Viscous-elastic-plastic behavior of bone using Berkovich nanoindentation (original) (raw)
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Philosophical Magazine, 2010
The indentation derived elastic modulus, E, of bovine compact bone was obtained by means of nanoindentation. The indentation modulus of the dry condition (i.e. under atmospheric conditions) is 40 % higher than when measured wet (i.e. immersed in buffer solution). Although this difference is independent of orientation, there is a % difference in indentation modulus within the same tested environment between longitudinal and transversal directions. In addition, the estimated indentation modulus of the same samples when tested wet in buffer solution after deep freezing (-15ºC) was not affected. The discrepancy between wet and dry results was attributed to the non mineralized phase contribution and rationalized by a simple mechanical model [1]. Anisotropy effects could be explained in terms of deformation mechanisms with orientation. The effect of frozen storage temperatures may be clarified considering the biomechanics of the helicoidal arrangement of lamellar bone. Viscoelastic effects were also considered and incorporated into the analysis of the force-displacement data.
Insight into differences in nanoindentation properties of bone
Journal of the Mechanical Behavior of Biomedical Materials, 2013
Nanoindentation provides the ideal framework to determine mechanical properties of bone at the tissue scale without being affected by the size, shape, and porosity of the bone. However, the values of tissue level mechanical properties vary significantly between studies. Since the differences in the bone sample, hydration state, and test parameters complicate direct comparisons across the various studies, these discrepancies in values cannot be compared directly. The objective of the current study is to evaluate and compare mechanical properties of the same bones using a broad range of testing parameters. Wild type C56BL6 mice tibiae were embedded following different processes and tested in dry and rehydrated conditions. Spherical and Berkovich indenter probes were used, and data analysis was considered within the elasto-plastic (Oliver-Pharr), viscoelastic and visco-elastic-plastic frameworks. The mean values of plane strain modulus varied significantly depending on the hydration state, probe geometry and analysis method. Indentations in dry bone analysed using a visco-elastic-plastic approach gave values of 34 GPa. After rehydrating the same bones and indenting them with a spherical tip and utilizing a viscoelastic analysis, the mean modulus value was 4 GPa, nearly an order of magnitude smaller. Results suggest that the hydration state, probe geometry and the limitations and assumptions of each analysis method influence significantly the measured mechanical properties. This is the first time that such a systematic study has been carried out and it has been concluded that the discrepancies in the mechanical properties of bone measured by nanoindentation found in the literature should not be attributed only to the differences on the bones themselves, but also to the testing and analysis protocols.
The effect of holding time on nanoindentation measurements of creep in bone
Journal of Biomechanics, 2011
Viscoelasticity may affect both the elastic and fracture characteristics of bone. Nanoindentation can be used to measure the creep behavior of bone by fitting the depth vs. time data at constant load to rheological models. However, the creep data may be influenced by latent effects arising during the loading phase of indentation. As such, the loading protocol, particularly the holding time, may affect the measured creep time constants. To characterize the effect of holding time on the measures, four cortical bone samples were prepared from four bovine femora and subjected to nanoindentation to measure the creep behavior. The creep time constants were found by fitting the indentation depth vs. time curve to three different rheological models: the standard linear solid, Burgers model, and a two-dashpot Kelvin model. All three models provided good fits to the data, which were relatively insensitive to the initial parameter estimates. The calculated creep time constants increased monotonically with increasing holding time for all three models. However, the relative differences between measurements within a single osteon, within a single sample, and between samples were maintained for creep holding times over 16 s. Hence, while the creep time constants measured by nanoindentation with hold times up to 30 s may not provide accurate property measurements, comparisons between samples are valid if all are assessed at the same holding time. Considering the long-term viscosity of bone tissue, Burgers model provided the best performance in terms of stability and goodness of fit, and is recommended for future studies.
Biomechanical evaluation of regenerating long bone by nanoindentation
Journal of Materials Science: Materials in Medicine, 2011
It is crucial to measure the mechanical function of regenerating bone in order to assess the mechanical performance of the regenerating portion as well as the efficiency of the regeneration methods. In this study, nanoindentation was applied to regenerating and intact rabbit ulnae to determine the material properties of hardness and elasticity; viscoelasticity was also investigated to precisely evaluate the material properties. Both intact and regenerating bones exhibited remarkable viscoelasticity manifested as a creep behavior during load hold at the maximum load, and the creep was significantly greater in the regenerating bone than the intact bone. The creep resulted in an overestimation of the hardness and Young's modulus. Hence, during nanoindentation testing of bones, the effect of creep should be eliminated. Moreover, the regenerating bone had lower hardness and Young's modulus than the intact bone. The nanoindentation technique proved to be a powerful approach for understanding the mechanical properties of regenerating bone.
