Estimates for the elastic moduli of random orthorhombic polycrystals

Our variational bounds are suggested to provide estimates on the possible scatter ranges for the macroscopic elastic moduli of random polycrystalline materials. Explicit expressions for the random aggregates of orthorhombic crystals are derived and calculated. The complicated general bounds are well approximated by the simple ones for specific spherical cell polycrystals, which are proposed also to represent practical equi-axed particulate aggregates. Hence the latter could be recommended for practical uses. The results for a number of polycrystals indicate that their macroscopic moduli may be determined with the accuracy from two to four significant digits.     

A comparison of ultrasound and computed tomography in evaluating the mechanical properties of trabecular bone

This study compared ultrasound parameters and bone mineral density (BMD) in the assessment of the mechanical properties of trabecular bone. The BMD of bovine tibial trabecular bone specimens was measured by CT scanning each specimen in all three orthogonal directions. Similarly, ultrasound velocity and attenuation measurements were also made in these directions. Specimens were then divided into three groups for mechanical testing. the ultimate strength, Young's modulus and energy absorption were measured for each specimen. It was found that BMD was independent of trabecular orientation while ultrasound velocity and attenuation values were significantly higher in the superior/inferior (SI) direction corresponding to the load bearing axis at stance. All mechanical properties were also significantly higher in the SI direction. The linear correlation demonstrated that ultrasound parameters, particularly ultrasound velocity, were better than BMD as predictors of compressive mechanical properties     

Quantification and visualization of anisotropy in trabecular bone

A number of methods for measuring anisotropy in trabecular bone using high‐resolution X‐ray computed tomography exist, which give different answers but have not been compared in detail. In this study, we examine the mean‐intercept length (MIL), star volume distribution (SVD) and star length distribution (SLD) methods, their algorithmic implementation for three‐dimensional (3D) data, and how their results relate to each other. A uniform ordered sampling scheme for determining which orientations to sample during analysis enhances the reproducibility of anisotropy and principal component direction determinations, with no evident introduction of biasing. This scheme also facilitates the creation of a 3D rose diagram that can be used to gain additional insights from the data. The directed secant algorithm that is frequently used for traversing pixel and voxel grids for these calculations is prone to bias unless a previously unreported normalization is used. This normalization ameliorates the bias present when using cubic voxels, and also permits calculations on data sets in which the slice spacing is not equal to the pixel spacing. Overall, the three methods for quantification of anisotropy give broadly similar results, but there are systematic divergences that can be traced to their differences in data and processing, and which may impact on their relative utility in estimating mechanical properties. Although discussed in the context of computed tomography of trabecular bone, the methods described here may be applied to any 3D data set from which fabric information is desired.     

Semi-analytical formulation for the guided waves-based reconstruction of elastic moduli

In this study an inverse procedure based on the propagation of guided ultrasonic waves is proposed for the characterization of the elastic material constants of plates. The procedure consists of an optimization problem in which the discrepancy between the dispersion curves obtained through a semi analytical finite element (SAFE) formulation and numerical or experimental dispersion curves is minimized. The numerical dispersion curves were obtained from the application of the commercial finite element analysis software ANSYS. Finally experimental data were obtained by adopting a hybrid broadband laser/PZT ultrasonic set-up in a pitch-catch configuration. For both numerical and experimental data, the joint time-frequency analysis of the continuous wavelet transform was used.The optimization scheme proposed in this study is based on an improved version of the simplex search method. The scheme inputs an initial guess of the material parameters in the SAFE formulation. The values of these parameters are iteratively updated until the discrepancy between the SAFE-based group velocity dispersion curves and the numerical or experimental curves is minimized. The scheme is designed to minimize the discrepancy associated with the lowest symmetric and anti-symmetric order mode simultaneously.The validity of the SAFE method coupled to the inverse procedure scheme is tested to characterize the elastic material properties of a 2.54 mm thick aluminum plate. As the SAFE formulation is valid for waveguides of arbitrary cross-section the paper represents the first step toward the integration of an inversion scheme applicable into the SAFE algorithm to characterize the material properties of waveguides of complex geometries and various boundary conditions.     

