Factors impacting nanoindentation testing results of the cuticle of dung beetle Copris ochus Motschulsky

1 Introduction Insects have been adapted to their living surround-ings. Two different adaptations they have were the pas-sive adaptation and the active adaptation. For examples,the passive adaptation of soil insects to the soil habitatresulted in shorter or vestigial additional legs, the bodybecoming smaller, thinner or flatter, and wings and eyesdiminishing; the stronger digging legs of some soil in-sects were a result of active adaptation for burrowing [1]. The biological character…     

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

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 micro-mechanical 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 (microN 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.     

Skin viscoelasticity studied in vitro by microprobe-based techniques

Time-dependent deformation of porcine skin was studied in vitro using specialized microprobe instruments. The deformation behavior of stratum corneum, dermis, and whole skin is examined in the context of results of creep strain, elastic stiffness, and viscoelastic constants obtained in terms of the hold time, loading/unloading rate, and maximum indentation depth (load). Skin time-dependent deformation is significantly influenced by dermis viscoelasticity up to a critical indentation depth (load) beyond which it is controlled by the outermost hard epidermis, particularly stratum corneum. Skin viscoelastic behavior under constant load (creep) and constant displacement (stress relaxation) is interpreted in the light of phenomenological observations and experimental trends.     

Precision of nanoindentation protocols for measurement of viscoelasticity in cortical and trabecular bone

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=8) 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.     

Analysis of indentation: implications for measuring mechanical properties with atomic force microscopy.

Indentation using the atomic force microscope (AFM) has potential to measure detailed micromechanical properties of soft biological samples. However, interpretation of the results is complicated by the tapered shape of the AFM probe tip, and its small size relative to the depth of indentation. Finite element models (FEMs) were used to examine effects of indentation depth, tip geometry, and material nonlinearity and heterogeneity on the finite indentation response. Widely applied infinitesimal strain models agreed with FEM results for linear elastic materials, but yielded substantial errors in the estimated properties for nonlinear elastic materials. By accounting for the indenter geometry to compute an apparent elastic modulus as a function of indentation depth, nonlinearity and heterogeneity of material properties may be identified. Furthermore, combined finite indentation and biaxial stretch may reveal the specific functional form of the constitutive law--a requirement for quantitative estimates of material constants to be extracted from AFM indentation data.     

An application of nanoindentation technique to measure bone tissue Lamellae properties

Measuring the microscopic mechanical properties of bone tissue is important in support of understanding the etiology and pathogenesis of many bone diseases. Knowledge about these properties provides a context for estimating the local mechanical environment of bone related cells thait coordinate the adaptation to loads experienced at the whole organ level. The objective of this study was to determine the effects of experimental testing parameters on nanoindentation measures of lamellar-level bone mechanical properties. Specifically, we examined the effect of specimen preparation condition, indentation depth, repetitive loading, time delay, and displacement rate. The nanoindentation experiments produced measures of lamellar elastic moduli for human cortical bone (average value of 17.7 +/- 4.0 GPa for osteons and 19.3 +/- 4.7 GPa for interstitial bone tissue). In addition, the hardness measurements produced results consistent with data in the literature (average 0.52 +/- 0.15 GPa for osteons and 0.59 +/- 0.20 GPa for interstitial bone tissue). Consistent modulus values can be obtained from a 500-nm-deep indent. The results also indicated that the moduli and hardnesses of the dry specimens are significantly greater (22.6% and 56.9%, respectively) than those of the wet and wet and embedded specimens. The latter two groups were not different. The moduli obtained at a 5-nm/s loading rate were significantly lower than the values at the 10- and 20-nm/s loading rates while the 10- and 20-nm/s rates were not significantly different. The hardness measurements showed similar rate-dependent results. The preliminary results indicated that interstitial bone tissue has significantly higher modulus and hardness than osteonal bone tissue. In addition, a significant correlation between hardness and elastic modulus was observed.     

