Compressive Yield Strain Research Articles

Open laminectomy plus posterolateral fusion versus open laminectomy plus transforaminal lumbar interbody fusion surgical approaches for fusing degenerated L4-L5 segment: A comparative finite element study

Various finite element (FE) studies reported the biomechanical effects of fusion surgeries in the lumbar spine. However, a comparative study on Open laminectomy plus Posterolateral Fusion (OL-PLF) and Open Laminectomy plus Transforaminal Lumbar Interbody Fusion (OL-TLIF) for fusing an L4-L5 segment has not been reported in the literature. The present comparative FE study evaluates the biomechanical variations in an L4-L5 segment fused using OL-PLF and OL-TLIF surgical approaches. The three-dimensional implanted models were constructed from a computed-tomography scan dataset using image processing software. The models were simulated for the physiological movements such as lateral bending, flexion and extension. The OL-TLIF model had a considerably larger peak equivalent strain than the OL-PLF model under extension (126 %), lateral bending (88 %) and flexion (13 %). However, in both implanted models, a peak equivalent strain above the compressive yield strain limit of the vertebra (0.007) was observed over 60 % of the L4-L5 fused segment, indicating an imminent post-operative bone failure under the imposed loading conditions. The maximum equivalent strain observed in the disc and endplates of the L3-L4 segment was substantially larger to initiate the adjacent segment degeneration. No discernible biomechanical benefits were observed for the OL-TLIF or OL-PLF approaches in fusing the L4-L5 segment.

Finite element analysis of implanted lumbar spine: Effects of open laminectomy plus PLF and open laminectomy plus TLIF surgical approaches on L3-L4 FSU

Several finite element (FE) studies reported performances of various lumbar fusion surgical approaches. However, comparative studies on the performance of Open Laminectomy plus Posterolateral Fusion (OL-PLF) and Open Laminectomy plus Transforaminal Interbody Fusion (OL-TLIF) surgical approaches are rare. In the current FE study, the variation in ranges of motions (ROM), stress-strain distributions in an implanted functional spinal unit (FSU) and caudal adjacent soft structures between OL-PLF and OL-TLIF virtual models were investigated. The implanted lumbar spine FE models were developed from subject-specific computed tomography images of an intact spine and solved for physiological loadings such as compression, flexion, extension and lateral bending. Reductions in the ROMs of L1-L5 (49 % to 59 %) and L3-L4 implanted FSUs (91 % to 96 %) were observed for both models. Under all the loading cases, the maximum von Mises strain observed in the implanted segment of both models exceeds the mean compressive yield strain for the vertebra. The maximum von Mises stress and strain observed on the caudal adjacent soft structures of both the implanted models are at least 22 % higher than the natural spine model. The findings indicate the risk of failure in the implanted FSUs and higher chances of adjacent segment degeneration for both models.

Electron beam weldability of TiZrNbTa refractory high-entropy alloy and TC4 titanium alloy

Electron beam weldability of TiZrNbTa refractory high-entropy alloy and TC4 titanium alloy

Assessment of plastic hinge length in reinforced concrete columns

Plastic hinge properties are crucial parameters in predicting the nonlinear response of structural elements. Because of the intricate material nonlinearity, precise determination of the plastic hinge length (PHL) has encountered several obstacles. Over the last few decades, there have been various definitions and models put forth to forecast this length, nevertheless, the outcomes displayed significant disparities. Therefore, the paper introduces a comprehensive method for determining PHL using certain criteria, including rebar strain profiles, concrete cover and core peak strains, curvature profiles, and damage observations. Furthermore, a set of four full-scale reinforced concrete (RC) columns measuring 400 mm × 400mm × 3000mm and featuring varying transverse reinforcement configurations were constructed and subjected to testing under a high axial load ratio (ALR). The tested results implied that it is necessary to separate the PHLs based on different criteria. The high axial compression load led to enhancing the PHLs, which were based on rebar compressive yield strains, curvature profiles, concrete cover and core peak strains. In contrast, it has a minor effect on PHL based on tensile yield strains. In addition, the amount of transverse reinforcement had an insignificant effect on all PHLs for tested columns. Hence, a revised equation was proposed to estimate the equivalent PHLs of rectangular RC columns based on tested results and a 114-column database. The proposed equation had better accuracy compared with some other model results in the literature.

