and stress
relaxation of articular cartilage in compression: Theory and Experiment,
J Biomech Engng, Trans ASME, 102:73-84, 1980.

3) Lai WM, Hou JS, Mow VC:  A Triphasic theory for the swelling and
deformational behavior of articular cartilage. J Biomech Engng, Trans
ASME, 113:245-258, 1991.

4) Lai WM, Mow VC, Zhu WB: Constitutive modeling of articular cartilage
and biomolecular solutions.  J Biomech Engng, Trans ASME,115:474-480, 1993.

5) Gu WY, Lai WM, Mow VC:  A mixture theory for charged hydrated soft
tissues containing multi-electrolytes: passive transport and swelling
behavior, J Biomech Engng, Trans ASME, 120:169-180, 1998.

6) Mow VC, Ateshian GA, Lai WM, Gu WY:  Effects of fixed charges on the
stress-relaxation behavior of hydrated soft tissues in confined
compression problem. In: Poroelasticity: Maurice Biot Memorial Issue, 
edited by AHD Cheng, E Detournay, Y Abousleiman, Pergamon Press,
pp4945-4962, 1998.

7) /Porous Media, /edited by W Ehlers, J Bluhm, 2002, Springer, pp459.

Zhigang Suo's picture

I don´t know if this is the right place, but I didn´t find anything about poroviscoelasticity in this forum. I´m trying to reproduce the code made by Suh and Bai, 1998 in MATLAB using the Biphasic Poroviscoelastic Model (BPVE). Anything working with this??

Thanks.

Zhigang Suo's picture

Here is a paper on poroviscoelasticity:

Yuhang Hu, Zhigang Suo. Viscoelasticity and poroelasticity in elastomeric gels. Acta Mechanica Solida Sinica 25, 441-457(2012). 

Hello

I'm working on a project & I'm in a trouble. I need to know creep
relations for a porous material under undrained condition and constant
stress. I'll be gratefull if you help me.

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