Nanoindentation response of cortical bone: dependency of subsurface voids

Nanoindentation test results in the axial direction of mouse femurs were the basis for the current study. Although the majority of the nanoindentation curves showed a reasonable consistency, some curves showed a significantly softer response. Detailed investigation, using focused ion beam-scanning electron microscopy, provided that the softer response is due to subsurface cavities such as lacunae. Finite element models were developed to simulate the nanoindentation of mice femur cortical bone samples with and without the incorporation of a single lacuna underneath the bone surface. Based on the material parameters determined for the cavity-free tissue, numerical simulations were run for different cases of cavity size, shape, and location. Spherical cavities with different size were considered at different distances from the surface. The results showed that subsurface cavities can lead to 50% higher indentation compared to an indentation in cavity-free material. Continuing with ellipsoidal cavities with the center located on the load axis, the results showed a nonlinear dependency of ellipsoid shape. Hence, the shape of the cavity is important for the nanoindentation response. The influence of horizontal and vertical offsets of spherical cavities was studied, thereby the results showed that an increasing horizontal offset caused a decreasing influence of the vertical distance from the surface. In perspective, the present study provides information that may help to get deeper knowledge of nanoindentation load–displacement mechanism taking place in samples with subsurface cavities.     

Linear viscoelasticity - bone volume fraction relationships of bovine trabecular bone

Trabecular bone has been previously recognized as time-dependent (viscoelastic) material, but the relationships of its viscoelastic behaviour with bone volume fraction (BV/TV) have not been investigated so far. Therefore, the aim of the present study was to quantify the time-dependent viscoelastic behaviour of trabecular bone and relate it to BV/TV. Uniaxial compressive creep experiments were performed on cylindrical bovine trabecular bone samples (\(\textit{n}\,{=}\,13\)) at loads corresponding to physiological strain level of 2000 \({\upmu }{\upvarepsilon }\). We assumed that the bone behaves in a linear viscoelastic manner at this low strain level and the corresponding linear viscoelastic parameters were estimated by fitting a generalized Kelvin–Voigt rheological model to the experimental creep strain response. Strong and significant power law relationships (\(r^2\,{=}\,0.73,\ p\,{<}\,0.001\)) were found between time-dependent creep compliance function and BV/TV of the bone. These BV/TV-based material properties can be used in finite element models involving trabecular bone to predict time-dependent response. For users’ convenience, the creep compliance functions were also converted to relaxation functions by using numerical interconversion methods and similar power law relationships were reported between time-dependent relaxation modulus function and BV/TV.     

"Creep currents" in single frog atrial cells may be generated by electrogenic Na/Ca exchange

The objective of these experiments was to test the hypothesis that the "creep currents" induced by Na loading of single frog atrial cells (Hume, J. R., and A. Uehara. 1986. Journal of General Physiology. 87:833) may be generated by an electrogenic Na/Ca exchanger. Creep currents induced by Na loading were examined over a wide range of membrane potentials. During depolarizing voltage-clamp pulses, outward creep currents were observed, followed by inward creep currents upon the return to the holding potential. During hyperpolarizing voltage-clamp pulses, creep currents of the opposite polarity were observed: inward creep currents were observed during the pulses, followed by outward creep currents upon the return to the holding potential. The current-voltage relations for inward and outward creep currents in response to depolarizing or hyperpolarizing voltage displacements away from the holding potential all intersect the voltage axis at a common potential, which indicates that inward and outward creep currents may have a common reversal potential under equilibrium conditions and may therefore be generated by a common mechanism. Measurements of inward creep currents confirm that voltage displacements away from the holding potential rapidly alter equilibrium conditions. Current-voltage relationships of inward creep currents after depolarizing voltage-clamp pulses are extremely labile and depend critically upon the amplitude and duration of outward creep currents elicited during preceding voltage-clamp pulses. An optical monitor of mechanical activity in single cells revealed (a) a similar voltage dependence for the outward creep currents induced by Na loading and tonic contraction, and (b) a close correlation between the time course of the decay of the inward creep current and the time course of mechanical relaxation. A mathematical model of electrogenic Na/Ca exchange (Mullins, L.J. 1979. Federation Proceedings. 35:2583; Noble, D. 1986. Cardiac Muscle. 171-200) can adequately account for many of the properties of creep currents. It is concluded that creep currents in single frog atrial cells may be attributed to the operation of an electrogenic Na/Ca exchange mechanism.     