Finite element analysis of an intact lumbar spine model: Effects of loading under different coordinate systems.

Finite element (FE) analysis has been used in studying the biomechanics of the lumbar spine. While some FE studies used a follower load technique that intended to replace the compressing effect of local muscle force, other studies considered satisfying the relationship between the human body's posture and the centre of gravity (CG) for investigating spine biomechanics. However, the above studies did not reveal the importance of a coordinate system that gratifies the posture-CG relation and follower load techniques. The present FE study compares the variation in ranges of motion (ROM) and stress-strain distributions due to the application of loading via different coordinate systems, follower (FCS) and global (GCS). A subject-specific computed tomography scan-based intact spine (L1-L5) FE model was developed and simulated for physiological movements. The FE results indicated a minimum deviation in ROM of 2.7° for the L1-L5 full model at all physiological activities between the defined coordinate systems. The observed variation for the L3-L4 functional spinal unit was between 4.7° and 19°. The von Mises strain in the vertebrae was between 0.0007 and 0.003 for the FCS case. In contrast, the peak von Mises strain for the GCS case was above the compressive yield strain limit of cancellous bone by 38.5%. The GCS model transferred the load unsymmetrically, whereas the distribution was symmetrical for the FCS case, without any potential risk of bone failure. These observations clearly indicate that the selection of the appropriate loading coordinate system is as crucial as the magnitude of loading.

Unique tension-compression asymmetry of nanoporous metallic glasses induced by surface effects

The mechanical properties of nanoporous (NP) metallic glasses (MGs) under uniaxial tension and compression are studied via molecular dynamics simulations in this work. The shrinking tendency within NP MGs, induced by the surface effects, results in the unique tension-compression asymmetry, i.e., the tensile yield strength is stronger than the compressive yield strength and the tensile yield strain is bigger than the compressive yield strain. This unique tension-compression asymmetry of NP MGs is contrary to that of the pore-free bulk MGs and the MGs with macroscopic pores. The strengthening phenomenon with the increase of the pore size is more remarkable for compression than tension due to the difference of elastic energy release during the deformation. Moreover, with the pore size decreasing, the deformation mechanism of NP MGs changes from catastrophic fracture with a single dominant shear band to homogeneous plastic deformation with multiple shear bands under both tensile loading and compressive loading. Our results are helpful in understanding the surface effects on NP materials and important for optimization design of NP materials.

Compressive behaviour of child and adult cortical bone

In this study, cortical bone tissue from children was investigated. It is extremely difficult to obtain human child tissue. Therefore, the only possibility was to use bone tissue, free from any lesion, collected from young bone cancer patients. The compressive mechanical behaviour of child bone tissue was compared to the behaviour of adult tissue. Moreover, two hypotheses were tested: 1) that the mechanical behaviour of both groups is correlated to ash density; 2) that yield strain is an invariant. Small parts of the diaphysis of femora or tibiae from 12 children (4-15 years) and 12 adults (22-61 years) were collected. Cylindrical specimens were extracted from the cortical wall along the longitudinal axis of the diaphysis. A total of 107 specimens underwent compressive testing (strain rate: 0.1 s(-1)). Only the specimens showing a regular load-displacement curve (94) were considered valid and thereafter reduced to ash. It was found that the child bone tissue had significant lower compressive Young's modulus (-34%), yield stress (-38%), ultimate stress (-33%) and ash density (-17%) than the adult tissue. Conversely, higher compressive ultimate strain was found in the child group (+24%). Despite specimens extracted from both children and adults, ash density largely described the variation in tissue strength and stiffness (R(2)=in the range of 0.86-0.91). Furthermore, yield strain seemed to be roughly an invariant to subject age and tissue density. These results confirm that the mechanical properties of child cortical bone tissue are different from that of adult tissue. However, such differences are correlated to differences in tissue ash density. In fact, ash density was found to be a good predictor of strength and stiffness, also for cortical bone collected from children. Finally, the present findings support the hypothesis that compressive yield strain is an invariant.

