Elastic Properties of Human Osteon and Osteonal Lamella Computed by a Bidirectional Micromechanical Model and Validated by Nanoindentation

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Radim Korsa ◽  
Jaroslav Lukes ◽  
Josef Sepitka ◽  
Tomas Mares
Keyword(s):  
Cortical Bone ◽  
Elastic Properties ◽  
Elastic Constants ◽  
Micromechanical Model ◽  
Degenerative Diseases ◽  
Coordinate Systems ◽  
Inverse Homogenization ◽  
Curvilinear Coordinate ◽  
Anisotropic Elastic ◽  
Good Agreement

Knowledge of the anisotropic elastic properties of osteon and osteonal lamellae provides a better understanding of various pathophysiological conditions, such as aging, osteoporosis, osteoarthritis, and other degenerative diseases. For this reason, it is important to investigate and understand the elasticity of cortical bone. We created a bidirectional micromechanical model based on inverse homogenization for predicting the elastic properties of osteon and osteonal lamellae of cortical bone. The shape, the dimensions, and the curvature of osteon and osteonal lamellae are described by appropriately chosen curvilinear coordinate systems, so that the model operates close to the real morphology of these bone components. The model was used to calculate nine orthotropic elastic constants of osteonal lamellae. The input values have the elastic properties of a single osteon. We also expressed the dependence of the elastic properties of the lamellae on the angle of orientation. To validate the model, we performed nanoindentation tests on several osteonal lamellae. We compared the experimental results with the calculated results, and there was good agreement between them. The inverted model was used to calculate the elastic properties of a single osteon, where the input values are the elastic constants of osteonal lamellae. These calculations reveal that the model can be used in both directions of homogenization, i.e., direct homogenization and also inverse homogenization. The model described here can provide either the unknown elastic properties of a single lamella from the known elastic properties at the level of a single osteon, or the unknown elastic properties of a single osteon from the known elastic properties at the level of a single lamella.

scholarly journals Measurement of the Anisotropic Dynamic Elastic Constants of Additive Manufactured and Wrought Ti6Al4V Alloys

Materials ◽  
2022 ◽  
Vol 15 (2) ◽  
pp. 638
Author(s):  
Ofer Tevet ◽  
David Svetlizky ◽  
David Harel ◽  
Zahava Barkay ◽  
Dolev Geva ◽  
...  
Keyword(s):  
Elastic Properties ◽  
Elastic Constants ◽  
Electron Backscatter Diffraction ◽  
Mechanical Design ◽  
Rolling Direction ◽  
Micro Computed Tomography ◽  
Phase Layer ◽  
Anisotropic Elastic ◽  
Hot Rolled ◽  
Pulse Echo

Additively manufactured (AM) materials and hot rolled materials are typically orthotropic, and exhibit anisotropic elastic properties. This paper elucidates the anisotropic elastic properties (Young’s modulus, shear modulus, and Poisson’s ratio) of Ti6Al4V alloy in four different conditions: three AM (by selective laser melting, SLM, electron beam melting, EBM, and directed energy deposition, DED, processes) and one wrought alloy (for comparison). A specially designed polygon sample allowed measurement of 12 sound wave velocities (SWVs), employing the dynamic pulse-echo ultrasonic technique. In conjunction with the measured density values, these SWVs enabled deriving of the tensor of elastic constants (Cij) and the three-dimensional (3D) Young’s moduli maps. Electron backscatter diffraction (EBSD) and micro-computed tomography (μCT) were employed to characterize the grain size and orientation as well as porosity and other defects which could explain the difference in the measured elastic constants of the four materials. All three types of AM materials showed only minor anisotropy. The wrought (hot rolled) alloy exhibited the highest density, virtually pore-free μCT images, and the highest ultrasonic anisotropy and polarity behavior. EBSD analysis revealed that a thin β-phase layer that formed along the elongated grain boundaries caused the ultrasonic polarity behavior. The finding that the elastic properties depend on the manufacturing process and on the angle relative to either the rolling direction or the AM build direction should be taken into account in the design of products. The data reported herein is valuable for materials selection and finite element analyses in mechanical design. The pulse-echo measurement procedure employed in this study may be further adapted and used for quality control of AM materials and parts.

