Poroelastic nanoindentation responses of hydrated bone
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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.
I. INTRODUCTION
Bone is both an important structural material, attracting significant interest both in the context of medicine and in biomimetic materials development. Bone in its natural state is a nanocomposite with three primary components: mineral, a carbonated apatite comprising approximately 75 wt% of bone (near 50 vol%)1; an organic matrix representing 15–20 wt% (around 33 vol%), of which 90% is the fibrillar protein collagen2; the balance (17 vol%) is water. As in most structural connective tissues, cells make up a very small component by volume. Bone is frequently considered as a two-phase composite consisting of a stiff mineral phase and a compliant hydrated protein matrix present in approximately equal volume fractions.3,4 A second approach to bone composite mechanics is to consider a water-saturated porous elastic (hybrid protein–mineral) network. Conceivably, depending on the properties studied, each approach has merit in the consideration of bone as a material, although for studa)
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 DOI: 10.1557/JMR.2008.0156 J. Mater. Res., Vol. 23, No. 5, May 2008
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ies of time-dependent mechanical responses the latter approach is preferred. Although bone is sometimes characterized using empirical viscoelastic analyses, a portion of the time dep
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