2002
Osteoporosis has become an important health and economic problem of our aging western society. This metabolic illness leads to a net bone loss and to a deterioration of trabecular architecture. Motivated by the fact that osteoporosis may also result in a degradation of intrinsic tissue quality this thesis focuses on the micro-and nanomechanical properties of human, bovine and rat bone. For the first time, to the best of our knowledge, mechanical properties of single bone lamellae are tested under dry and physiological conditions. Stable thermal equilibrium conditions can be achieved for the latter that allow for tests at body temperature and under fully wet conditions. This study represents a first step towards extension of knowledge of the structure-function relationships down to the lamellar level. Adjacent thin and thick lamellae of the same bone structural unit (BSU) are significantly different in terms of hardness and indentation modulus. The two types of lamellae show a significantly different increase of mechanical properties when the water content is removed by drying. In this context morphological models are employed to discuss the mechanical properties (bone lamellation theory). The BSU is found to be the basic bone component with individual morphological and also mechanical properties. Significant differences are seen between BSU of osteonal, trabecular and interstitial microstructures dissected from the human femoral neck. Human interstitial and bovine plexiform bone do not show a significantly different indentation modulus. Depth-dependent indentation measurements, which are done for this purpose, further extend our current knowledge of the technique. Structure-function relationships are investigated on the BSU-level by applying two morphological and two mechanical techniques on identical BSUs of two donors. The dependence of the mechanical properties on the mineral content (as measured by microradiography) and the orientation of the collagen fibers (as measured by polarized light microscopy) are investigated. The reported correlations between macroscopic mechanical properties and these morphological parameters are not generally confirmed on the BSU-level by the nanoindentation data of this twocase study. The indentation modulus is validated by a comparison with a traction experiment of a bovine bone microspecimen. This experiment raises confidence in the absolute value of this elastic parameter. The influence of the material anisotropy on the measured indentation modulus is determined for bovine cortical bone. As a first step to apply the nanomechanical tool in the context of preclinical studies, a set of rat vertebrae were tested. Given the small number of specimens, this study does not show a general significance of low protein diet, ovariectomy and essential aminoacids on intrinsic tissue properties. Zusammenhang wird auch der Einfluß der Anisotropie der Kuhkompakta auf den gemessenen Indentationsmodul ermittelt. In einem ersten Schritt, diese nanomechanische Charakterisierungsmethode im Rahmen einer präklinischen Studie anzuwenden, wird ein Kollektiv von Rattenwirbelkörpern gemessen. Diese Studie, die sich auf eine eventuell zu niedrige Zahl an Tieren stützt, zeigt keinen generellen Einfluß der zugrundeliegenden Behandlung. Weder eine operative Entnahme der Gebährmutter in Verbindung mit einer geringen Aufnahme an Eiweissen noch eine Behandlung mit essentiellen Aminosäuren zeigen eine globale Beeinflussung der intrinsischen Gewebeeigenschaften. Diese Doktorarbeit motiviert, die bisherigen Kenntnisse bezüglich der intrinsischen Eigenschaften des Knochengewebes durch weitere Nanoindentationsstudien zu erweitern. Es wird erwartet, daß Zusammenhänge zwischen den nanomechanischen Parametern und dem Beschädigungsgrad von alterndem und/oder osteoporotischem Gewebe gefunden wird. Dies kann einen wesentlichen Beitrag zur Entwicklung neuer Strategien, um die Qualität des Knochengewebes zu verbessern, leisten. 2.2 The effect of drying and re-wetting on the stiffness of single bone lamellae Chapter 3 Depth dependency of indentation modulus and hardness for human and bovine microstructures Chapter 4 Mineral content, collagen fiber orientation and mechanical properties of human compact BSU: a two-case study Chapter 5 How is the indentation modulus of bone tissue related to its macroscopic elastic response? A validation study Chapter 6 The influence of ovariectomy, low protein diet and treatment with essential amino acids on the tissue properties of rat vertebrae: a preclinical study Conclusions & outlook Acknowledgements Curriculum vitae down to single trabeculae and beams of cortical bone were performed (
Journal of Biomedical Materials Research Part A, 2006
Understanding the pathophysiology of metabolic bone disease requires the characterization of both the quantity as well as the quality (i.e., microarchitecture and material properties) of the bone tissue. Nanoindentation provides a powerful yet simple method to measure the nano/micro mechanical properties of bone, but no uniform testing methodology exists. This study examines the effects of embedding materials, rate and depth of indentation, and storage time on the measured modulus. Nineteen trabecular bone samples were evaluated for the study. Although there was an 8-fold increase in the stiffness of the soft to hard epoxy, bone tissue modulus was not affected by the stiffness of the embedding materials, but hardness was affected by both the embedding material modulus, for example from 0.70 Ϯ 0.20 GPa (ME low ) to 0.45 Ϯ 0.21 GPa (ME Med ) (p Ͻ 0.01), and viscosity (p Ͻ 0.01). No significant differences were found with regard to the tested rates and depths of indentation for either elastic modulus or hardness. The tissue modulus tested at the 6-month time point was significantly greater in comparison with that tested at 0 or 3 months (p Ͻ 0.01). The hardness, however, did not significantly change over the span of 6 months. The results show that while nanoindentation is powerful, it is particularly sensitive to certain testing variables.