Specimen Specific Multiscale Model for the Anisotropic Elastic Properties of Human Cortical Bone Tissue

2007 ◽  
Author(s):  
Justin M. Deuerling ◽  
Weimin Yue ◽  
Alejandro A. Espinoza ◽  
Ryan K. Roeder
Keyword(s):  
Cortical Bone ◽  
Elastic Properties ◽  
Structural Information ◽  
Transversely Isotropic ◽  
Longitudinal Axis ◽  
Orientation Distribution ◽  
Tissue Properties ◽  
Apatite Crystals ◽  
Micromechanical Models ◽  
Anisotropic Elastic

The elastic constants of cortical bone are orthotropic or transversely isotropic depending on the anatomic origin of the tissue. Micromechanical models have been developed to predict anisotropic elastic properties from structural information. Many have utilized microstructural features such as osteons, cement lines and Haversian canals to model the tissue properties [1]. Others have utilized nanoscale features to model the mineralized collagen fibril [2]. Quantitative texture analysis using x-ray diffraction techniques has shown that elongated apatite crystals exhibit a preferred orientation in the longitudinal axis of the bone [3]. The orientation distribution of apatite crystals provides fundamental information influencing the anisotropy of the extracellular matrix (ECM) but has not been utilized in existing micromechanical models.

scholarly journals Specimen-specific multi-scale model for the anisotropic elastic constants of human cortical bone

2009 ◽  
Vol 42 (13) ◽  
pp. 2061-2067 ◽  
Author(s):  
Justin M. Deuerling ◽  
Weimin Yue ◽  
Alejandro A. Espinoza Orías ◽  
Ryan K. Roeder
Keyword(s):  
Cortical Bone ◽  
Elastic Constants ◽  
Scale Model ◽  
Multi Scale ◽  
Human Cortical Bone ◽  
Anisotropic Elastic

Elastic Anisotropy of Human Cortical Bone Secondary Osteons Measured by Nanoindentation

2008 ◽  
Vol 131 (2) ◽  
Author(s):  
Giampaolo Franzoso ◽  
Philippe K. Zysset
Keyword(s):  
Cortical Bone ◽  
Elastic Properties ◽  
Elastic Constants ◽  
Elastic Anisotropy ◽  
Elastic Model ◽  
Indentation Modulus ◽  
Lamellar Bone ◽  
Macroscopic Level ◽  
Human Cortical Bone ◽  
Secondary Osteons

The identification of anisotropic elastic properties of lamellar bone based on nanoindentation data is an open problem. Therefore, the purpose of this study was to develop a method to estimate the orthotropic elastic constants of human cortical bone secondary osteons using nanoindentation in two orthogonal directions. Since the indentation modulus depends on all elastic constants and, for anisotropic materials, also on the indentation direction, a theoretical model quantifying the indentation modulus from the stiffness tensor of a given material was implemented numerically (Swadener and Pharr, 2001, “Indentation of Elastically Anisotropic Half-Spaces by Cones and Parabolae of Revolution,” Philos. Mag. A, 81(2), pp. 447–466). Nanoindentation was performed on 22 osteons of the distal femoral shaft: A new holding system was designed in order to indent the same osteon in two orthogonal directions. To interpret the experimental results and identify orthotropic elastic constants, an inverse procedure was developed by using a fabric-based elastic model for lamellar bone. The experimental indentation moduli were found to vary with the indentation direction and showed a marked anisotropy. The estimated elastic constants showed different degrees of anisotropy among secondary osteons of the same bone and these degrees of anisotropy were also found to be different than the one of cortical bone at the macroscopic level. Using the log-Euclidean norm, the relative distance between the compliance tensors of the estimated mean osteon and of cortical bone at the macroscopic level was 9.69%: Secondary osteons appeared stiffer in their axial and circumferential material directions, and with a greater bulk modulus than cortical bone, which is attributed to the absence of vascular porosity in osteonal properties. The proposed method is suitable for identification of elastic constants from nanoindentation experiments and could be adapted to other (bio)materials, for which it is possible to describe elastic properties using a fabric-based model.

On the effective anisotropic elastic properties of porous hydroxyapatite, porous collagen, and cortical bone: A homogenization scheme with percolation threshold concept

2018 ◽  
Vol 24 (4) ◽  
pp. 1091-1102 ◽  
Author(s):  
Mai-Ba Vu ◽  
Tuan Nguyen-Sy
Keyword(s):  
Percolation Threshold ◽  
Cortical Bone ◽  
Elastic Properties ◽  
Organic Content ◽  
Homogenization Theory ◽  
High Porosity ◽  
Porous Hydroxyapatite ◽  
Threshold Concept ◽  
Homogenization Scheme ◽  
Anisotropic Elastic

The objective of this study is to model the effective anisotropic elastic properties of porous hydroxyapatite, wet collagen, and cortical bone by an advanced homogenization scheme with a percolation threshold concept. The theoretical basis of the anisotropic homogenization theory is first presented. A homogenization scheme with a percolation threshold concept is then introduced and validated against experimental data for porous hydroxyapatite as well as bone after decollagenization. It is also validated on a porous collagen that is a result of the demineralization of bone. Even though aligned collagen fibers are considered, similar values of the elastic stiffnesses [Formula: see text] and [Formula: see text] were found for demineralized bone due to its very high porosity. Finally the proposed method is used to model cortical bone as a mixture of hydroxyapatite mineral and soft organic content that is in turn a mixture of collagen fiber and pores filled by water. Good agreement between modeled and measured data is observed. The model presented herein is simpler than existing multi-scale homogenization schemes in the literature, but its results fit very well with the experimented trends.