Poroelastic behavior of trabecular bone: The effect of strain rate

A one dimensional poroelastic model of trabecular bone was developed to investigate the pore pressure effect on mechanical behavior. The poroclastic properties were determined based upon the assumed drained Poisson's ratio of 0.3 and the experimental results reported in the literature. Even though the free escape of the fluid through the loading end was allowed during deformation, model predictions showed that the pore pressure generation within the trabecular bone would cause significant variations in total stress. The total stress increase resulted in a stiffening of the trabecular bone, which supports the concept of hydraulic stiffening that has been advocated by several investigators. Model predictions showed a good agreement to the mechanical behaviors of trabecular bone specimens with marrow in a uniaxial strain condition observed in a previous study. These results support the hypothesis that the trabecular bone is poroelastic and the pore pressure effect on the mechanical behavior at the continuum level is significant. Thus, the incorporation of the fluid effect in future studies is recommended to improve our understanding of trabecular bone mechanics.     

Methodological principles for fractal analysis of trabecular bone

A standardized methodology for the fractal analysis of histological sections of trabecular bone has been established.
A modified box counting method has been developed for use on a PC-based image analyser. The effect of image analyser settings, magnification, image orientation and threshold levels was determined. Also, the range of scale over which trabecular bone is effectively fractal was determined and a method formulated to calculate objectively more than one fractal dimension from the modified Richardson plot.
The results show that magnification, image orientation and threshold settings have little effect on the estimate of fractal dimension. Trabecular bone has a lower limit below which it is not fractal (λ < 25 μm) and the upper limit is 4250 μm. There are three distinct fractal dimensions for trabecular bone (sectional fractals), with magnitudes greater than 1.0 and less than 2.0.
It has been shown that trabecular bone is effectively fractal over a defined range of scale. Also, within this range, there is more than one fractal dimension, describing spatial structural entities. Fractal analysis is a model-independent method for describing a complex multifaceted structure, which can be adapted for the study of other biological systems. This may be at the cell, tissue or organ level and complements conventional histomorphometric and stereological techniques.     

In-plane elastic moduli and plastic collapse strength of regular hexagonal honeycombs with dual imperfections

The in-plane elastic modulus, Poisson's ratio and plastic collapse strength of regular hexagonal honeycombs with dual imperfections of non-straight and variable-thickness cell edges were theoretically derived from a model of curved cell edges with Plateau borders. Finite element analyses (FEA) on the stiffness and strength of regular hexagonal honeycombs with dual imperfections were also performed and then compared to the theoretical modeling. Both analytical and numerical results indicate that the in-plane elastic moduli and plastic collapse strength of regular hexagonal honeycombs with dual imperfections depend on their relative density, the solid distribution in cell edges and the curvature of cell edges. Meanwhile, the effects of dual imperfections on the in-plane elastic moduli and plastic collapse strength of regular hexagonal honeycombs are more drastic as compared to those of each single imperfection. Also, it is found that the normalized in-plane elastic modulus and plastic collapse strength of regular hexagonal honeycombs with dual imperfections are approximately equal to the products of those with each single imperfection.     

Fragility, DSC and elastic moduli studies on tellurite–vanadate glasses containing molybdenum

Ternary xMoO₃–40TeO₂–(60 − x)V₂O₅ glasses with 0 ? x ? 60 (in mol%) have been prepared by normal melt quenching method. DSC curves of these glasses have been investigated. The glass transition properties that have been measured and reported in this paper, include the glass transition temperature (T_g), glass transition width (ΔT_g), heat capacity change at glass transition (ΔC_P) and calculated fragility (F). Thermal stability, Poisson’s ratio, fragility and glass forming tendency of these glasses have been evaluated, to determine relationship between chemical composition and the thermal stability or to interpret the structure of glass. In addition, Makishima and Makenzie’s theory was applied for calculation of Young’s modulus, bulk modulus and shear modulus, indicating a strong relation between elastic properties and structure of glass. Generally, results of this work show that glass with x = 60 has the highest shear, bulk and Young’s moduli which make it as suitable candidate for the manufacture of strong glass fibers in technological applications; but it should be mentioned that glass with x = 20 has higher handling temperature and super resistance against thermal attack.     

