Estimating material elasticity by spherical indentation load-relaxation tests on viscoelastic samples of finite thickness

A two-step viscoelastic spherical indentation method is proposed to compensate for 1) material relaxation and 2) sample thickness. In the first step, the indenter is moved at a constant speed and the reaction force is measured. In the second step, the indenter is held at a constant position and the relaxation response of the material is measured. Then the relaxation response is fit with a multi-exponential function which corresponds to a three-branch general Maxwell model. The relaxation modulus is derived by correcting the finite ramp time introduced in the first step. The proposed model takes into account the sample thickness, which is important for applications in which the sample thickness is less than ten times the indenter radius. The model is validated numerically by finite element simulations. Experiments are carried out on a 10% gelatin phantom and a chicken breast sample with the proposed method. The results for both the gelatin phantom and the chicken breast sample agree with the results obtained from a surface wave method. Both the finite element simulations and experimental results show improved elasticity estimations by incorporating the sample thickness into the model. The measured shear elasticities of the 10% gelatin sample are 6.79 and 6.93 kPa by the proposed finite indentation method at sample thickness of 40 and 20 mm, respectively. The elasticity of the same sample is estimated to be 6.53 kPa by the surface wave method. For the chicken breast sample, the shear elasticity is measured to be 4.51 and 5.17 kPa by the proposed indentation method at sample thickness of 40 and 20 mm, respectively. Its elasticity is measured by the surface wave method to be 4.14 kPa. © 2011 IEEE.

Ultrastructural mechanical and material characterization of fossilized bone

Bone plays a key role in the paleontological and archeological records and can provide insight into the biology, ecology and the environment of ancient vertebrates. Examination of bone at the tissue level reveals a definitive relationship between nanomechanical properties and the local organic content, mineral content, and microstructural organization. However, it is unclear as to how these properties change following fossilization, or diagenesis, where the organic phase is rapidly removed and the remaining mineral phase is reinforced by the deposition of apatites, calcites, and other minerals. While the process of diagenesis is poorly understood, its outcome clearly results in the potential for dramatic alteration of the mechanical response of biological tissues. In this study, fossilized specimens of mammalian long bones, collected from Colorado and Wyoming, were studied for mechanical variations. Nanoindentation performed in both longitudinal and transverse directions revealed preservation of bone's natural anisotropy as transverse modulus values were consistently smaller than longitudinal values. Additionally, modulus values of fossilized bone from 35.0 to 89.1 GPa increased linearly with logarithm of the sample's age. Future studies will aim to clarify what mechanical and material elements of bone are retained during diagenesis as bone becomes part of the geologic milieu. © 2007 Materials Research Society.

Effects of gelatin on mechanical properties of hydroxyapatite-gelatin nano-composltes

A biomimetic reactor has been developed to synthesize hydroxyapatite- gelatin (HAP-GEL) nanocomposites that mimic ultra-structures of natural bone. We hypothesize that in the reactor, gelatin concentration controls morphology and packing structures of HAP crystals. To test the hypothesis, three types of mechanical tests were conducted, including nanoindentation, compression, and fracture tests. Nanoindentation tests in conjunction with computer modeling were used to assess effects on gelatin-induced microstructures of HAP. The results showed that increasing gelatin content increased both the plane strain modulus and the fracture toughness. The gelatin appeared to shorten the HAP crystal distance, which consolidated the internal structure of the composite and made the material more rigid. The fracture toughness KIC increased partially due to the effect of fiber bridging between gelatin molecules. The highest fracture toughness (1.12 MPa·1/2) was equivalent to that of pure hydroxyapatite. The compressive strength of the HAP-GEL (107.7±26.8 MPa) was, however, less sensitive to microstructural changes and was within the range of natural cortical bone (human 170 MPa, pig: 100 MPa). The compression strength was dominated by void inclusions while the nanoindentation response reflected ultra-structural arrangement of the crystals. The gelatin concentration is likely to modify crystal arrangement as demonstrated in TEM experiments but not void distribution at macroscopic levels. © 2006 Materials Research Society.

