Acta Mechanica Solida Sinica

, Volume 25, Issue 5, pp 441–458 | Cite as

Viscoelasticity and Poroelasticity in Elastomeric Gels

Article

Abstract

An elastomeric gel is a mixture of a polymer network and a solvent. In response to changes in mechanical forces and in the chemical potential of the solvent in the environment, the gel evolves by two concurrent molecular processes: the conformational change of the network, and the migration of the solvent. The two processes result in viscoelasticity and poroelasticity, and are characterized by two material-specific properties: the time of viscoelastic relaxation and the effective diffusivity of the solvent through the network. The two properties define a material-specific length. The material-specific time and length enable us to discuss macroscopic observations made over different lengths and times, and identify limiting conditions in which viscoelastic and poroelastic relaxations have either completed or yet started. We formulate a model of homogeneous deformation, and use several examples to illustrate viscoelasticity-limited solvent migration, where the migration of the solvent is pronounced, but the size of the gel is so small that the rate of change is limited by viscoelasticity. We further describe a theory that evolves a gel through inhomogeneous states. Both infinitesimal and finite deformation are considered.

Key words

elastomer gel viscoelasticity poroelasticity creep stress relaxation 

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References

  1. [1]
    Jeong, B., Bae, Y.H., Lee, D.S. and Kim, S.W., Biodegradable block copolymers as injectable drug-delivery systems. Nature, 1997, 388: 860–862.CrossRefGoogle Scholar
  2. [2]
    Langer, R., Drug delivery and targeting. Nature, 1998, 392: 5–10.Google Scholar
  3. [3]
    Beebe, D.J., Moore, J.S., Bauer, J.M., Yu, Q., Liu, R.H., Devadoss, C. and Jo, B.H., Functional hydrogel structures for autonomous flow control inside microfluidic channels. Nature, 2000, 404: 588–590.CrossRefGoogle Scholar
  4. [4]
    Suo, Z., Theory of dielectric elastomers. Acta Mechanica Solida Sinica, 2010, 23: 549–577.CrossRefGoogle Scholar
  5. [5]
    Richter, A., Paschew, G., Klatt, S., Lienig, J., Arndt, K.-F. and Adler, H.-J.P., Review on hydrogel-based pH sensors and microsensors. Sensors, 2008, 8: 561–581.CrossRefGoogle Scholar
  6. [6]
    Gerlach, G., Guenther, M., Sorber, J., Subchaneck, G., Arndt, K.-F. and Richter, A., Chemical and pH sensors based on the swelling behavior of hydrogels. Sensors and Actuators B: Chemical, 2005, 111–112: 555–561.CrossRefGoogle Scholar
  7. [7]
    Luo, Y. and Shoichet, M.S., A photolabile hydrogel for guided three-dimensional cell growth and migration. Nature Material, 2004, 3: 249–253.CrossRefGoogle Scholar
  8. [8]
    Nowak, A.P., Breedveld, V., Pakstis, L., Ozbas, B., Pine, D.J., Pochan, D. and Deming, T.J., Rapidly recovering hydrogel scaffolds from self-assembling diblock copolypeptide amphiphiles. Nature, 2002, 417: 424–428.CrossRefGoogle Scholar
  9. [9]
    Cai, S., Lou, Y., Ganguly, P., Robisson, A. and Suo, Z., Force generated by a swelling elastomer subject to constraint. Journal of Applied Physics, 2010, 107: 03535–103535–7.Google Scholar
  10. [10]
    Bergaya, F., Theng, B.K.G. and Lagaly, G., Handbook of Clay Science. UK: Elsevier, 2006.Google Scholar
  11. [11]
    Coussy, O., Poromechanics. England: John Wiley & Sons Ltd, 2004.MATHGoogle Scholar