Accumulation of in-vivo fatigue microdamage and its relation to biomechanical properties in ageing human cortical bone

Bone matrix accumulates microdamage in the form of microcracks as a result of everyday cyclic loading activities. In two very recent studies, which used conventional histological stains and light microscopy techniques, the amount of this in-vivo microdamage in the cortices of long bones has been shown to increase with age. These articles have suggested that in-vivo microcracks may have an effect on the material properties of the tissue. However, a precise quantitative relationship between the number of microcracks and the mechanical properties of these same bones has not been produced before, and in particular the way the microcracks may affect the stiffness, the strength or possibly the toughness of the tissue. This article presents an examination of the in-vivo microdamage in human bones by the use of laser scanning confocal microscopy, which offers better discrimination and allows examination of the cracks in-situ . Quantification of in-vivo fatigue microcracks was performed by counting the microcrack numerical density and surface density in specimens for which we have previously derived a full set of mechanical properties as a function of age. It is shown that bone microdamage relates more to the toughness (measured by three different measures) of ageing bone tissue than to its stiffness and strength. The result allows us (i) to re-evaluate the fragility of ageing human bone and put more emphasis on its energy-related resistance to fracture than perhaps on its stiffness or strength and also (ii) to understand more fully the causal relationship and interactions between microcracks and tissue toughness.     

Atomic force microscopy investigation of the dependence of cellular elastic moduli on glutaraldehyde fixation

The atomic force microscope (AFM) has provided nanoscale analyses of surfaces of cells that exhibit strong adhesive and cell spreading properties. However, it is frequently reported that prior fixation is required for reliable imaging of cells with lower adhesive properties. In the present study, the AFM is used to assess the effects of fixation by glutaraldehyde on the elastic modulus of a human rhabdomyosarcoma transfectant cell line RDX2C2. Our results show a sharp increase in the elastic modulus for even mild fixation (0.5% glutaraldehyde for 60 s), accompanied by a dramatic improvement in imaging reproducibility. An even larger increase is seen in NIH-3T3 mouse fibroblasts, although in that case fixation is not typically necessary for successful imaging. In addition, our results suggest that treatment with glutaraldehyde restricts the content of the resulting images to features nearer to the cell surface.     

Strain rate dependent poroelastic behavior of bovine vertebral trabecular bone

It is widely accepted that the pressure variation of interstitial fluid is one of the most important factors in bone physiology. In order to understand the role of interstitial fluid on porous bony structure, a consideration for the biomechanical interactions between fluid and solid constituents within bone is required. In this study, a poroelastic theory was applied to investigate the elastic behavior of calf vertebral trabecular bone composed of the porous solid trabeculae and the viscous bone marrow. The poroelastic behavior of trabecular bone in a uniaxial stress condition was simulated using a commercial finite difference analysis software (FLAC, Itasca Consulting Group, USA), and tested for 5 different strain rates, i. e., 0.001, 0.01, 0.1, and 10 per second. The material properties of the calf vertebral trabecular bone were utilized from the previous experimental study. Two asymptotic poroelastic responses, the drained and undrained deformations, were predicted. From the predicted results for the simulated five strain rates, it was found that the pore pressure generation has a linearly increasing behavior when the strain rate is the highest at 10 per second, otherwise it showed a nonlinear behavior. The pore pressure generation with respect to the strain was found to be increased as the strain rate increased. The elastic moduli predicted at each strain were 208.3, 212.2, 337.6, 593.1, and 602.2 MPa, respectively. Based on the results of the present study, it was suggested that the calf vertebral trabecular bone could be modeled as a poroelastic material and its strain rate dependent material behavior could be predicted.     