Electrical actuation and readout in a nanoelectromechanical resonator based on a laterally suspended zinc oxide nanowire.

In this paper, we present experimental results describing enhanced readout of the vibratory response of a doubly clamped zinc oxide (ZnO) nanowire employing a purely electrical actuation and detection scheme. The measured response suggests that the piezoelectric and semiconducting properties of ZnO effectively enhance the motional current for electromechanical transduction. For a doubly clamped ZnO nanowire resonator with radius ~10 nm and length ~1.91 µm, a resonant frequency around 21.4 MHz is observed with a quality factor (Q) of ~358 in vacuum. A comparison with the Q obtained in air (~242) shows that these nano-scale devices may be operated in fluid as viscous damping is less significant at these length scales. Additionally, the suspended nanowire bridges show field effect transistor (FET) characteristics when the underlying silicon substrate is used as a gate electrode or using a lithographically patterned in-plane gate electrode. Moreover, the Young's modulus of ZnO nanowires is extracted from a static bending test performed on a nanowire cantilever using an AFM and the value is compared to that obtained from resonant frequency measurements of electrically addressed clamped–clamped beam nanowire resonators.

Enhancement of magnetostriction in internally-biased Terfenol-D 2-2 composites

A key issue in the fabrication of Terfenol-D 2-2 composites with internal magnetic field biasing is the selection of appropriate constituent materials to obtain high magnetostriction while keeping optimum magnetomechanical properties. The fabrication process is costly and time consuming and, therefore, numerical methods to predict their properties are useful. In this paper, finite element analysis (FEA) of the magnetostriction of such composites has been carried out using the commercial package ABAQUS. It has been shown that composites fabricated using Nd2Fe14B for the permanent magnetic material layers possess the highest internal fields within the Terfenol-D layers, although the overall strain of these composites is limited to approximately 800 × 10-6 due to the high elastic modulus of Nd2Fe14B. Simulations showed that the strain can be enhanced by choosing a different material with a lower elastic modulus for the permanent magnetic layer even though the internal field is lower. The simulations showed that the strain can increase by 12% if the Nd 2Fe14B layer is substituted by SmCo5; by 23% if it is substituted by Sm2Co17; and by 35% if it is substituted by Alnico. © 2008 IEEE.

Predicting surface vibration from underground railways through inhomogeneous soil

Noise and vibration from underground railways is a major source of disturbance to inhabitants near subways. To help designers meet noise and vibration limits, numerical models are used to understand vibration propagation from these underground railways. However, the models commonly assume the ground is homogeneous and neglect to include local variability in the soil properties. Such simplifying assumptions add a level of uncertainty to the predictions which is not well understood. The goal of the current paper is to quantify the effect of soil inhomogeneity on surface vibration. The thin-layer method (TLM) is suggested as an efficient and accurate means of simulating vibration from underground railways in arbitrarily layered half-spaces. Stochastic variability of the soils elastic modulus is introduced using a KL expansion; the modulus is assumed to have a log-normal distribution and a modified exponential covariance kernel. The effect of horizontal soil variability is investigated by comparing the stochastic results for soils varied only in the vertical direction to soils with 2D variability. Results suggest that local soil inhomogeneity can significantly affect surface velocity predictions; 90 percent confidence intervals showing 8 dB averages and peak values up to 12 dB are computed. This is a significant source of uncertainty and should be considered when using predictions from models assuming homogeneous soil properties. Furthermore, the effect of horizontal variability of the elastic modulus on the confidence interval appears to be negligible. This suggests that only vertical variation needs to be taken into account when modelling ground vibration from underground railways. © 2012 Elsevier Ltd. All rights reserved.

Ultra-structural defects cause low bone matrix stiffness despite high mineralization in osteogenesis imperfecta mice.