First Principles Study of Electronic and Elastic Properties of AlY

2014 ◽  
Vol 1047 ◽  
pp. 45-50
Author(s):  
Mani Shugani ◽  
Mahendra Aynyas ◽  
S.P. Sanyal
Keyword(s):  
Elastic Properties ◽  
Elastic Constants ◽  
Ground State ◽  
Full Potential ◽  
Augmented Plane Wave ◽  
Plane Wave Method ◽  
Lattice Constants ◽  
Ground State Properties ◽  
Experimental Values ◽  
Good Agreement

We have used full potential linear augmented plane wave method within thegeneralized gradient approximation to investigate the structural, electronic and elastic properties of the AlY. The ground state properties are determined for the AlY. The calculated ground state properties such as lattice constants, bulk modulus and elastic constants agree well with the experimental values. From band structure curves it is found that AlY is metallic in nature. The elastic constants are in good agreement with previous theoretical and experimental results.

Prediction of Cortical Bone Elastic Constants by a Two-Level Micromechanical Model Using a Generalized Self-Consistent Method

2005 ◽  
Vol 128 (3) ◽  
pp. 309-316 ◽  
Author(s):  
X. Neil Dong ◽  
X. Edward Guo
Keyword(s):  
Experimental Data ◽  
Cortical Bone ◽  
Elastic Constants ◽  
Micromechanical Model ◽  
Transversely Isotropic ◽  
Two Phase ◽  
Self Consistent ◽  
Isotropic Elasticity ◽  
Consistent Method ◽  
Haversian Canals

A two-level micromechanical model of cortical bone based on a generalized self-consistent method was developed to take into consideration the transversely isotropic elasticity of many microstructural features in cortical bone, including Haversian canals, resorption cavities, and osteonal and interstitial lamellae. In the first level, a single osteon was modeled as a two-phase composite such that Haversian canals were represented by elongated pores while the surrounding osteonal lamellae were considered as matrix. In the second level, osteons and resorption cavities were modeled as multiple inclusions while interstitial lamellae were regarded as matrix. The predictions of cortical bone elasticity from this two-level micromechanical model were mostly in agreement with experimental data for the dependence of transversely isotropic elasticity of human femoral cortical bone on porosity. However, variation in cortical bone elastic constants was greater in experimental data than in model predictions. This could be attributed to variations in the elastic properties of microstructural features in cortical bone. The present micromechanical model of cortical bone will be useful in understanding the contribution of cortical bone porosity to femoral neck fractures.

scholarly journals Anisotropic elastic properties of human femoral cortical bone and relationships with composition and microstructure in elderly

2019 ◽  
Vol 90 ◽  
pp. 254-266 ◽  
Author(s):  
Xiran Cai ◽  
Hélène Follet ◽  
Laura Peralta ◽  
Marc Gardegaront ◽  
Delphine Farlay ◽  
...  
Keyword(s):  
Cortical Bone ◽  
Elastic Properties ◽  
Anisotropic Elastic

Brillouin Light Scattering Investigation of the Elastic Properties of Ta/Al Metallic Superlattices

1994 ◽  
Vol 356 ◽  
Author(s):  
G. Carlotti ◽  
D. Fioretto ◽  
G. Socino ◽  
Hua Xia ◽  
An Hu ◽  
...  
Keyword(s):  
Light Scattering ◽  
Elastic Properties ◽  
Elastic Constants ◽  
Anomalous Behavior ◽  
Brillouin Light Scattering ◽  
Si Substrates ◽  
Phase Velocities ◽  
Frequency Position ◽  
Light Scattering Technique ◽  
Good Agreement

AbstractThe Brillouin light scattering technique has been exploited for investigating the elastic properties of periodic superlattices made by alternating layers of Ta and Al. These multilayers, deposited by d.c. sputtering on glass and Si substrates, present a polycrystalline structure with (110) and (111) texture for the Ta and Al layers, respectively. They have total thicknesses of about 0.5 μm and periods ranging from 4 to 10 nm. Measurement of the phase velocities of the Rayleigh and Sezawa acoustic modes from the frequency position of the corresponding Brillouin peaks, yielded informaton on the effective elastic constants of the superlattices. for large periods (8-10 nm) the values determined experimentally are in good agreement with those calculated from the elastic constants of the bulk materials, while for lower periods (4-6 nm) the estimated elastic constants exhibit a marked increase. This anomalous behavior has been attributed to the presence of a transition layer at each interface, where Ta and Al interdiffuse, as observed by x-ray and electron microscopy experiments.

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