Cellulosic aerogels as ultra-lightweight materials. Part 2: Synthesis and properties 2nd ICC 2007, Tokyo, Japan, October 25–29, 2007

Abstract Ultra-lightweight cellulose aerogels can be obtained in three steps: (1) preparation of a cellulose solution in molten N-methylmorpholine-N-oxide monohydrate (NMMO·H2O) at 110–120°C and casting of the viscous mass into moulds; (2) extraction of the solidified castings with ethanol to initiate cellulose aggregation and to remove NMMO·H2O so that the fragile, fine-porous texture of cellulose II is largely retained; and (3) drying of the lyogel using supercritical carbon dioxide (scCO2). According to this approach, cellulosic aerogels were prepared from eight commercial cellulosic materials and pulps and analysed for selected chemical, physicochemical and mechanical parameters. The results reveal that all aerogels obtained from 3% cellulose containing NMMO·H2O melts had a largely uniform mesoporous structure with an average pore size of ∼9–12 nm, surface area of 190–310 m2 g-1, and specific density of 0.046–0.069 g cm-3, but rather low mechanical stability expressed as compressive yield strain of 2.9–5.5%. All samples showed viscoelastic behaviour, with Young's modulus ranging from ∼5 to 10 N mm-2. Doubling the cellulose content in the NMMO·H2O melt from 3% to 6% increased Young's modulus by one order of magnitude. Shrinkage of the fragile cellulose bodies during scCO2 drying was still considerable and is subject to further investigations. Influencing parameters such as scCO2 pressure, cellulose content, regenerating solvent and the number of regenerating baths were optimised.

Bone strength at the distal radius can be estimated from high-resolution peripheral quantitative computed tomography and the finite element method

Bone strength is a fundamental contributor to fracture risk, and with the recent development of in vivo 3D bone micro-architecture measurements by high-resolution peripheral quantitative computed tomography, the finite element (FE) analysis may provide a means to assess patient bone strength in the distal radius. The purpose of this study was to determine an appropriate FE procedure to estimate bone strength by comparison with experimental data. Models based on a homogeneous tissue modulus or a modulus scaled according to computed tomography attenuation were assessed, and these were solved by linear and non-linear FE analyses to estimate strength. The distal radius from fresh, human cadaver forearms (5 male/5 female, ages 55 to 93) was dissected free and four 9.1 mm sections were cut beginning at the subchondral plate to provide 40 test specimens. The sections were scanned using an in vivo protocol providing 3D image data with an 82 microm voxel size. All specimens were mechanically tested in uniaxial compression, and elastic and yield properties were determined. Linear FE analyses were performed on all specimens (N=40), and non-linear analyses using an asymmetric, bilinear yield strain criteria were performed on a sub-sample (N=10) corresponding to the normal clinical measurement site. Experimentally determined apparent elastic properties correlated highly with ultimate stress (R2=0.977, p<0.05, N=31) for the 31 specimens tested to failure. Subsequently, a linear FE analysis estimating apparent elastic properties also correlated highly with failure, and the correlation was higher when moduli were determined from scaled CT-attenuation values than a homogeneous modulus (R2=0.983 vs. R2=0.972, p<0.05, N=31). A non-linear analysis based on tensile and compressive yield strains of 0.0295 and 0.0493 for homogeneous models, and 0.0127 and 0.0212 for scaled models directly estimated ultimate stress, and correlated highly (R2=0.951 vs. R2=0.937, p<0.05, N=5). The linear relation between stiffness and strength may be unique to radius compressive loading. It supports the use of a linear FE analysis to determine bone strength by regression equations established here. Scaled tissue modulus models performed better than homogeneous modulus models, and the advantage of a scaled model is its potential to account for mineralization changes. The combined numerical-experimental procedure for FE model validation on the patient micro-CT technology demonstrated that bone strength can be estimated non-invasively, and this may provide important insight into fracture risk in patient populations.