Bone is a complex material with a hierarchical multi-scale organization from the molecule to the organ scale. The genetic bone disease, osteogenesis imperfecta, is primarily caused by mutations in the collagen type I genes, resulting in bone fragility. Because the basis of the disease is molecular with ramifications at the whole bone level, it provides a platform for investigating the relationship between structure, composition, and mechanics throughout the hierarchy. Prior studies have individually shown that OI leads to: 1. increased bone mineralization, 2. decreased elastic modulus, and 3. smaller apatite crystal size. However, these have not been studied together and the mechanism for how mineral structure influences tissue mechanics has not been identified. This lack of understanding inhibits the development of more accurate models and therapies. To address this research gap, we used a mouse model of the disease (oim) to measure these outcomes together in order to propose an underlying mechanism for the changes in properties. Our main finding was that despite increased mineralization, oim bones have lower stiffness that may result from the poorly organized mineral matrix with significantly smaller, highly packed and disoriented apatite crystals. Using a composite framework, we interpret the lower oim bone matrix elasticity observed as the result of a change in the aspect ratio of apatite crystals and a disruption of the crystal connectivity.

Moderate speed impact damage to 2D-braided glass-carbon composites

Hybrid glass-carbon 2D braided composites with varying carbon contents are impacted using a gas gun by impactors of masses 12.5 and 44.5. g, at impact energies up to 50. J. The damage area detected by ultrasound C-scan is found to increase roughly linearly with impact energy, and is larger for the lighter impactor at the same impact energy. The area of whitening of the glass tows on the distal side corresponds with the measured C-scan damage area. X-ray imaging shows more intense damage, at the same impact energy, for a higher-mass impactor. Braids with more glass content have a modest increase in density, decrease in modulus, and reduction in the C-scan area and dent depth at the impact site, particularly at the higher impact energies. Impact damage is found to reduce significantly the compressive strength, giving up to a 26% reduction at the maximum impact energy. © 2012 Elsevier Ltd.

Extracellular-matrix tethering regulates stem-cell fate.

To investigate how substrate properties influence stem-cell fate, we cultured single human epidermal stem cells on polydimethylsiloxane (PDMS) and polyacrylamide (PAAm) hydrogel surfaces, 0.1 kPa-2.3 MPa in stiffness, with a covalently attached collagen coating. Cell spreading and differentiation were unaffected by polydimethylsiloxane stiffness. However, cells on polyacrylamide of low elastic modulus (0.5 kPa) could not form stable focal adhesions and differentiated as a result of decreased activation of the extracellular-signal-related kinase (ERK)/mitogen-activated protein kinase (MAPK) signalling pathway. The differentiation of human mesenchymal stem cells was also unaffected by PDMS stiffness but regulated by the elastic modulus of PAAm. Dextran penetration measurements indicated that polyacrylamide substrates of low elastic modulus were more porous than stiff substrates, suggesting that the collagen anchoring points would be further apart. We then changed collagen crosslink concentration and used hydrogel-nanoparticle substrates to vary anchoring distance at constant substrate stiffness. Lower collagen anchoring density resulted in increased differentiation. We conclude that stem cells exert a mechanical force on collagen fibres and gauge the feedback to make cell-fate decisions.

Comparison between granular pillared, organo- and inorgano-organo-bentonites for hydrocarbon and metal ion adsorption

Granular reactive materials have higher permeability and are therefore desirable for in situ groundwater pollution control. Three granular bentonites were prepared: an Al-pillared bentonite (PBg), an organo-bentonite (OBg) using a quaternary ammonium cation (QAC), and an inorgano-organo-bentonite (IOBg), using both the pillaring agent and the QAC. Powdered IOB (IOBp) was also prepared to test the effect of particle size. The modified bentonites were characterised with X-ray diffraction (XRD), Fourier transform infrared spectrometry (FT-IR), thermal gravimetric analysis (TGA) and uniaxial compression tests. The d-spacing increased only with QAC intercalation. The Young's modulus of IOBg was twice as high as OBg. Batch adsorption tests were performed with aqueous multimetal solutions of Pb2+, Cu2+, Cd2+, Zn2+ and Ni2+ ions, with liquid dodecane and with aqueous dodecane solutions. Metal adsorption fit the Langmuir isotherm. Adsorption occurred within 30min for PBg, while the granular organo-bentonite needed at least 12h to reach equilibrium. IOBp had the maximum adsorption capacity at higher metal concentration and lower adsorbent content (Cu2+: 2.2, Ni2+: 1.7, Zn2+: 1.4, Cd2+: 0.9 and Pb2+: 0.7 all in mmolg-1). The dual pillaring of the QAC and Al hydroxide increased the adsorption. The adsorption of liquid dodecane was in the order IOBg>OBg>PBg (3.2>2.7>1.7mmolg-1). Therefore IOBg has potential for the removal of toxic compounds found in soil, groundwater, storm water and wastewater. © 2012 Elsevier B.V.

