The Modified Super-Ellipsoid Yield Criterion for Human Trabecular Bone

2004 ◽  
Vol 126 (6) ◽  
pp. 677-684 ◽  
Author(s):  
Harun H. Bayraktar ◽  
Atul Gupta ◽  
Ron Y. Kwon ◽  
Panayiotis Papadopoulos ◽  
Tony M. Keaveny
Keyword(s):  
Finite Element ◽  
High Resolution ◽  
Trabecular Bone ◽  
Yield Surface ◽  
Shear Loading ◽  
Finite Element Models ◽  
Normal Strain ◽  
Multiaxial Loading ◽  
Yield Behavior ◽  
Strain Space

Despite the importance of multiaxial failure of trabecular bone in many biomechanical applications, to date no complete multiaxial failure criterion for human trabecular bone has been developed. By using experimentally validated nonlinear high-resolution, micro-mechanical finite-element models as a surrogate for multiaxial loading experiments, we determined the three-dimensional normal strain yield surface and all combinations of the two-dimensional normal-shear strain yield envelope. High-resolution finite-element models of three human femoral neck trabecular bone specimens obtained through micro-computed tomography were used. In total, 889 multiaxial-loading cases were analyzed, requiring over 41,000 CPU hours on parallel supercomputers. Our results indicated that the multiaxial yield behavior of trabecular bone in strain space was homogeneous across the specimens and nearly isotropic. Analysis of stress-strain curves along each axis in the 3-D normal strain space indicated uncoupled yield behavior, whereas substantial coupling was seen for normal-shear loading. A modified super-ellipsoid surface with only four parameters fit the normal strain yield data very well with an arithmetic error±SD less than −0.04±5.1%. Furthermore, the principal strains associated with normal-shear loading showed excellent agreement with the yield surface obtained for normal strain loading (arithmetic error±SD<2.5±6.5%). We conclude that the four-parameter “Modified Super-Ellipsoid” yield surface presented here describes the multiaxial failure behavior of human femoral neck trabecular bone very well.

Preparation of On-Axis Cylindrical Trabecular Bone Specimens Using Micro-CT Imaging

2004 ◽  
Vol 126 (1) ◽  
pp. 122-125 ◽  
Author(s):  
Xiang Wang, ◽  
Xiangyi Liu, and ◽  
Glen L. Niebur
Keyword(s):  
Finite Element ◽  
High Resolution ◽  
Coordinate System ◽  
Trabecular Bone ◽  
Cylindrical Specimen ◽  
Longitudinal Axis ◽  
Ct Imaging ◽  
Finite Element Models ◽  
Micro Ct ◽  
Average Deviation

The Orientation of trabecular bone specimens for mechanical testing must be carefully controlled. A method for accurately preparing on-axis cylindrical specimens using high-resolution micro-CT imaging was developed. Sixteen cylindrical specimens were prepared from eight bovine tibiae. High-resolution finite element models were generated from micro-CT images of parallelepipeds and used to determine the principal material coordinate system of each parallelepiped. A cylindrical specimen was then machined with a diamond coring bit. The resulting specimens were scanned again to evaluate the orientation. The average deviation between the principal fabric orientation and the longitudinal axis of the cylindrical specimen was only 4.70±3.11°.

scholarly journals The Quartic Piecewise-Linear Criterion for the Multiaxial Yield Behavior of Human Trabecular Bone

2015 ◽  
Vol 137 (1) ◽  
Author(s):  
Arnav Sanyal ◽  
Joanna Scheffelin ◽  
Tony M. Keaveny
Keyword(s):  
Finite Element ◽  
Trabecular Bone ◽  
Volume Fraction ◽  
Yield Criterion ◽  
Shear Loading ◽  
Bone Volume ◽  
Mechanical Anisotropy ◽  
Bone Volume Fraction ◽  
Human Trabecular Bone ◽  
Strain Space