Nanoindentation testing and finite element simulations of cortical bone allowing for anisotropic elastic and inelastic mechanical response

Anisotropy is one of the most peculiar aspects of cortical bone mechanical behaviour, and the numerical approach can be successfully used to investigate aspects of bone tissue mechanics that analytical methods solve in approximate way or do not cover. In this work, nanoindentation experimental tests and finite element simulations were employed to investigate the elastic-inelastic anisotropic mechanical properties of cortical bone. The model allows for anisotropic elastic and post-yield behaviour of the tissue. A tension-compression mismatch and direction-dependent yield stresses are allowed for. Indentation experiments along the axial and transverse directions were simulated with the purpose to predict the indentation moduli and hardnesses along multiple orientations. Results showed that the experimental transverse-to-axial ratio of indentation moduli, equal to 0.74, is predicted with a ～3% discrepancy regardless the post-yield material behaviour; whereas, the transverse-to-axial hardness ratio, equal to 0.86, can be correctly simulated (discrepancy ～6% w.r.t. the experimental results) only employing an anisotropic post-elastic constitutive model. Further, direct comparison between the experimental and simulated indentation tests evidenced a good agreement in the loading branch of the indentation curves and in the peak loads for a transverse-to-axial yield stress ratio comparable to the experimentally obtained transverse-to-axial hardness ratio. In perspective, the present work results strongly support the coupling between indentation experiments and FEM simulations to get a deeper knowledge of bone tissue mechanical behaviour at the microstructural level. The present model could be used to assess the effect of variations of constitutive parameters due to age, injury, and/or disease on bone mechanical performance in the context of indentation testing.     

Robust strategies for automated AFM force curve analysis--I. Non-adhesive indentation of soft, inhomogeneous materials

The atomic force microscope (AFM) has found wide applicability as a nanoindentation tool to measure local elastic properties of soft materials. An automated approach to the processing of AFM indentation data, namely, the extraction of Young's modulus, is essential to realizing the high-throughput potential of the instrument as an elasticity probe for typical soft materials that exhibit inhomogeneity at microscopic scales. This paper focuses on Hertzian analysis techniques, which are applicable to linear elastic indentation. We compiled a series of synergistic strategies into an algorithm that overcomes many of the complications that have previously impeded efforts to automate the fitting of contact mechanics models to indentation data. AFM raster data sets containing up to 1024 individual force-displacement curves and macroscopic compression data were obtained from testing polyvinyl alcohol gels of known composition. Local elastic properties of tissue-engineered cartilage were also measured by the AFM. All AFM data sets were processed using customized software based on the algorithm, and the extracted values of Young's modulus were compared to those obtained by macroscopic testing. Accuracy of the technique was verified by the good agreement between values of Young's modulus obtained by AFM and by direct compression of the synthetic gels. Validation of robustness was achieved by successfully fitting the vastly different types of force curves generated from the indentation of tissue-engineered cartilage. For AFM indentation data that are amenable to Hertzian analysis, the method presented here minimizes subjectivity in preprocessing and allows for improved consistency and minimized user intervention. Automated, large-scale analysis of indentation data holds tremendous potential in bioengineering applications, such as high-resolution elasticity mapping of natural and artificial tissues.     

In-vivo indentation of human skin

Indentation tests were carried out on the forehead skin of volunteers under loading pressures of 0-5 KPa. The indentation was found to increase asymptomatically with loading pressure. In an attempt to develop a quantitative index for aging of the skin, its response to indentation loading was analyzed in reference to its glycosaminoglycan (GAG) containing ground substance and fibers' network microstructure. An analytic model that considers the skin as an incompressible solid-fluid mixture was developed and utilized to simulate the skin's indentation response. Following parameter fitting, the predicted results are in close agreement with the data. The model can thus serve as a tool for evaluating the effect of changes in the dermis components which accompany aging.     