A coordination-based approach to elasticity of floppy and stiff random networks

We study the role of connectivity on the linear and nonlinear elastic behavior of amorphous systems using a two-dimensional random network of harmonic springs as a model system. A natural characterization of these systems arises in terms of the network coordination relative to that of an isostatic network $\delta z$; a floppy network has $\delta z<0$, while a stiff network has $\delta z>0$. Under the influence of an externally applied load we observe that the response of both floppy and rigid network are controlled by the same critical point, corresponding to the onset of rigidity. We use numerical simulations to compute the exponents which characterize the shear modulus, the amplitude of non-affine displacements, and the network stiffening as a function of $\delta z$, derive these theoretically and make predictions for the mechanical response of glasses and fibrous networks.

Adhesive properties of gecko-inspired mimetic via micropatterned carbon nanotube forests

The adhesive properties of the gecko foot have inspired designs of advanced micropatterned surfaces with increased contact areas. We have fabricated micropatterned pillars of vertically aligned carbon nanotube forests with a range of pillar diameters, heights, and spacings (or pitch). We used nanoindentation to measure their elastic and orthogonal adhesion properties and derive their scaling behavior. The patterning of nanotube forests into pillar arrays allows a reduction of the effective modulus from 10 to 15 MPa to 0.1-1 MPa which is useful for developing maximum conformal adhesion. © 2012 American Chemical Society.

Insight into differences in nanoindentation properties of bone.

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 analyzed 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 between the bones themselves, but also to the testing and analysis protocols.

Stiffness of sands through a laboratory test database

Deformations of sandy soils around geotechnical structures generally involve strains in the range small (0·01%) to medium (0·5%). In this strain range the soil exhibits non-linear stress-strain behaviour, which should be incorporated in any deformation analysis. In order to capture the possible variability in the non-linear behaviour of various sands, a database was constructed including the secant shear modulus degradation curves of 454 tests from the literature. By obtaining a unique S-shaped curve of shear modulus degradation, a modified hyperbolic relationship was fitted. The three curve-fitting parameters are: an elastic threshold strain γe, up to which the elastic shear modulus is effectively constant at G0; a reference strain γr, defined as the shear strain at which the secant modulus has reduced to 0·5G0; and a curvature parameter a, which controls the rate of modulus reduction. The two characteristic strains γe and γr were found to vary with sand type (i.e. uniformity coefficient), soil state (i.e. void ratio, relative density) and mean effective stress. The new empirical expression for shear modulus reduction G/G0 is shown to make predictions that are accurate within a factor of 1·13 for one standard deviation of random error, as determined from 3860 data points. The initial elastic shear modulus, G0, should always be measured if possible, but a new empirical relation is shown to provide estimates within a factor of 1·6 for one standard deviation of random error, as determined from 379 tests. The new expressions for non-linear deformation are easy to apply in practice, and should be useful in the analysis of geotechnical structures under static loading.

Brillouin scattering of cluster-assembled carbon films

The low frequency vibrational spectrum of cluster beam deposited carbon films was studied by Brillouin light scattering. In thin films the values of both bulk modulus and shear modulus has been estimated from the shifts of surface phonon peaks. The values found indicate a mainly sp2 coordinated random network with low density. In thick films a bulk longitudinal phonon peak was detected in a spectral range compatible with the value of the index of refraction and of the elastic constants of thin films. High surface roughness, combined with a rather strong bulk central peak, prevented the observation of surface phonon features. © 1998 Elsevier Science Ltd. All rights reserved.