Damage in trabecular bone at small strains

Evidence that damage decreases bone quality, increases fracture susceptibility, and serves as a remodeling stimulus motivates further study of what loading magnitudes induce damage in trabecular bone. In particular, whether damage occurs at the smaller strains characteristic of habitual, as opposed to traumatic, loading is not known. The overall goal of this study was to characterize damage accumulation in trabecular bone at small strains (0.20 - 0.45% strain). A continuum damage mechanics approach was taken whereby damage was quantified by changes in modulus and residual strain. Human vertebral specimens (n = 7) were tested in compression using a multi-cycle load - unload protocol in which the maximum applied strain for each cycle, epsilonmax, was increased incrementally from epsilonmax = 0.20% on the first loading cycle to epsilonmax = 0.45% on the last cycle. Modulus and residual strain were measured for each cycle. Both changes in modulus and residual strains commenced at small strains, beginning as early as 0.24 and 0.20% strain, respectively. Strong correlations between changes in modulus and residual strains were observed (r = 0.51 - 0.98). Fully nonlinear, high-resolution finite element analyses indicated that even at small apparent strains, tissue-level strains were sufficiently high to cause local yielding. These results demonstrate that damage in trabecular bone occurs at apparent strains less than half the apparent compressive yield strain reported previously for human vertebral trabecular bone. Further, these findings imply that, as a consequence of the highly porous trabecular structure, tissue yielding can initiate at very low apparent strains and that this local failure has detectable and negative consequences on the apparent mechanical properties of trabecular bone.

Effects of grain size from micro scale to nanoscales on the yield strain of brass under compressive and tensile stresses using a Kelvin probing technique

Effects of grain size on the yield strain of brass (70–30), respectively, under tensile and compressive stresses were investigated using a Kelvin probe, a highly sensitive instrument for measuring the electron work function (EWF) of materials. The average grain size under study varied from 20 nm to 80 μm. The nanocrystalline structure was generated by sandblasting followed by recovery treatment. Results of the EWF measurement demonstrated that the yield strain differed as applied stress changed from tensile to compressive. The magnitude of compressive yield strain is larger than that of tensile yield strain. It was observed that with a decrease in grain size, the difference in magnitude between the compressive yield strain and the tensile yield strain decreased. The mechanism responsible for the difference in yield strain and the effect of grain size on the yield strain are discussed.

Effects of grain size from micro scale to nanoscales on the yield strain of brass under compressive and tensile stresses using a Kelvin probing technique

Abstract Effects of grain size on the yield strain of brass (70–30), respectively, under tensile and compressive stresses were investigated using a Kelvin probe, a highly sensitive instrument for measuring the electron work function (EWF) of materials. The average grain size under study varied from 20 nm to 80 μm. The nanocrystalline structure was generated by sandblasting followed by recovery treatment. Results of the EWF measurement demonstrated that the yield strain differed as applied stress changed from tensile to compressive. The magnitude of compressive yield strain is larger than that of tensile yield strain. It was observed that with a decrease in grain size, the difference in magnitude between the compressive yield strain and the tensile yield strain decreased. The mechanism responsible for the difference in yield strain and the effect of grain size on the yield strain are discussed.

Contribution of inter-site variations in architecture to trabecular bone apparent yield strains

Apparent yield strains for trabecular bone are uniform within an anatomic site but can vary across site. The overall goal of this study was to characterize the contribution of inter-site differences in trabecular architecture to corresponding variations in apparent yield strains. High-resolution, small deformation finite element analyses were used to compute apparent compressive and tensile yield strains in four sites (n = 7 specimens per site): human proximal tibia, greater trochanter, femoral neck, and bovine proximal tibia. These sites display differences in compressive, but not tensile, apparent yield strains. Inter-site differences in architecture were captured implicitly in the model geometries, and these differences were isolated as the sole source of variability across sites by using identical tissue properties in all models. Thus, the effects inter-site variations in architecture on yield strain could be assessed by comparing computed yield strains across site. No inter-site differences in computed yield strains were found for either loading mode (p > 0.19), indicating that, within the context of small deformations, inter-site variations in architecture do not affect apparent yield strains. However, results of ancillary analyses designed to test the validity of the small deformation assumption strongly suggested that the propensity to undergo large deformations constitutes an important contribution of architecture to inter-site variations in apparent compressive yield strains. Large deformations substantially reduced apparent compressive, but not tensile, yield strains. These findings indicate the importance of incorporating large deformation capabilities in computational analyses of trabecular bone. This may be critical when investigating the biomechanical consequences of trabecular thinning and loss.

