Nonlinear Behavior of Trabecular Bone at Small Strains

2000 ◽  
Vol 123 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Elise F. Morgan ◽  
Oscar C. Yeh ◽  
Wesley C. Chang ◽  
Tony M. Keaveny
Keyword(s):  
Trabecular Bone ◽  
Nonlinear Behavior ◽  
Strain Range ◽  
Small Strain ◽  
Tangent Modulus ◽  
Anatomic Site ◽  
Stress Strain ◽  
Strain Behavior ◽  
Loading Mode ◽  
Initial Modulus

Study of the behavior of trabecular bone at strains below 0.40 percent is of clinical and biomechanical importance. The goal of this work was to characterize, with respect to anatomic site, loading mode, and apparent density, the subtle concave downward stress–strain nonlinearity that has been observed recently for trabecular bone at these strains. Using protocols designed to minimize end-artifacts, 155 cylindrical cores from human vertebrae, proximal tibiae, proximal femora, and bovine proximal tibiae were mechanically tested to yield at 0.50 percent strain per second in tension or compression. The nonlinearity was quantified by the reduction in tangent modulus at 0.20 percent and 0.40 percent strain as compared to the initial modulus. For the pooled data, the mean±SD percentage reduction in tangent modulus at 0.20 percent strain was 9.07±3.24 percent in compression and 13.8±4.79 percent in tension. At 0.40 percent strain, these values were 23.5±5.71 and 35.7±7.10 percent, respectively. The magnitude of the nonlinearity depended on both anatomic site p<0.001 and loading mode p<0.001, and in tension was positively correlated with density. Calculated values of elastic modulus and yield properties depended on the strain range chosen to define modulus via a linear curve fit p<0.005. Mean percent differences in 0.20 percent offset yield strains were as large as 10.65 percent for some human sites. These results establish that trabecular bone exhibits nonlinearity at low strains, and that this behavior can confound intersite comparisons of mechanical properties. A nonlinear characterization of the small strain behavior of trabecular bone was introduced to characterize the initial stress–strain behavior more thoroughly.

Mechanical Properties of Kevlar® KM2 Single Fiber

2005 ◽  
Vol 127 (2) ◽  
pp. 197-203 ◽  
Author(s):  
Ming Cheng ◽  
Weinong Chen ◽  
Tusit Weerasooriya
Keyword(s):  
Isotropic Material ◽  
Axial Stress ◽  
Axial Loading ◽  
Strain Range ◽  
Transversely Isotropic ◽  
Axial Direction ◽  
Strain Response ◽  
Transversely Isotropic Material ◽  
Stress Strain ◽  
Strain Behavior

Kevlar® KM2 fiber is a transversely isotropic material. Its tensile stress-strain response in the axial direction is linear and elastic until failure. However, the overall deformation in the transverse directions is nonlinear and nonelastic, although it can be treated linearly and elastically in infinitesimal strain range. For a linear, elastic, and transversely isotropic material, five material constants are needed to describe its stress-strain response. In this paper, stress-strain behavior obtained from experiments on a single Kevlar KM2 fiber are presented and discussed. The effects of loading rate and the influence of axial loading on transverse and transverse loading on axial stress-strain responses are also discussed.

Cyclic Plastic Deformation of a Circular Plate With Work Hardening

1984 ◽  
Vol 106 (4) ◽  
pp. 336-341
Author(s):  
R. Winter
Keyword(s):  
Fatigue Life ◽  
Low Cycle Fatigue ◽  
Nonlinear Behavior ◽  
Strain Curve ◽  
Strain Range ◽  
Cyclic Strain ◽  
Cyclic Stress ◽  
Cycle Fatigue ◽  
Stress Strain ◽  
Element Analysis

An experimental and theoretical study was performed of the nonlinear behavior of a simply supported flat circular aluminum plate under reversed cyclic central load. The application is for the analysis of cyclic stress and strain of structural components in the plastic range for predicting low-cycle fatigue life. The main purpose was to determine the relative accuracy of an elastic-plastic large deformation finite element analysis when the material properties input data are derived from monotonic (noncyclic) stress-strain curves versus that derived from cyclic stress-strain curves. The results showed that large errors could be induced in the theoretical prediction of cyclic strain range when using the monotonic stress-strain curve, which could lead to large errors in predicting low-cycle fatigue life. The use of cyclic stress-strain curves, according to the model developed by Morrow, et al., proved to be accurate and convenient.