Nonlinear viscoelastic, thermodynamically consistent, models for biological soft tissue

The mechanical behavior of most biological soft tissue is nonlinear viscoelastic rather than elastic. Many of the models previously proposed for soft tissue involve ad hoc systems of springs and dashpots or require measurement of time-dependent constitutive coefficient functions. The model proposed here is a system of evolution differential equations, which are determined by the long-term behavior of the material as represented by an energy function of the type used for elasticity. The necessary empirical data is time independent and therefore easier to obtain. These evolution equations, which represent non-equilibrium, transient responses such as creep, stress relaxation, or variable loading, are derived from a maximum energy dissipation principle, which supplements the second law of thermodynamics. The evolution model can represent both creep and stress relaxation, depending on the choice of control variables, because of the assumption that a unique long-term manifold exists for both processes. It succeeds, with one set of material constants, in reproducing the loading-unloading hysteresis for soft tissue. The models are thermodynamically consistent so that, given data, they may be extended to the temperature-dependent behavior of biological tissue, such as the change in temperature during uniaxial loading. The Holzapfel et al. three-dimensional two-layer elastic model for healthy artery tissue is shown to generate evolution equations by this construction for biaxial loading of a flat specimen. A simplified version of the Shah-Humphrey model for the elastodynamical behavior of a saccular aneurysm is extended to viscoelastic behavior.     

Biphasic indentation of articular cartilage--II. A numerical algorithm and an experimental study

Part I (Mak et al., 1987, J. Biomechanics 20, 703-714) presented the theoretical solutions for the biphasic indentation of articular cartilage under creep and stress-relaxation conditions. In this study, using the creep solution, we developed an efficient numerical algorithm to compute all three material coefficients of cartilage in situ on the joint surface from the indentation creep experiment. With this method we determined the average values of the aggregate modulus. Poisson's ratio and permeability for young bovine femoral condylar cartilage in situ to be HA = 0.90 MPa, vs = 0.39 and k = 0.44 x 10(-15) m4/Ns respectively, and those for patellar groove cartilage to be HA = 0.47 MPa, vs = 0.24, k = 1.42 x 10(-15) m4/Ns. One surprising finding from this study is that the in situ Poisson's ratio of cartilage (0.13-0.45) may be much less than those determined from measurements performed on excised osteochondral plugs (0.40-0.49) reported in the literature. We also found the permeability of patellar groove cartilage to be several times higher than femoral condyle cartilage. These findings may have important implications on understanding the functional behavior of cartilage in situ and on methods used to determine the elastic moduli of cartilage using the indentation experiments.     

Nanoindentation response of nickel surface using molecular dynamics simulation

The mechanisms of dislocation nucleation on a nickel (Ni) (001) surface under nanoindentation behaviours are investigated using molecular dynamics simulation. The characteristic mechanisms include the molecular models of a thermal layer (TL) and thermal with a free layer (TFL), multi-step load/unload cycles, tilt angles and shapes of the indenter, and slip vectors. The model of a TL has higher reaction force than a TFL. The maximum forces of nanoindentation decrease with increasing time of the multi-step load/unload cycle. The indenter with the tilt angle has larger force to act on the molecular model than the indenter along the normal direction. The effect of the indentation shape is presented such that the conical tip has larger load force to act on the molecular model. The defects along Shockley partials on the (111) plane are produced during nanoindentation involving nucleation, glide and slip.     

Biomechanical properties of human articular cartilage under compressive loads

The function of articular cartilage is to support and distribute loads and to provide lubrication in the diarthrodial joints. Cartilage function is described by proper mechanical and rheological properties, strain and depth-dependent, which are not completely assessed. Unconfined and confined compression are commonly used to evaluate the Young's modulus (E) and the aggregate modulus (H(A)), respectively. The Poisson's ratio (nu) can be calculated indirectly from the equilibrium compression data, or using the biphasic indentation technique; it has recently been optically evaluated by using video microscopy during unconfined compression. The transient response of articular cartilage during confined compression depends on its permeability k; a constant value of k can be easily identified by a simple analytical model of confined compression tests, whereas more complex models or direct measurements (permeation tests) are needed to study the permeability dependence on deformation. A poroelastic finite element model of articular cartilage was developed for this purpose. The elastic parameters (E,nu) of the model were evaluated performing unconfined compression creep tests on human articular cartilage disks, whereas k was identified from the confined test response. Our combined experimental and computational method can be used to identify the parameters that define the permeability dependence on deformation, as a function of depth from articular surface.     