Compressive and Shear Properties of Commercially Available Polyurethane Foams

The shear properties of rigid polyurethane (PU-R) foams, routinely used to simulate cancellous bone, are not well characterized. The present assessment of the shear and compressive properties of four grades of Sawbones "Rigid cellular" PU-R foam tested 20 mm gauge diameter dumb-bell specimens in torsion and under axial loading. Shear moduli ranged from 13.3 to 99.7 MPa, shear strengths from 0.7 MPa to 4.2 MPa. Compressive yield strains varied little with density while shear yield strains had peak values with "200 kgm-3" grade. PU-R foams may be used to simulate the elastic but not failure properties of cancellous bone.

Relationships between material properties and CT scan data of cortical bone with and without metastatic lesions

Breast, prostate, lung, and other cancers can metastasize to bone and lead to pathological fracture. To lay the groundwork for new clinical techniques for assessing the risk of pathological fracture, we identified relationships between density measured using quantitative computed tomography (rhoQCT), longitudinal mechanical properties, and ash density (rhoAsh) of cortical bone from femoral diaphyses with and without metastatic lesions from breast, prostate, and lung cancer (bone with metastases from six donors; bone without metastases from one donor with cancer and two donors without cancer). Moderately strong linear relationships between rhoQCT and elastic modulus, strength, and rhoAsh were found for bone with metastases (0.73<r<0.93, P<0.05). After accounting for differences in rhoQCT, the elastic modulus, compressive strength, tensile yield strain, and rhoAsh of bone with metastatic lesions differed from those of bone from donors without cancer (P<0.01). However, differences in tensile strength or compressive yield strain, after controlling for rhoQCT, were not found. Thus, these cancers degrade the elastic modulus and compressive strength, but not the tensile strength, of cortical bone beyond the amount that would be expected from decreased density alone. The rhoQCT-mechanical property relationships reported may be useful for evaluating bone integrity and assessing the risk of fracture of bone with metastases.

Dependence of yield strain of human trabecular bone on anatomic site

Understanding the dependence of human trabecular bone strength behavior on anatomic site provides insight into structure-function relationships and is essential to the increased success of site-specific finite element models of whole bones. To investigate the hypothesis that the yield strains of human trabecular bone depend on anatomic site, the uniaxial tensile and compressive yield properties were compared for cylindrical specimens from the vertebra (n=61), proximal tibia (n=31), femoral greater trochanter (n=23), and femoral neck (n=27) taken from 61 donors (67+/-15years). Test protocols were used that minimized end artifacts and loaded specimens along the main trabecular orientation. Yield strains by site (mean+/-S.D.) ranged from 0.70+/-0.05% for the trochanter to 0.85+/-0.10% for the femoral neck in compression, from 0.61+/-0.05% for the trochanter to 0.70+/-0.05% for the vertebra in tension, and were always higher in compression than tension (p<0.001). The compressive yield strain was higher for the femoral neck than for all other sites (p<0.001), as was the tensile yield strain for the vertebra (p<0.007). Analysis of covariance, with apparent density as the covariate, indicated that inter-site differences existed in yield stress even after adjusting statistically for density (p<0.035). Coefficients of variation in yield strain within each site ranged from only 5-12%, consistent with the strong linear correlations (r(2)=0.94-0.98) found between yield stress and modulus. These results establish that the yield strains of human trabecular bone can differ across sites, but that yield strain may be considered uniform within a given site despite substantial variation in elastic modulus and yield stress.

High-resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular bone

The ability to predict trabecular failure using microstructure-based computational models would greatly facilitate study of trabecular structure-function relations, multiaxial strength, and tissue remodeling. We hypothesized that high-resolution finite element models of trabecular bone that include cortical-like strength asymmetry at the tissue level, could predict apparent level failure of trabecular bone for multiple loading modes. A bilinear constitutive model with asymmetric tissue yield strains in tension and compression was applied to simulate failure in high-resolution finite element models of seven bovine tibial specimens. Tissue modulus was reduced by 95% when tissue principal strains exceeded the tissue yield strains. Linear models were first calibrated for effective tissue modulus against specimen-specific experimental measures of apparent modulus, producing effective tissue moduli of (mean+/-S.D.) 18.7+/-3.4GPa. Next, a parameter study was performed on a single specimen to estimate the tissue level tensile and compressive yield strains. These values, 0.60% strain in tension and 1.01% strain in compression, were then used in non-linear analyses of all seven specimens to predict failure for apparent tensile, compressive, and shear loading. When compared to apparent yield properties previously measured for the same type of bone, the model predictions of both the stresses and strains at failure were not statistically different for any loading case (p>0.15). Use of symmetric tissue strengths could not match the experimental data. These findings establish that, once effective tissue modulus is calibrated and uniform but asymmetric tissue failure strains are used, the resulting models can capture the apparent strength behavior to an outstanding level of accuracy. As such, these computational models have reached a level of fidelity that qualifies them as surrogates for destructive mechanical testing of real specimens.