  12. [12]
    Cleary, M.R., Elastic and dynamic response regimes of fluid-impregnated solids with diverse microstructures. International Journal of Solids and Structures, 1978, 14: 795–819.CrossRefGoogle Scholar
  13. [13]
    Rice, J.R. and Cleary, M.P., Some basic stress-diffusion solutions for fluid-saturated elastic porous media with compressible constituents. Reviews of Geophysics and Space Physics, 1976, 14: 227–241.CrossRefGoogle Scholar
  14. [14]
    Rice, J.R., Pore pressure effects in inelastic constitutive formulations for fissured rock aasses. In: Advances in Civil Engineering Through Engineering Mechanics (Proceedings of 2nd ASCE Engineering Mechanics Division Specialty Conference, Raleigh, N.C., 1977), American Society of Civil Engineers, New York, 1977: 295–297.Google Scholar
  15. [15]
    Mow, V.C., Kuei, S.C., Lai, W.M. and Armstrong, C.G., Biphasic creep and stress relaxation of articular cartilage compression: theory and experiments. Journal of Biomechanical Engineering, 1980, 102: 73–84.CrossRefGoogle Scholar
  16. [16]
    Kovach, I.S., A molecular theory of cartilage viscoelasticity. Biophysical Chemistry, 1996, 59: 61–73.CrossRefGoogle Scholar
  17. [17]
    Huang, C.-Y., Mow, V.C. and Ateshian, G.A., The role of flow-independent viscoelasticity in the biphasic tensile and compressive responses of articular cartilage. Journal of Biomechanical Engineering, 2001, 123: 410–417.CrossRefGoogle Scholar
  18. [18]
    Li, L.P., Herzog, W. and Korhonen, R.K., The role of viscoelasticity of collagen fibers in articular cartilage: axial tension versus compression. Medical Engineering & Physics, 2005, 27: 51–57.CrossRefGoogle Scholar
  19. [19]
    Leipzig, N.D. and Athanasiou, K.A., Unconfined creep compression of chondrocytes. Journal of Biomechanics, 2005, 38: 77–85.CrossRefGoogle Scholar
  20. [20]
    Cheng, S. and Bilston, L.E., Unconfined compression of white matter. Journal of Biomechanics, 2007, 40: 117–124.CrossRefGoogle Scholar
  21. [21]
    Ji, B. and Bao, G., Cell and molecular biomechanics: perspectives and challenges. Acta Mechanica Solida Sinica, 2011, 24: 27–51.CrossRefGoogle Scholar
  22. [22]
    Buehler, M.J., Multiscale mechanics of biological and biologically inspired materials and structures. Acta Mechanica Solida Sinica, 2010, 23: 471–483.CrossRefGoogle Scholar
  23. [23]
    Biot, M.A., Theory of deformation of a porous viscoelastic anisotropic solid. Journal of Applied Physics, 1956, 27: 459–467.MathSciNetCrossRefGoogle Scholar
  24. [24]
    Biot, M.A., Mechanics of deformation and acoustic propagation in porous media. Journal of Applied Physics, 1962, 33: 1482–1497.MathSciNetCrossRefGoogle Scholar
  25. [25]
    Biot, M.A., Theory of stability and consolidation of a porous medium under initial stress. Journal of Mathematics and Mechanics, 1963, 12: 521–541.MathSciNetMATHGoogle Scholar
  26. [26]
    Freudenthal, A.M. and Spillers, W.R., Solutions for the infinite layer and the half-space for quasi-static consolidating elastic and viscoelastic media. Journal of Applied Physics, 1962, 33: 2661–2668.MathSciNetCrossRefGoogle Scholar
  27. [27]
    Abousleiman, Y., Cheng, A.H.-D. and Roegiers, J.-C., A micromechanically consistent poroviscoelasticity theory for rock mechanics applications. International Journal of Rock Mechanics and Mining Sciences and Geomechanics, 1993, 30: 1177–1180.CrossRefGoogle Scholar
  28. [28]