Journal of Biomechanics, 2010
Nanoindentation has recently gained attention as a characterization technique for mechanical properties of biological tissues, such as bone, on the sub-micron level. However, optimal methods to characterize viscoelastic properties of bones are yet to be established. This study aimed to compare the time-dependent viscoelastic properties of bone tissue obtained with different nanoindentation methods. Bovine cortical and trabecular bone samples (n ¼8) from the distal femur and proximal tibia were dehydrated, embedded and polished. The material properties determined using nanoindentation were hardness and reduced modulus, as well as time-dependent parameters based on creep, loading-rate, dissipated energy and semi-dynamic testing under load control. Each loading protocol was repeated 160 times and the reproducibility was assessed based on the coefficient of variation (CV). Additionally, three well-characterized polymers were tested and CV values were calculated for reference. The employed methods were able to characterize time-dependent viscoelastic properties of bone. However, their reproducibility varied highly (CV 9-40%). The creep constant increased with increasing dwell time. The reproducibility was best with a 30 s creep period (CV 18%). The dissipated energy was stable after three repeated load cycles, and the reproducibility improved with each cycle (CV 23%). The viscoelastic properties determined with semi-dynamic test increased with increase in frequency. These measurements were most reproducible at high frequencies (CV 9-10%). Our results indicate that several methods are feasible for the determination of viscoelastic properties of bone material. The high frequency semi-dynamic test showed the highest precision within the tested nanoindentation protocols.
Journal of Biomechanical Engineering, 2012
The characterization of the biomechanical properties of newly formed bone tissue around implants is important to understand the osseointegration process. The objective of this study is to investigate the evolution of the hardness and indentation modulus of newly formed bone tissue as a function of healing time. To do so, a nanoindentation device is employed following a multimodality approach using histological analysis. Coin-shaped implants were placed in vivo at a distance of 200 μm from the cortical bone surface, leading to an initially empty cavity of 200 μm * 4.4 mm. Three New Zealand White rabbits were sacrificed after 4, 7, and 13 weeks of healing time. The bone samples were embedded and analyzed using histological analyses, allowing to distinguish mature and newly formed bone tissue. The bone mechanical properties were then measured in mature and newly formed bone tissue. The results are within the range of hardness and apparent Young’s modulus values reported in previous lit...
Plastic behaviour of microstructural constituents of cortical bone tissue: a nanoindentation study
International Journal of Experimental and Computational Biomechanics, 2013
A mechanical behaviour of bone tissues is defined by mechanical properties of its microstructural constituents. Also, those properties are important as an input for finiteelement models of cortical bone to simulate its deformation and fracture behaviours at the microstructural level. The aim of this study was to investigate a post-yield behaviour of osteonal cortical bone's microstructural constituents at different loading rates, maximum load levels and dwell times; nanoindentation with a spherical-diamond-tip indenter was employed to determine it. The nanoindentation results revealed significant difference in stiffness values of cortical bone's microstructural features − interstitial matrix and osteons. Similarly, interstitial matrix exhibited a stiffer post-yield behaviour compared to that of osteons that reflects the relationship between the post-yield behaviour and collagen maturity. In addition, both osteons and interstitial matrix demonstrated a time-dependent behaviour. However, in order to assess elastic-plastic behaviour accurately, an effect of viscosity on nanoindentation results was reduced by using a time-delay method.
Load-displacement relations for nanoindentation of viscoelastic materials
Journal of Applied Physics, 2006
A model based on the Burgers viscoelastic concept has been developed to describe the nanoindentation behaviors of polymeric materials. An analytical solution of displacement at the indenter tip has been derived based on the analog of the governing equation of elasticity in the time coordinate system to the governing equation of the viscoelastic model in Laplace transform coordinate system. The solution consists of the elastic, viscous, and plastic displacements during loading and unloading. Nanoindentation experiments have been conducted for poly͑methyl methacrylate͒, polycarbonate, hydroxyethyl methacrylate copolymer, amorphous syndiotactic polystyrene, and fast-cure acrylic polymers to provide data for validating the model. The results show excellent agreement between experimental load-displacement data and model prediction for both the loading and unloading before the contact area decreases for all five polymers. The viscosity decreases but the hardness increases with increasing loading rate. Young's moduli of the interior material obtained by the present study are close to those reported in the literature. Additional analysis showed that the prediction by both the Kelvin and Maxwell viscoelastic models does not agree with the experimental data generated in this study.