Effects of Test Temperature and Prior Aging on the Cyclic Stress-Strain Behavior of Lead Free Solders

2019 ◽  
Author(s):  
Mohammad Ashraful Haq ◽  
Mohd Aminul Hoque ◽  
Jeffrey C. Suhling ◽  
Pradeep Lall
Keyword(s):  
Strain Range ◽  
Peak Stress ◽  
Cyclic Stress ◽  
Lead Free ◽  
Stress Strain ◽  
Plastic Strain Range ◽  
Strain Behavior ◽  
Loop Area ◽  
Prior Aging ◽  
Lead Free Solders

Abstract In temperature changing environments, solder joints often experience fatigue failure due to cyclic mechanical stresses and strains induced by mismatches in the coefficients of thermal expansion. These stresses and strains lead to damage accumulation and contribute to the crack initiation, crack propagation, and eventually to failure. In this study, we have investigated the cyclic stress-strain behavior of SAC305 and SAC_Q reflowed lead free solders that occur at various testing temperatures and with various prior aging conditions. Lead free solder uniaxial test specimens with circular cross-section have been prepared using vacuum suction method and then were aged for 0 to 20 days at 125 °C. The samples were then subjected to cyclic stress-strain loading using a Micro-mechanical tester at different testing temperatures from T = 25 C to T = 100 C. The evolution of hysteresis loops with duration of prior aging was characterized by measuring the strain energy density dissipated per cycle (loop area), peak stress, and plastic strain range. It was observed that aging degrades the mechanical fatigue properties due to microstructural coarsening. At elevated temperatures, a drop in the loop area and peak stress and an increase in the plastic strain range for both lead free reflowed solder materials were obtained. In addition, SAC_Q samples had a higher loop area and peak stress compared to SAC305.

Effect of Hydrolysis on Mechanical Behavior of Bioabsorbable Composites

2014 ◽  
Vol 783-786 ◽  
pp. 1274-1279 ◽  
Author(s):  
Satoshi Kobayashi ◽  
Shusaku Yamaji
Keyword(s):  
Mechanical Behavior ◽  
Interfacial Strength ◽  
Nonlinear Behavior ◽  
Critical Energy ◽  
Stress Strain ◽  
Critical Energy Release Rate ◽  
Strain Behavior ◽  
Strain Relationship ◽  
Theoretical Results ◽  
Good Agreement

In this study, effect of hydrolysis in simulated body environment on mechanical behavior oftricalcium phosphate (TCP)/Poly(L-lactic acid) (PLLA) composites were analytically characterized.In order to predict stress-strain behavior after hydrolysis, damage micromechanical analysis proposedby the authors were utilized. In this model, nonlinear behavior in stress strain relationship weresimulated considering interfacial debonding between TCP particle and PLLA matrix. For the purposeof deciding the interfacial strength, such as critical energy release rate, curve fitting was conducted onthe result of the composites with 15wt% TCP content. Theoretical results on 5wt% and 10wt%composites using the interfacial strength obtained were in good agreement with experimental results.This result indicated that interfacial strength was independent from TCP fraction.

Dependence of Yield Strain on Anatomic Site for Human Trabecular Bone

1999 ◽  
Author(s):  
Elise F. Morgan ◽  
Yves P. Arramon ◽  
David L. Kopperdahl ◽  
Tony M. Keaveny
Keyword(s):  
Trabecular Bone ◽  
Volume Fraction ◽  
Failure Criteria ◽  
Trabecular Architecture ◽  
Yield Strain ◽  
Anatomic Site ◽  
Strain Behavior ◽  
Human Trabecular Bone ◽  
Strain Adaptation ◽  
Testing Protocols

Abstract The yield strain behavior of trabecular bone has gained increased importance as evidence accumulates that remodeling and failure criteria can be expressed as a function of strain alone (Turner et al., 1997; Silva et al., 1998). These findings rely on the results of previous studies in which yield strains were found to be isotropic and generally independent of volume fraction (Turner, 1989; Kopperdahl and Keaveny, 1998; Chang et al., 1999), although relatively little work has been done to substantiate these results for human trabecular bone. Thorough consideration of the dependence of yield strain on volume fraction should include analyses of trabecular bone from different anatomic sites since site-dependent differences in trabecular architecture have been well-correlated with mechanical properties (Goulet et al., 1994). However, differences in testing protocols and in definitions of modulus and yield point (Linde, 1994) have led to discrepancies in reported yield strain values in the literature (Kopperdahl and Keaveny, 1998). This prevents inter-study comparisons of the yield strain behavior of human trabecular bone across different anatomic sites, and yet characterizing this behavior is a fundamental step both. In the validation of uniform strain adaptation models and in the development of failure criteria.