    Abousleiman, Y., Cheng, A.H.-D., Jiang, C. and Roegiers, J.-C., Poroviscoelastic analysis of borehole and cylinder problems. Acta Mechanica, 1996, 119: 199–219.CrossRefGoogle Scholar
  29. [29]
    Vgenopoulou, I. and Beckos, D.E., Dynamic behavior of saturated poroviscoelastic media. Acta Mechanica, 1991, 95: 185–195.CrossRefGoogle Scholar
  30. [30]
    Schanz, M. and Cheng, A.H.-D., Dynamic analysis of a one-dimensional poroviscoelastic column. Journal of Applied Mechanics, 2001, 68: 192–198.CrossRefGoogle Scholar
  31. [31]
    Hoang, S.K. and Abousleiman, Y.N., Poroviscoelasticity of transversely isotropic cylinders under laboratory loading conditions. Mechanics Research Communication, 2010, 37: 298–306.CrossRefGoogle Scholar
  32. [32]
    Mak, A.F., Unconfined compression of hydrated viscoelastic tissues: a biphasic poroviscoelastic analysis. Biorheology, 1986, 23: 371–383.CrossRefGoogle Scholar
  33. [33]
    DiSilvestro, M.R. and Suh, J.-K.F., A cross-validation of the biphasic poroviscoelastic model of articular cartilage in unconfined compression, indentation and confined compression. Journal of Biomechanics, 2001, 34: 519–525.CrossRefGoogle Scholar
  34. [34]
    DiSilvestro, M.R., Zhu, Q., Wong, M., Jurvelin, J.S. and Suh, J.-K.F., Biphasic poroviscoelastic simulation of the unconfined compression of articular cartilage: I-Simultaneous prediction of reaction force and lateral displacement. Journal of Biomechanical Engineering, 2001, 123: 191–197.CrossRefGoogle Scholar
  35. [35]
    Wilson, W., van Donkelaar, C.C., van Rietbergen, B. and Huiskes, R., A fibril-reinforced poroviscoelastic swelling model for articular cartilage. Journal of Biomechanics, 2005, 38: 1195–1204.CrossRefGoogle Scholar
  36. [36]
    Olberding, J.E., and Suh, J.-K.F., A dual optimization method for the material parameter identification of a biphasic poroviscoelastic hydrogel: potential application to hypercompliant soft tissues. Journal of Biomechanics, 2006, 39: 2468–2475.CrossRefGoogle Scholar
  37. [37]
    Julkunen, P., Wilson, W., Jurvelin, J.S., Rieppo, J., Qu, C.-J., Lammi, M.J. and Korhonen, R.K., Stress-relaxation of human patellar articular cartilage in unconfined compression: prediction of mechanical response by tissue composition and structure. Journal of Biomechanics, 2008, 41: 1978–1986.CrossRefGoogle Scholar
  38. [38]
    Hoang, S.K. and Abousleiman, Y.N., Poroviscoelastic two-dimensional anisotropic solution with application to articular cartilage testing. Journal of Engineering Mechanics, 2009, 135: 367–374.CrossRefGoogle Scholar
  39. [39]
    Chiravarambath, S., Simha, N.K., Namani, R. and Lewis, J.L., Poroviscoelastic cartilage properties in the mouse from indentation. Journal of Biomechanical Engineering, 2009, 131: 011004.CrossRefGoogle Scholar
  40. [40]
    Raghunathan, S., Evans, D. and Sparks, J.L., Poroviscoelastic modeling of liver biomechanical response in unconfined compression. Annals of Biomedical Engineering, 2010, 38: 1789–1800.CrossRefGoogle Scholar
  41. [41]
    Galli, M., Fornasiere, E., Gugnoni, J. and Oyen, M.L., Poroviscoelastic characterization of particle-reinforced gelatin gels using indentation and homogenization. Journal of the Mechanical Behavior of Biomedical Materials, 2011, 4: 610–617.CrossRefGoogle Scholar
  42. [42]
    Ferry, J.D., Viscoelastic Properties of Polymers, 3rd. New York: John Wiley and Sons, 1980.Google Scholar
  43. [43]
