Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-30T06:06:35.506Z Has data issue: false hasContentIssue false
  • English
  • Français

Poroelastic nanoindentation responses of hydrated bone

Published online by Cambridge University Press:  31 January 2011

Michelle L. Oyen
Michelle L. Oyen*
Affiliation:
Cambridge University, Engineering Department, Cambridge CB2 1PZ, United Kingdom
*
a)Address all correspondence to this author. e-mail: [email protected] This author was an editor of this journal during the review and decision stage. For the JMR policy on review and publication of manuscripts authored by editors, please refer to http://www.mrs.org/publications/jmr/policy.html
Get access

Abstract

Indentation techniques are used for the measurement of mechanical properties of a wide range of materials. Typical elastic analysis for spherical indentation is applicable in the absence of time-dependent deformation, but is inappropriate for materials with time-dependent creep responses active in the experimental time frame. In the current work, a poroelastic analysis—a mechanical theory incorporating fluid motion through a porous elastic network—is used to examine spherical indentation creep responses of hydrated biological materials. Existing analytical and finite element solutions for the poroelastic Hertzian indentation problem are reviewed, and a poroelastic parameter identification scheme is developed. Experimental data from nanoindentation of hydrated bone immersed in water and polar solvents (ethanol, methanol, acetone) are examined within the poroelastic framework. Immersion of bone in polar solvents with decreasing polarity results in increased stiffness, decreased Poisson’s ratio, and decreased hydraulic permeability. Nanoindentation poroelastic analysis results are compared with existing literature for bone poroelasticity at larger length scales, and the effective pore size probed in indentation creep experiments was estimated to be 1.6 nm, consistent with the scale of fundamental collagen–apatite interactions. Results for water permeability in bone were compared with studies of water diffusion through fully dense bone.