Durometer Hardness and the Stress-Strain Behavior of Elastomeric Materials

2003 ◽  
Vol 76 (2) ◽  
pp. 419-435 ◽  
Author(s):  
H. J. Qi ◽  
K. Joyce ◽  
M. C. Boyce
Keyword(s):  
Constitutive Model ◽  
Hardness Test ◽  
Hardness Measurement ◽  
Biological Tissues ◽  
Stress Strain ◽  
Strain Behavior ◽  
Initial Modulus ◽  
Nonlinear Stress ◽  
Simulation Results ◽  
D Values

Abstract The Durometer hardness test is one of the most commonly used measurements to qualitatively assess and compare the mechanical behavior of elastomeric and elastomeric-like materials. This paper presents nonlinear finite element simulations of hardness tests which act to provide a mapping of measured Durometer Shore A and D values to the stress-strain behavior of elastomers. In the simulations, the nonlinear stress-strain behavior of the elastomers is first represented using the Gaussian (neo-Hookean) constitutive model. The predictive capability of the simulations is verified by comparison of calculated conversions of Shore A to Shore D values with the guideline conversion chart in ASTM D2240. The simulation results are then used to determine the relationship between the neo-Hookean elastic modulus and Shore A and Shore D values. The simulation results show the elastomer to undergo locally large deformations during hardness testing. In order to assess the potential role of the limiting extensibility of the elastomer on the hardness measurement, simulations are conducted where the elastomer is represented by the non-Gaussian Arruda-Boyce constitutive model. The limiting extensibility is found to predict a higher hardness value for a material with a given initial modulus. This effect is pronounced as the limiting extensibility decreases to less than 5 and eliminates the one-to-one mapping of hardness to modulus. However, the durometer hardness test still can be used as a reasonable approximation of the initial neo-Hookean modulus unless the limiting extensibility is known to be small as is the case in many materials, such as some elastomers and most soft biological tissues.

Comparison of Tensile and Shear Behavior of Carbon-Black-Filled Elastomers

1987 ◽  
Vol 60 (4) ◽  
pp. 761-780 ◽  
Author(s):  
N. Nakajima ◽  
J. J. Scobbo ◽  
E. R. Harrell
Keyword(s):  
Carbon Black ◽  
Tensile Stress ◽  
High Speed ◽  
Complex Viscosity ◽  
Small Strain ◽  
Shear Behavior ◽  
Dynamic Shear ◽  
Stress Strain ◽  
Strain Behavior ◽  
Tensile Tester

Abstract Four NBR's and 2 SBR's with 40 phr carbon black and one SBR with 56 phr carbon black were characterized in both tensile stress-strain behavior and small-strain dynamic-shear behavior. The room temperature tensile stress-strain behavior was determined at strain rates of 0.00690, 0.0187, 0.0975, 0.0162, and 0.253 s−1. For dynamic-shear observations, loss and storage moduli were used to calculate the complex viscosity-frequency curve at small deformations and frequencies of 0.1 to 100 rad/s. Also, these data from tensile and shear experiments were compared with previous data from a capillary rheometer, high-speed tensile tester, and oscillatory tensile tester. Strain-time correspondence was found applicable to large-deformation tensile data up to the yield point. The formation of an anisotropic aggregate density in elongational deformation explains the higher viscosity and modulus for tensile behavior relative to small-strain shear behavior at similar conditions. In shear deformation and flow, the formation of an anisotropic density of aggregates does not seem to occur appreciably.

scholarly journals The Effects of Installation on the Elastic Stiffness Coefficients of Spudcan Foundations

2021 ◽  
Vol 9 (4) ◽  
pp. 429
Author(s):  
Wen-Long Lin ◽  
Zhen Wang ◽  
Fei Liu ◽  
Jiang-Tao Yi
Keyword(s):  
Small Strain ◽  
Elastic Stiffness ◽  
Stress Strain ◽  
Soft Clays ◽  
Strain Behavior ◽  
Installation Effects ◽  
Stiffness Coefficients ◽  
Strain Calculation ◽  
Dual Stage ◽  
Jack Up

Subjected to pre-load, spudcan foundations, widely utilized to support offshore jack-up rigs, may penetrate in a few diameters into soft clays before mobilizing sufficient resistance from soil. While its stress–strain behavior is known to be affected by the embedment condition and soil backflow, the small-strain calculation with wished-in-place assumption was previously adopted to analyze its elastic stiffness coefficients. This study takes advantage of a recently developed dual-stage Eulerian–Lagrangian (DSEL) technique to re-evaluate the elastic stiffness coefficients of spudcans after realistically modelling the deep, continuous spudcan penetration. A numerical parametric exercise is conducted to investigate the effects of strength non-homogeneity, embedment depths, and the spudcan’s size on the elastic stiffness. On these bases, an expression is provided such that the practicing engineers can conveniently factor the installation effects into the estimation of elastic stiffness coefficients of spudcans.

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