Viscoelastic effects during depth-sensing indentation of cortical bone tissues

Abstract

When using nanoindentation to measure the mechanical properties of biological tissues, viscoelastic effects may be significant and may affect the accuracy of the results. In this study, a method for correcting viscoelastic effects during nanoindentation is described. The correction formula involved is re-derived using a three-element nonlinear visco-plasto-elastic material tensor model. This method is then applied to forelimb and femur bone samples taken from two species (C57 BL/6N and ICR) of mice. After correcting for viscoelastic effects, elastic modulus and hardness results are found to be independent of experimental conditions, such as the unloading rate. Measured mechanical properties also correlate well with the calcium content of the bone samples.

Indentation of bone tissue: a short review

“…Moreover a viscoelastic analysis may be done, extracting the storage and loss moduli of the tested material [44]. Indentation analysis was recently also extended to isotropic viscoelastic materials [7,41,43]. Using this theory, a creep function can be identified for bone using the loading and/or the constant load part (creep) of the indentation curve [2].…”

Deformation partitioning provides insight into elastic, plastic, and viscous contributions to bone material behavior

“…The roles of bone's constituent phases and how they contribute to the nanomechanical response and viscoelastic behavior have also been studied to provide insight into tissuelevel behavior (Bushby et al, 2004;Bembey et al, 2005Bembey et al, , 2006aOyen, 2006;Tang et al, 2006;Oyen and Ko, 2007;Oyen, 2008;Oyen et al, 2008). The composite material of bone gains its high strength from a stiff mineral phase (≈50 wt%), highly elastic organic phase (≈30 wt%), and water (≈20 wt%) (Gong et al, 1964;Hayes, 1991).…”

Nanoindentation Measurement of Mechanical Properties of Soft Solid Covered By a Thin Liquid Film

“…1(b) is the situation we already considered in our previous work on power-law viscoelasticity effects during unloading of a dry sample (11,12). In particular, just before and just after unloading at time t h following a constant load holding as shown in the load cycle P-t in Fig.…”

“…The first is that biological tissues are usually highly viscoelastic, but the standard protocol, to analyze nanoindentation data to yield material properties-due to Oliver and Pharr (6)-assumes the sample to be purely elastic during unloading. We-along with other researchers (7)(8)(9)(10)(11)(12)(13)(14)-have addressed the problem associated with strong viscoelasticity during unloading. In particular, a method was developed to correct for general, power-law viscoelasticity effects (11), and the usefulness and accuracy of this method have been demonstrated in a wide range of viscoelastic samples (9,11), including bone samples (12).…”