Keywords

BonePorosityViscoelasticity
Type
Articles
Information
Journal of Materials Research , Volume 23 , Issue 5 , May 2008 , pp. 1307 - 1314
Copyright
Copyright © Materials Research Society 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1Huiskes, R.van Rietbergen, B.: Biomechanics of bone in Basic Orthopaedic Biomechanics and Mechanobiology, 3rd ed. edited by V.C. Mow and R. Huiskes Lippincott, Williams and Wilkins Philadelphia 2005 Chap. 4 123–179Google Scholar
2Kaplan, F.S., Hayes, W.C., Keaveny, T.M., Boskey, A., Einhorn, T.A.Iannotti, J.P.: Form and function of bone in Orthopaedic Basic Science, edited by S.R. Simon AAOS Rosemont, IL 1994Google Scholar
3Katz, J.L.: Hard tissue as a composite material. I. Bounds on the elastic behavior. J. Biomech. 4, 455 1971Google Scholar
4Oyen, M.L.Ko, C-C.: Finite element modeling of bone ultrastructure as a two-phase composite in Mechanical Properties of Bioinspired and Biological Materials,, edited by C. Viney, K. Katti, F-J. Ulm, and C. Hellmich, Mater. Res. Soc. Symp. Proc. 844, Warrendale, PA, 2005), Y8.7, pp. 263–268Google Scholar
5Cowin, S.C.: Bone poroelasticity. J. Biomech. 32, 217 1999CrossRefGoogle ScholarPubMed
6Wang, H.F.: Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology Princeton University Press Princeton, NJ 2000Google Scholar
7Schuh, C.A.: Nanoindentation studies of materials. Mater. Today 9, 32 2006Google Scholar
8Ebenstein, D.Pruitt, L.: Nanoindentation of biological materials. Nano Today 1, 26 2006Google Scholar
9Field, J.S.Swain, M.V.: A simple predictive model for spherical indentation. J. Mater. Res. 8, 297 1993Google Scholar
10Oliver, W.C.Pharr, G.M.: Improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 1992Google Scholar
11Lee, E.H.Radok, J.R.M.: Contact problem for viscoelastic bodies. J. Appl. Mech. 27, 438 1960Google Scholar
12Ting, T.C.T.: The contact stresses between a rigid indentor and a viscoelastic half-space. J. Appl. Mech. 88, 845 1966Google Scholar
13Johnson, K.L.: Contact Mechanics Cambridge University Press Cambridge, UK 1985CrossRefGoogle Scholar
14Oyen, M.L.Bushby, A.J.: Viscoelastic effects in small-scale indentation of biological materials. I. J. Surf. Sci. Eng. (2007, in press)Google Scholar
15Oyen, M.L.: Analytical techniques for indentation of viscoelastic materials. Philos. Mag. 86, 5625 2006Google Scholar
16Oyen, M.L.: Spherical indentation creep following ramp loading. J. Mater. Res. 20, 2094 2005CrossRefGoogle Scholar
17Oyen, M.L.Ko, C-C.: Examination of local variations in viscous, elastic, and plastic indentation responses in healing bone. J. Mater. Sci.: Mater. Med. 18, 623 2007Google Scholar
18Lakes, R.S.: Materials with structural hierarchy. Nature 361, 511 1993CrossRefGoogle Scholar
19Bembey, A.K., Oyen, M.L., Bushby, A.J.Boyde, A.: Viscoelastic properties of bone as a function of hydration state determined by nanoindentation. Philos. Mag. 86, 5691 2006CrossRefGoogle Scholar
20Bembey, A.K., Bushby, A.J., Boyde, A., Ferguson, V.L.Oyen, M.L.: Hydration effects on bone micro-mechanical properties. J. Mater. Res. 21, 1962 2006CrossRefGoogle Scholar
21Mattice, J.M., Lau, A.G., Oyen, M.L.Kent, R.W.: Spherical indentation load-relaxation of soft biological tissues. J. Mater. Res. 21, 2003 2006Google Scholar
22Agbezuge, L.K.Deresiewicz, H.: On the indentation of a consolidating half-space. Israel J. of Technol. 12, 322 1974Google Scholar
23Selvadurai, A.P.S.: Stationary damage modeling of poroelastic contact. Int. J. Solids Struct. 41, 2043 2004CrossRefGoogle Scholar
24Oyen, M.L.: Sensitivity of polymer nanoindentation creep properties to experimental variables. Acta Mater. 55, 3633 2007Google Scholar
25Oyen, M.L.: Spherical indentation creep following ramp loading in Fundamentals of Nanoindentation and Nanotribology III,, edited by K.J. Wahl, N. Huber, A.B. Mann, D.F. Bahr, and Y-T. Cheng (Mater. Res. Soc. Symp. Proc. 841, Warrendale, PA, 2005) p.211–216CrossRefGoogle Scholar
26Gibson, L.J.Ashby, M.F.Cellular Solids: Structure and Properties, 2nd ed.Cambridge University Press Cambridge, UK 1997CrossRefGoogle Scholar
27CRC Handbook of Chemistry and Physics, 73rd ed. D.R. Lide, editor CRC Press, Inc. Boca Raton, FL 1992–1993Google Scholar
28Zysset, P.K., Guo, X.E., Hoffler, C.E., Moore, K.E.Goldstein, S.A.: Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur. J. Biomech. 32, 1005 1999Google Scholar
29McCutchen, C.W.: Cartilage is poroelastic, not viscoelastic (including an exact theorem about strain energy and viscous loss, and an order of magnitude relation for equilibration time). J. Biomech. 15, 325 1982Google Scholar
30Vollrath, F.: Strength and structure of spiders’ silks. Rev. Mol. Biotechnol. 74, 67 2000Google Scholar
31Ntim, M.M., Bembey, A.K., Ferguson, V.L.Bushby, A.J.: Hydration effects on the viscoelastic properties of collagen in Mechanical Behavior of Biological and Biomimetic Materials,, edited by A.J. Bushby, V.L. Ferguson, C-C. Ko, and M.L. Oyen (Mater. Res. Soc. Symp. Proc. 898E, Warrendale, PA, 2006), 0898-L05-02Google Scholar
32Bembey, A.K., Oyen, M.L., Ferguson, V.L., Bushby, A.J.Boyde, A.: Effect of water on mechanical properties of mineralized tissue composites in Mechanics of Biological and Bio-Inspired Materials,, edited by C. Viney, K. Katti, C. Hellmich, U. Wegst (Mater. Res. Soc. Symp. Proc. 975E, Warrendale, PA, 2007), 0975-DD09-04Google Scholar
33Lakes, R.S.: Deformation mechanisms of negative Poisson’s ratio materials: Structural aspects. J. Mater. Sci. 26, 2287 1991CrossRefGoogle Scholar
34Yasuda, H., Lamaze, C.E.Peterlin, A.: Diffusive and hydraulic permeabilities of water in water-swollen polymer membrane. J. Polym. Sci., Part A-2 9, 1117 1971Google Scholar
35Fernandez-Seara, M.A., Wehrli, S.L.Wehrli, F.X.: Diffusion of exchangeable water in cortical bone studied by nuclear magnetic resonance. Biophys. J. 82, 522 2002Google Scholar
36Sasaki, N.Enyo, A.: Viscoelastic properties of bone as a function of water content. J. Biomech. 28, 809 1995Google Scholar
37Swadener, J.G., Rho, J-Y.Pharr, G.M.: Effects of anisotropy on elastic moduli measured by nanoindentation in human tibial cortical bone. J. Biomed. Mater. Res. 57, 108 20013.0.CO;2-6>CrossRefGoogle ScholarPubMed
38Smit, T.H., Huyghe, J.M.Cowin, S.C.: Estimation of the poroelastic parameters of cortical bone. J. Biomech. 35, 829 2002Google Scholar