The fatigue behavior and delamination properties in fiber reinforced aramid laminates

The fuselage-wing intersection suffers from the cyclic bending moment of variable amplitude. Therefore, the influence of cyclic bending moment on the delamination and the fatigue crack propagation behavior in AFRP/A1 laminate of fuselage-wing was investigated in this study. The cyclic bending moment fatigue test in AFRP/A1 laminate was performed with five levels of bending moment. The shape and size of the delamination zone formed along the fatigue crack between aluminum sheet and aramid fiber-adhesive layer were measured by an ultrasonic C-scan. The relationships between da/dN and K, between the cyclic bending moment and the delamination zone size, and between the fiber bridging behavior and the delamination zone were studied. As results, fiber failures were not observed in the delamination zone in this study ; the fiber bridging modification factor increases and the fatigue crack growth rate decrease ; and the shape of delamination zone is semi-elliptic with the contour decreasing nonlinearly toward the crack tip.     

Immunoelectron microscopic localization of elastic tissue components in archival tissue samples

Tissue samples that have been stored for many years, in different media and under a variety of conditions, have been examined by modern techniques of immunoelectron microscopy, using antibodies against elastic tissue components. A range of post-embedding restorative procedures has been identified, which will allow reliable immunolocalization of antibodies against the elastic tissue component of such specimens. These methods have been applied successfully to autopsy-derived material, fixed in buffered formaldehyde, to archival material stored frozen at ?70 or ?20·C, to specimens fixed for electron microscopy and stored for many years in buffer, and even to archival material from formaldehyde-fixed, paraffin-embedded blocks, reprocessed for electron microscopic examination. The successful restorative methods included pre-treatment of the sections with 6***M guanidine hydrochloride, or 1M Tris/saline, each containing 100 ***mM dithiothreitol (a reducing agent) followed by alkylation with 220 mM iodoacetamide. The application of these techniques allowed reliable study of elastic tissue antibody distributions in archival tissues that could not be obtained again, as well as comparative studies with tissues processed many years previously.     

A biomechanical study of osteoporotic vertebral trabecular bone: The use of micro-CT and high-resolution finite element analysis

Osteoporosis is one of the most dangerous skeletal diseases in relation to the highest fracture risk in vertebral bones. A considerable amount of work has been done to investigate the biomechanical characteristics of osteoporotic vertebral trabecular bone. Previous researchers studied the elastic characteristics using a micro-finite element (micro-FE) model, used to analyze realistic trabecular architectures in full detail, based on micro-computed tomography (μCT). Since osteoporotic compression fracture is closely associated with the mechanical characteristics of the vertebral trabecular bone and there were few micro-FE models to account for all of the elastic and plastic characteristics in vertebral trabecular bone, this study analyzed the effect of voxel resolution on the plastic characteristics as well as the elastic characteristics of three-dimensional (3D) osteoporotic lumbar trabecular bone models. Also, we evaluated the effect of specimen geometry on this problem. It has been reported that a cubic specimen with side length 6.5mm was suggested as standard specimens for the experimental test of trabecular bone. Current study examined whether or not the effect of the specimen geometry on the experimental test may be also applied to the simulated compression test of trabecular bone specimens. The experimental test employing the rapid prototyping (RP) technique and INSTRON test machine is performed to indirectly validate the results of the simulated compression test by micro-FE analysis. The review finished with the verification about the effects of the simulated compression test.     

Hybrid experimental/numerical technique for determination of the complex dynamic moduli of elastic porous materials

Polyurethane (PU) and other plastic foams are widely used as passive acoustic absorbers. For optimal design, it is often necessary to know the viscoelastic properties of these materials in the frequency range relevant to their application. An experimental/numerical technique has been implemented to determine the Young and shear dynamic moduli and loss factor of poroelastic materials under low-frequency 40–520Hz random excitation. The method consists of measuring the dynamic response of the sample at its surface, and matching the response with the predictions from a finite element model in which the two complex elastic moduli are the adjustable parameters. Results are presented for measurements made in air, under standard pressure and temperature conditions, and compared with predictions based on Okuno’s model. The dependence of elastic moduli on the dimension of the sample and its boundary conditions is also studied. This paper was recommended for publication in revised form by Associate Editor Hong Hee Yoo Professor Yeon June Kang received his B.S. and M.S. degrees in Mechanical Design and Production Engineering from Seoul National University in 1988 and 1990, respectively. He then went on to receive a Ph.D. degree in Acoustics and Vibra-tion from School of Mechanical Engineering, Purdue University in 1994. After his Ph.D., he continued to work as a Postdoctoral Research Associate at Ray W. Herrick Laboratories, Purdue University until 1996. Since 1997, Dr. Kang is working at the Department of Mechanical and Aerospace Engineering, Seoul National University. Dr. Kang’s research interests are in the area of acoustical materials, noise and vibration in automotive engineering, and Korean Bells.     