Modelling and simulation of porcine liver tissue indentation using finite element method and uniaxial stress–strain data

We hypothesize that both compression and elongation stress–strain data should be considered for modeling and simulation of soft tissue indentation. Uniaxial stress–strain data were obtained from in vitro loading experiments of porcine liver tissue. An axisymmetric finite element model was used to simulate liver tissue indentation with tissue material represented by hyperelastic models. The material parameters were derived from uniaxial stress–strain data of compressions, elongations, and combined compression and elongation of porcine liver samples. in vitro indentation tests were used to validate the finite element simulation. Stress–strain data from the simulation with material parameters derived from the combined compression and elongation data match the experimental data best. This is due to its better ability in modeling 3D deformation since the behavior of biological soft tissue under indentation is affected by both its compressive and tensile characteristics. The combined logarithmic and polynomial model is somewhat better than the 5-constant Mooney–Rivlin model as the constitutive model for this indentation simulation.     

The nanoindentation responses of nickel surfaces with different crystal orientations

Molecular dynamics (MD) simulations are applied to elucidate the anisotropic characteristics in the material responses for crystallographic nickel substrates with (100), (110) and (111) surface orientations during nanoindentation, compensating for the experimental limitation of nanoindentation—particularly for pure nickel substrates of three crystallographic orientations. This study examines several factors under indentation: three-dimensional phases of plastic deformation which correspond to atomic stress distributions, pile-up patterns at maximum indentation depth, and extracted material properties at different crystallographic orientations. The present results reveal that the strain energy of the substrate exerted by the tip is stored by the formation of the homogeneous nucleation, and is dissipated by the dislocation sliding of the {111} plane. The steep variations of the indentation curve from the local peak to the local minimums are affected by the numbers of slip angle of {111} sliding plane. The pile-up patterns of the three nickel substrates prove that the crystalline nickel materials demonstrate the pile-up phenomenon from nanoindentation on the nano-scale. The three crystallographic nickel substrates exhibit differing amounts of pile-up dislocation spreading at different crystallographic orientations. Finally, the effects of surface orientation in material properties of FCC nickel material on the nano-scale are observable through the slip angle numbers of {111} sliding planes which influence hardness values, as well as the cohesive energy of different crystallographic surfaces that indicate Young's modulus.     

Development of residual strains in human vertebral trabecular bone after prolonged static and cyclic loading at low load levels

Development of irreversible residual strains in trabecular bone may be a mechanism by which age-related non-traumatic vertebral fractures occur. To investigate this concept, static and cyclic loading tests were conducted at low loading levels for cylindrical cores of cadaveric vertebral trabecular bone. Stresses were applied equivalent to elastic strains of either 750 or 1,500 microstrain. Creep strains were measured during the tests, which lasted for 125,000 seconds (about 35 h), and for an additional 125,000 seconds after complete unloading. Emphasis was placed on the residual strains that developed, defined as the strain remaining at the end of the unloading phase. The results indicated that appreciable residual strains did develop, and were similar for static and cyclic loading. Irrespective of the applied load levels and loading modes, the residual strains that remained after the unloading phase were similar in magnitude to the originally applied elastic strain. Extrapolation of the observed residual strains to full recovery indicated that the time that would be required for full recovery was over 20 times longer than the duration of the applied loads. These results indicate that human vertebral trabecular bone does not creep in a linear viscoelastic fashion at low stress levels, and that creep mechanisms dominate the residual strains regardless of the loading mode. Taken together, these findings support the concept that non-traumatic vertebral fractures may be related to long-term creep effects because the trabecular bone does not have sufficient time to recover mechanically from creep deformations accumulated by prolonged static or cyclic loading.