    Schapery, R.A., Nonlinear viscoelastic and viscoplastic constitutive equations based on thermodynamics. Mechanics of Time-dependent Materials, 1997, 1: 209–240.CrossRefGoogle Scholar
  44. [44]
    Hu, Y., Zhao, X., Vlassak, J.J. and Suo, Z., Using indentation to characterize the poroelasticity of gels. Applied Physics Letters, 2010, 96: 121904.CrossRefGoogle Scholar
  45. [45]
    Cai, S., Hu, Y., Zhao, X. and Suo, Z., Poroelasticity of a covalently crosslinked alginate hydrogel under compression. Journal of Applied Physics, 2010, 108: 113514.CrossRefGoogle Scholar
  46. [46]
    Hu, Y., Chen, X., Whitesides, G.M., Vlassak, J.J. and Suo, Z., Indentation of polydimethylsiloxane submerged in organic solvents. Journal of Material Research, 2011, 26: 785–795.CrossRefGoogle Scholar
  47. [47]
    Constantinides, G., Kalcioglu, Z.I., McFarland, M., Smith, J.F. and Van Vliet, K.J., Probing mechanical properties of fully hydrated gels and biological tissues. Journal of Biomechanics, 2008, 41: 3285–3289.CrossRefGoogle Scholar
  48. [48]
    Kaufman, J.D., Miller, G.J., Morgan, E.F. and Klapperich, C.M., Time-dependent mechanical characterization of poly (2-hydroxyethylmethacrylate) hydrogels using nanoindentation and unconfined compression. Journal of Material Research, 2008, 23: 1472–1481.CrossRefGoogle Scholar
  49. [49]
    Zhao, X., Huebsch, N., Mooney, D.J. and Suo, Z., Stress-relaxation behavior in gels with ionic and covalent crosslinks. Journal of Applied Physics, 2010, 107: 063509.CrossRefGoogle Scholar
  50. [50]
    Charras, G.T., Mitchison, T.J. and Mahadevan, L., Animal cell hydraulics. Journal of Cell Science, 2009, 122: 3233–3241.CrossRefGoogle Scholar
  51. [51]
    Rosenbluth, M.J., Crow, A., Shaevitz, J.W. and Fletcher, D.A., Slow stress propagation in adherent cells. Biophysical Journal, 2008, 95: 6052–6059.CrossRefGoogle Scholar
  52. [52]
    Darling, E.M., Zauscher, S., Block, J.A. and Guilak, F., A thin-layer model for viscoelastic, stress-relaxation testing of cells using atomic force microscopy: do cell properties reflect metastatic potential? Biophysical Journal, 2007, 92: 1784–1791.CrossRefGoogle Scholar
  53. [53]
    Forgacs, G., Foty, R.A., Shafrir, Y. and Steinberg, M.S., Viscoelastic properties of living embryonic tissues: a quantitative study. Biophysical Journal, 1998, 74: 2227–2234.CrossRefGoogle Scholar
  54. [54]
    Hong, W., Zhao, X., Zhou, J. and Suo, Z., A theory of coupled diffusion and large deformation in polymeric gels. Journal of the Mechanics and Physics of Solids, 2008, 56: 1779–1793.CrossRefGoogle Scholar
  55. [55]
    Silberstein, M.N. and Boyce, M.C., Constitutive modeling of the rate, temperature, and hydration dependent deformation response of Nafion to monotonic and cyclic loading. Journal of Power Sources, 2010, 195: 5692–5706.CrossRefGoogle Scholar
  56. [56]
    Zhao, X., Koh, S.J.A. and Suo, Z., Nonequilibrium thermodynamics of dielectric elastomers. International Journal of Applied Mechanics, 2011, 3: 203–217.CrossRefGoogle Scholar
  57. [57]
    Hong, W., Modeling viscoelastic dielectrics. Journal of the Mechanics and Physics of Solids, 2011, 59: 637–650.MathSciNetCrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2012

Authors and Affiliations

  1. 1.School of Engineering and Applied Sciences, Kavli Institute for Nanobio Science and TechnologyHarvard UniversityCambridgeUSA

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