Yield strain behavior of trabecular bone

If bone adapts to maintain constant strains and if on-axis yield strains in trabecular bone are independent of apparent density, adaptive remodeling in trabecular bone should maintain a constant safety factor (yield strain/functional strain) during habitual loading. To test the hypothesis that yield strains are indeed independent of density, compressive (n = 22) and tensile (n = 22) yield strains were measured without end-artifacts for low density (0.18 +/- 0.04 g cm(-3)) human vertebral trabecular bone specimens. Loads were applied in the superior-inferior direction along the principal trabecular orientation. These 'on-axis' yield strains were compared to those measured previously for high-density (0.51 +/- 0.06 g cm(-3)) bovine tibial trabecular bone (n = 44). Mean (+/- S.D.) yield strains for the human bone were 0.78 +/- 0.04% in tension and 0.84 +/- 0.06% in compression; corresponding values for the bovine bone were 0.78 +/- 0.04 and 1.09 +/- 0.12%, respectively. Tensile yield strains were independent of the apparent density across the entire density range (human p = 0.40, bovine p = 0.64, pooled p = 0.97). By contrast, compressive yield strains were linearly correlated with apparent density for the human bone (p < 0.001) and the pooled data (p < 0.001), and a suggestive trend existed for the bovine data (p = 0.06). These results refute the hypothesis that on-axis yield strains for trabecular bone are independent of density for compressive loading, although values may appear constant over a narrow density range. On-axis tensile yield strains appear to be independent of both apparent density and anatomic site.

放電焼結法により作製したＲｕＡｌ金属間化合物バルク体の機械的特性

RuAl is one of the potentially useful intermetallics with a high melting temperature(2333K) as a structural material. Ru100-xAlx(x=45, 47.5, 50, 52.5, 55at%) powders were prepared by mechanical alloying (MA). The MA powders were subsequently consolidated by Plasma Activated Sintering process(PAS) at 1673-1773K for 10 minutes under 50MPa pressure. Each compact had sub-micron structure, which were consist of Ru and RuAl for 45, 47.5 and 50 at%Al compacts, RuAl and RuAl2 for 52.5 and 55 at%Al compacts. Compressive tests were carried out for Ru-Al compacts at room temperature. Some of them below 50 at%Al exhibited compressive yield stress of 2.0-2.8 GPa and compressive yield strain of more than 25%.

Differences between the tensile and compressive strengths of bovine tibial trabecular bone depend on modulus

The conflicting conclusions regarding the relationship between the tensile and compressive strengths of trabecular bone remain unexplained. To help resolve this issue, we compared measurements of the tensile (n = 22) and compressive (n = 22) yield strengths, and yield strains, of trabecular bone specimens taken from 38 bovine proximal tibiae. We also studied how these failure properties depended on modulus and apparent density. To enhance accuracy, trabecular orientation was controlled, and each specimen had a reduced section where strains were measured with a miniature extensometer. We found that the mean yield strength was 30% lower for tensile loading. However, the difference between individual values of the tensile and compressive strengths increased linearly with increasing modulus and density, being negligible for low moduli, but substantial for high moduli. By contrast, both the tensile and compressive yield strains were independent of modulus and density, with the yield strain being 30% lower for tensile loading. Thus, the difference between the tensile and compressive strengths of bovine tibial trabecular bone depends on the modulus, but the difference between yield strains does not. This phenomenon may explain in part that conflicting conclusions reached previously on the tensile and compressive strengths of trabecular bone since the mean modulus has varied among different studies. Realizing that our data pertain only directly to bovine tibial trabecular bone for longitudinal loading, our results nevertheless suggest that failure parameters based on strains may provide more powerful and general comparisons of the failure properties for trabecular bone than measures based on stress.