Damping properties of an elastic element

Russian Engineering Research - A new method is proposed for ongoing measurement of the dissipative properties of an elastic element in a mechanical system. The theoretical basis of the method is...     

复合材料纵向弹性模量疲劳衰减规律研究

研究了载荷大小和铺设角度对疲劳载荷作用下复合材料的纵向弹性模量连续衰减规律产生的影响,由此构建了一个量化描述模型,对材料纵向弹性模量的衰减进行预测。为验证模型的合理性,设计了一套通过测量不同单向板应力应变关系来获取材料纵向弹性模量的疲劳试验方案,并对一系列不同铺设角的碳纤维复合材料单向板进行了大量疲劳试验。分析结果表明,所构建的衰减模型较合理地描述了复合材料纵向弹性模量的疲劳衰减规律。     

The effect on the fatigue strength of bone cement of adding sodium fluoride

New bone cements that include several additives are currently being investigated and tested. One such additive is sodium fluoride (NaF), which promotes bone formation, facilitating implant integration and success. The influence of NaF on the fatigue performance of the cement as used in biomedical applications was tested in this paper. In fact fatigue failure of the cement mantle is a major factor limiting the longevity of a cemented implant. An experimental bone cement with added NaF (12 wt%) was investigated. The fatigue strength of the novel bone cement was evaluated in comparison with the cement without additives; fatigue tests were conducted according to current standards. The load levels were arranged based on a validated, statistically based optimization algorithm. The curve of stress against number of load cycles and the endurance limit were obtained and compared for both formulations. The results showed that the addition of NaF (12 wt%) to polymethylmethacrylate (PMMA) bone cement does not affect the fatigue resistance of the material. Sodium fluoride can safely be added to the bone cement without altering the fatigue performance of the PMMA bone cement.     

Acoustic emission from trabecular bone during mechanical testing: the effect of osteoporosis and osteoarthritis

This study examines the relation between the nature of acoustic emission signals emitted from cancellous bone under compression and the mechanical properties of the tissue. The examined bone specimens were taken from 12 normal, 31 osteoporotic and six osteoarthritic femoral heads. The mechanical behaviour of the osteoporotic bone specimens was found to be significantly different from that of the normal specimens both in the pre-yield and post-yield ranges. In the osteoarthritic bones only the elastic behaviour was significantly different. The rates of acoustic events before yield and beyond it were found to be significantly higher both in the osteoporotic and osteoarthritic bone specimens. The average peak amplitude of the signals was also significantly higher in the diseased bones. Stepwise regression analysis showed that a combination of the acoustic emission parameters could significantly predict some mechanical properties of the bone. The energy absorbed during compression and the ultimate compressive stress of the specimens could be estimated from the rate of pre-yield acoustic events, the average amplitude of the signals and the rate of post-yield events. However, the explanation power of the acoustic emission parameters was only moderate. The nature of acoustic emission signals was thus demonstrated to be a potential tool for assessing bone quality.     

Effective elastic properties of damaged isotropic solids

In continuum damage mechanics, damaged solids have been represented by the effective elastic stiffness into which local damage is smoothly smeared. Similarly, damaged solids may be represented in terms of effective elastic compliances. By virtue of the effective elastic compliance representation, it may become easier to derive the effective engineering constants of damaged solids from the effective elastic compliances, all in closed form. Thus, in this paper, by using a continuum modeling approach based on both the principle of strain energy equivalence and the equivalent elliptical micro-crack representation of local damage, the effective elastic compliance and effective engineering constants are derived in terms of the undamaged (virgin) elastic properties and a scalar damage variable for both damaged two- and three-dimensional isotropic solids.