Prior multiaxial strength studies on trabecular bone have either not addressed large variations in bone volume fraction and microarchitecture, or have not addressed the full range of multiaxial stress states. Addressing these limitations, we utilized micro-computed tomography (μCT) based nonlinear finite element analysis to investigate the complete 3D multiaxial failure behavior of ten specimens (5 mm cube) of human trabecular bone, taken from three anatomic sites and spanning a wide range of bone volume fraction (0.09–0.36), mechanical anisotropy (range of E3/E1 = 3.0–12.0), and microarchitecture. We found that most of the observed variation in multiaxial strength behavior could be accounted for by normalizing the multiaxial strength by specimen-specific values of uniaxial strength (tension, compression in the longitudinal and transverse directions). Scatter between specimens was reduced further when the normalized multiaxial strength was described in strain space. The resulting multiaxial failure envelope in this normalized-strain space had a rectangular boxlike shape for normal–normal loading and either a rhomboidal boxlike shape or a triangular shape for normal-shear loading, depending on the loading direction. The finite element data were well described by a single quartic yield criterion in the 6D normalized-strain space combined with a piecewise linear yield criterion in two planes for normal-shear loading (mean error ± SD: 4.6 ± 0.8% for the finite element data versus the criterion). This multiaxial yield criterion in normalized-strain space can be used to describe the complete 3D multiaxial failure behavior of human trabecular bone across a wide range of bone volume fraction, mechanical anisotropy, and microarchitecture.

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

2000 ◽  
Vol 33 (12) ◽  
pp. 1575-1583 ◽  
Author(s):  
Glen L Niebur ◽  
Michael J Feldstein ◽  
Jonathan C Yuen ◽  
Tony J Chen ◽  
Tony M Keaveny
Keyword(s):  
Finite Element ◽  
High Resolution ◽  
Trabecular Bone ◽  
Finite Element Models ◽  
Strength Asymmetry

Convergence Behavior of High-Resolution Finite Element Models of Trabecular Bone

1999 ◽  
Vol 121 (6) ◽  
pp. 629-635 ◽  
Author(s):  
G. L. Niebur ◽  
J. C. Yuen ◽  
A. C. Hsia ◽  
T. M. Keaveny
Keyword(s):  
Finite Element ◽  
High Resolution ◽  
Trabecular Bone ◽  
Tissue Level ◽  
Finite Element Models ◽  
Trabecular Thickness ◽  
Convergence Behavior ◽  
Loading Mode ◽  
Element Size ◽  
High Resolution Models

The convergence behavior of finite element models depends on the size of elements used, the element polynomial order, and on the complexity of the applied loads. For high-resolution models of trabecular bone, changes in architecture and density may also be important. The goal of this study was to investigate the influence of these factors on the convergence behavior of high-resolution models of trabecular bone. Two human vertebral and two bovine tibial trabecular bone specimens were modeled at four resolutions ranging from 20 to 80 μm and subjected to both compressive and shear loading. Results indicated that convergence behavior depended on both loading mode (axial versus shear) and volume fraction of the specimen. Compared to the 20 μm resolution, the differences in apparent Young’s modulus at 40 μm resolution were less than 5 percent for all specimens, and for apparent shear modulus were less than 7 percent. By contrast, differences at 80 μm resolution in apparent modulus were up to 41 percent, depending on the specimen tested and loading mode. Overall, differences in apparent properties were always less than 10 percent when the ratio of mean trabecular thickness to element size was greater than four. Use of higher order elements did not improve the results. Tissue level parameters such as maximum principal strain did not converge. Tissue level strains converged when considered relative to a threshold value, but only if the strains were evaluated at Gauss points rather than element centroids. These findings indicate that good convergence can be obtained with this modeling technique, although element size should be chosen based on factors such as loading mode, mean trabecular thickness, and the particular output parameter of interest.

scholarly journals Incorporation of Load Induced Thermal Strain in Finite Element Models

10.14311/1079 ◽  
2009 ◽  
Vol 49 (1) ◽  
Author(s):  
A. Law ◽  
M. Gillie ◽  
P. Pankaj
Keyword(s):  
Finite Element ◽  
Yield Surface ◽  
Thermal Strain ◽  
Finite Element Models ◽  
In Fire

Load induced thermal strains (LITS) are an integral part of the behaviour of concrete in fire; their existence has been well documented and modelled by different researchers. More thorough representation of LITS is needed to accurately represent their plastic constituents in finite element models. This paper develops a technique to allow the evolution of LITS in accordance with the rules developed in several academic models. The technique is implemented with a simple Drucker-Prager yield surface and the results assessed. 

Fast and accurate specimen-specific simulation of trabecular bone elastic modulus using novel beam–shell finite element models

2011 ◽  
Vol 44 (8) ◽  
pp. 1566-1572 ◽  
Author(s):  
Jef Vanderoost ◽  
Siegfried V.N. Jaecques ◽  
Georges Van der Perre ◽  
Steven Boonen ◽  
Jan D'hooge ◽  
...  
Keyword(s):  
Finite Element ◽  
Elastic Modulus ◽  
Trabecular Bone ◽  
Finite Element Models ◽  
Shell Finite Element ◽  
Bone Elastic Modulus
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