Abstract
A gel, an aggregate of polymers with solvents, has dual attributes of solid and liquid as solvent migrates in and out of the polymer network. Indentation has recently been used to characterize the mechanical properties of gels. This paper evaluates the effects of large deformation and material nonlinearity on gel indentation through theoretical modeling and finite element analysis. It is found that large deformation significantly affects the interpretation of the experimental observations and the classical relation between indentation force and depth has limitations for large deformation. The material nonlinearity does not play a very important role on indentation experiment so that the poroelasticity is a good approximation. Based on these observations, this paper proposes an alternative approach to measure the mechanical properties of gels, namely, uniaxial compression experiment.
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References
Duncan, R.: The dawning era of polymer therapeutics. Nature Reviews Drug Discovery 2, 347–360 (2003)
Peppas, N. A., Hilt, J. Z., Khademhosseini, A., et al.: Hydrogels in biology and medicine: From molecular principles to bionanotechnology. Advanced Materials 18, 1345–1360 (2006)
Lee, K. Y., Mooney, D. J.: Hydrogels for tissue engineering. Chemical Reviews 101, 1869–1879 (2001)
Varghese, S., Elisseeff, J. H.: Hydrogels for musculoskeletal tissue engineering. Polymers for Regenerative Medicine. (2006). DOI: 10.1007/12-072
Zhang, J. H., Daubert, C. R., Foegeding, E. A.: Fracture analysis of alginate gels. Journal of Food Science 70, E425–E431 (2005)
Cai, S. Q., Lou, Y. C., Ganguly, P., et al.: Force generated by a swelling elastomer subject to constraint. Journal of Applied Physics 107, (2010)
John, G., Jadhav, S. R., Hong, E.: Phase-selective molecular gels: A new tool for recovery of an oil from oil spills/petroleum products. Abstracts of Papers of the American Chemical Society 241, 18–28 (2011)
Ebenstein, D. M., Pruitt, L. A.: Nanoindentation of soft hydrated materials for application to vascular tissues. Journal of Biomedical Materials Research Part A 69A, 222–232 (2004)
Kaufman, J. D., Miller, G. J., Morgan, E. F., et al.: Timedependent mechanical characterization of poly(2-hydroxyethyl methacrylate) hydrogels using nanoindentation and unconfined compression. Journal of Materials Research 23, 1472–1481 (2008)
Lake, S. P., Hald, E. S., Barocas, V. H.: Collagen-agarose cogels as a model for collagen-matrix interaction in soft tissues subjected to indentation. Journal of Biomedical Materials Research Part A 99A, 507–515 (2011)
Kalcioglu, Z. I., Mahmoodian, R., Hu, Y. H., et al.: From macro-to microscale poroelastic characterization of polymeric hydrogels via indentation. Soft Matter 8, 3393–3398 (2012)
Hu, Y. H., Zhao, X. H., Vlassak, J. J., et al.: Using indentation to characterize the poroelasticity of gels. Applied Physics Letters 96, 121904 (2010)
Cai, S. Q., Hu, Y. H., Zhao, X. H., et al.: Poroelasticity of a covalently crosslinked alginate hydrogel under compression. Journal of Applied Physics 108, 113514 (2010)
Hu, Y. H., Chan, E. P., Vlassak, J. J., et al.: Poroelastic relaxation indentation of thin layers of gels. Journal of Applied Physics 110, 086103 (2011)
Chan, E. P., Hu, Y. H., Johnson, P. M., et al.: Spherical indentation testing of poroelastic relaxations in thin hydrogel layers. Soft Matter 8, 1492–1498 (2012)
Long, R., Hall, M. S., Wu, M. M., et al.: Effects of gel thickness on microscopic indentation measurements of gel modulus. Biophysical Journal 101, 643–650 (2011)
Quinn, T. M., Grodzinsky, A. J.: Longitudinal modulus and hydraulic permeability of poly(methacrylic acid) gels — effects of charge-density and solvent content. Macromolecules 26, 4332–4338 (1993)
Yu, H. Y., Sanday, S. C., Rath, B. B.: The effect of substrate on the elastic properties of films determined by the indentation test — axisymmetrical boussinesq problem. Journal of the Mechanics and Physics of Solids 38, 745–764 (1990)
Hong, W., Zhao, X. H., Zhou, J. X., et al.: A theory of coupled diffusion and large deformation in polymeric gels. Journal of the Mechanics and Physics of Solids 56, 1779–1793 (2008)
Galli, M., Oyen, M. L.: Fast identification of poroelastic parameters from indentation tests. Cmes-Computer Modeling in Engineering & Sciences 48, 241–269 (2009)
Galli, M., Comley, K. S. C., Shean, T. A. V., et al.: Viscoelastic and poroelastic mechanical characterization of hydrated gels. Journal of Materials Research 24, 973–979 (2009)
Hong, W., Liu, Z. S., Suo, Z. G.: Inhomogeneous swelling of a gel in equilibrium with a solvent and mechanical load. International Journal of Solids and Structures 46, 3282–3289 (2009)
Zhang, J. P., Zhao, X. H., Suo, Z. G., et al.: A finite element method for transient analysis of concurrent large deformation and mass transport in gels. Journal of Applied Physics 105, 093522 (2009)
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Duan, Z., An, Y., Zhang, J. et al. The effect of large deformation and material nonlinearity on gel indentation. Acta Mech Sin 28, 1058–1067 (2012). https://doi.org/10.1007/s10409-012-0122-7
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DOI: https://doi.org/10.1007/s10409-012-0122-7