Mechanical property determination of bone through nano- and micro-indentation testing and finite element simulation

Abstract

Measurement of the mechanical properties of bone is important for estimating the stresses and strains exerted at the cellular level due to loading experienced on a macro-scale. Nano-and micromechanical properties of bone are also of interest to the pharmaceutical industry when drug therapies have intentional or non-intentional effects on bone mineral content and strength. The interactions that can occur between nano-and micro-indentation creep test condition parameters were considered in this study, and average hardness and elastic modulus were obtained as a function of indentation testing conditions (maximum load, load/unload rate, load-holding time, and indenter shape). The results suggest that bone reveals different mechanical properties when loading increases from the nano-to the micro-scale range (μN to N), which were measured using low-and high-load indentation testing systems. A four-parameter visco-elastic/plastic constitutive model was then applied to simulate the indentation load vs. depth response over both load ranges. Good agreement between the experimental data and finite element model was obtained when simulating the visco-elastic/plastic response of bone. The results highlight the complexity of bone as a biological tissue and the need to understand the impact of testing conditions on the measured results.

A viscoelastic, viscoplastic model of cortical bone valid at low and high strain rates

“…The shorter time constants agree well with previously reported values between 1 and 13 ls [7,20], while the longer time constants are in agreement with the values reported by Melnis and Knets in the 27-592 ms range [9]. The longer time constants also fall in the range of values that can be calculated from the values reported by Bargren et al [16] and Zhang et al [17] for modulus and viscosity.…”

“…After fitting, each parameter is within an order of magnitude across the three separate data sets, indicating the modeling framework is capturing the underlying mechanisms of deformation and rate sensitivity, rather than simply acting as a curve-fitting tool. The values for the first viscosity term, g 1 , agree well with the values published by Bargren et al [16] and Zhang et al [17], while the second viscos- ity term values are in good agreement with the findings published by Tennyson et al [5], Lewis and Goldsmith [7], and Katsamanis and Raftopoulos [10]. The characteristic time constants for each parameter fit, as calculated by the ratio of the viscosity and elasticity of each of the two viscoelastic branches, are presented in Table 2.…”

“…Within the literature a Voigt model is often used to characterize the viscoelastic behavior of cortical bone. The resulting viscosity values range widely from 2.1 Â 10 4 to 2.3 Â 10 9 Pa s with the corresponding long-term elastic constants ranging from 11 to 19.3 GPa [4][5][6][7][8][9][10]16,17]. It has been shown, however, that a linear viscoelastic theory with only one relaxation mechanism does not apply to bone over the wide range of strain rates of interest in this study [9,13].…”

Effect of using different types of methods for the derivation of elastic modulus of bone - A critical survey

“…This leads to a formation of residual impression in the test material. The dimensions of the residual impression and the contact area are then measured directly to determine the hardness of the specimen.This method has the ability to give a spatial resolution of around 1 μm [37] to determine bone's mechanical properties and to achieve bone's nearly accurate young's modulus in several directions because of the highly anisotropic [6,[38][39][40][41][42][43][44] nature of trabecular bone.Nanoindentation also has the capability of producing large indent matrices in a very short period of time with stability especially for mapping the mechanical properties of complex surfaces [45]. Moreover it uses advance depth sensing indentation method, to produce a load displacement curve which is used to measure the stiffness and elastic properties of the sample using various approaches [46].…”

Temporal evolution of skeletal regenerated tissue: what can mechanical investigation add to biological?

“…We simulated a numerical indentation test. We have run these numerical simulations on a semiinfinite medium [20,21,28]. The indenter was assumed to be rigid.…”