Bone is a complex material that exhibits an amount of plasticity before bone fracture takes place, where the nonlinear relationship between stress and strain is of importance to understand the mechanism behind the fracture. This brief presents our study on the examination of the stress–strain relationship of bovine femoral cortical bone and the relationship representation by employing the Ramberg–Osgood (R–O) equation. Samples were taken and prepared from different locations (upper, middle, and lower) of bone diaphysis and were then subjected to the uniaxial tensile tests under longitudinal and transverse loading conditions, respectively. The stress–strain curves obtained from tests were analyzed via linear regression analysis based on the R–O equation. Our results illustrated that the R–O equation is appropriate to describe the nonlinear stress–strain behavior of cortical bone, while the values of equation parameters vary with the sample locations (upper, middle, and lower) and loading conditions (longitudinal and transverse).

References

References
1.
Morgan
,
E. F.
,
Unnikrisnan
,
G. U.
, and
Hussein
,
A. I.
,
2018
, “
Bone Mechanical Properties in Healthy and Diseased States
,”
Annu. Rev. Biomed. Eng.
,
20
, pp.
119
143
.
2.
Chen
,
D. X. B.
,
2019
,
Extrusion Bio-Printing of Scaffolds for Tissue Engineering Applications
, Springer, Cham, Switzerland.
3.
Naghieh
,
S.
, and
Chen
,
X. B.
,
2019
, “
Scaffold Design
,”
Extrusion Bioprinting of Scaffolds for Tissue Engineering Applications
,
Springer International Publishing
,
Basel, Switzerland
.
4.
Naghieh
,
S.
,
Ravari
,
M. R. K.
,
Badrossamay
,
M.
,
Foroozmehr
,
E.
, and
Kadkhodaei
,
M.
,
2015
, “
Finite Element Analysis for Predicting the Mechanical Properties of Bone Scaffolds Fabricated by Fused Deposition Modeling (FDM)
,”
Advanced Machining and Machine Tools Conference
, Tehran, Iran, Nov. 4–5, pp.
450
454
.
5.
Sarker
,
M. D.
,
Naghieh
,
S.
,
Mcinnes
,
A. D.
,
Schreyer
,
D. J.
, and
Chen
,
X.
,
2018
, “
Strategic Design and Fabrication of Nerve Guidance Conduits for Peripheral Nerve Regeneration
,”
Biotechnol. J.
,
13
(
7
), p.
1700635
.
6.
Naghieh
,
S.
,
Sarker
,
M.
,
Izadifar
,
M.
, and
Chen
,
X.
,
2018
, “
Dispensing-Based Bioprinting of Mechanically-Functional Hybrid Scaffolds With Vessel-Like Channels for Tissue Engineering Applications—A Brief Review
,”
J. Mech. Behav. Biomed. Mater.
,
78
, pp.
298
314
.
7.
Sarker
,
M.
,
Naghieh
,
S.
,
McInnes
,
A. D.
,
Schreyer
,
D. J.
, and
Xiongbiao
,
C.
,
2018
, “
Regeneration of Peripheral Nerves by Nerve Guidance Conduits: Influence of Design, Biopolymers, Cells, Growth Factors, and Physical Stimuli
,”
Prog. Neurobiol.
,
171
, pp.
125
150
.
8.
Naghieh
,
S.
,
Karamooz-Ravari
,
M. R.
,
Sarker
,
M.
,
Karki
,
E.
, and
Chen
,
X.
,
2018
, “
Influence of Crosslinking on the Mechanical Behavior of 3D Printed Alginate Scaffolds: Experimental and Numerical Approaches
,”
J. Mech. Behav. Biomed. Mater.
,
80
, pp.
111
118
.
9.
Naghieh
,
S.
,
Sarker
,
M.
,
Karamooz-Ravari
,
M.
,
McInnes
,
A.
,
Chen
,
X.
,
Naghieh
,
S.
,
Sarker
,
M. D.
,
Karamooz-Ravari
,
M. R.
,
McInnes
,
A. D.
, and
Chen
,
X.
,
2018
, “
Modeling of the Mechanical Behavior of 3D Bioplotted Scaffolds Considering the Penetration in Interlocked Strands
,”
Appl. Sci.
,
8
(
9
), p.
1422
.
10.
Sarker
,
M. D.
,
Naghieh
,
S.
,
Sharma
,
N. K.
, and
Chen
,
X.
,
2018
, “
3D Biofabrication of Vascular Networks for Tissue Regeneration: A Report on Recent Advances
,”
J. Pharm. Anal.
,
8
(
5
), pp.
277
296
.
11.
Sarker
,
M.
,
Chen
,
X. B.
, and
Schreyer
,
D. J.
,
2015
, “
Experimental Approaches to Vascularisation Within Tissue Engineering Constructs
,”
J. Biomater. Sci. Polym. Ed.
,
26
(
12
), pp.
683
734
.
12.
Sarker
,
M.
, and
Chen
,
X. B.
,
2017
, “
Modeling the Flow Behavior and Flow Rate of Medium Viscosity Alginate for Scaffold Fabrication With a Three-Dimensional Bioplotter
,”
ASME J. Manuf. Sci. Eng.
,
139
(
8
), p.
081002
.
13.
Ariful Islam Sarker
,
M.
,
Izadifar
,
M.
,
Schreyer
,
D.
, and
Chen
,
X.
,
2018
, “
Influence of Ionic Cross Linkers (Ca2+/Ba2+/Zn2+) on the Mechanical and Biological Properties of 3D Bioplotted Hydrogel Scaffolds
,”
J. Biomater. Sci. Polym. Ed.
,
29
(
10
), pp.
1126
1154
.
14.
Iyo
,
T.
,
Maki
,
Y.
,
Sasaki
,
N.
, and
Nakata
,
M.
,
2004
, “
Anisotropic Viscoelastic Properties of Cortical Bone
,”
J. Biomech.
,
37
(
9
), pp.
1433
1437
.
15.
Naghieh
,
S.
,
Badrossamay
,
M.
,
Foroozmehr
,
E.
, and
Kharaziha
,
M.
,
2017
, “
Combination of PLA Micro-Fibers and PCL-Gelatin Nano-Fibers for Development of Bone Tissue Engineering Scaffolds
,”
Int. J. Swarm Intell. Evol. Comput.
,
6
(
1
), pp.
1
4
.
16.
Naghieh
,
S.
,
Foroozmehr
,
E.
,
Badrossamay
,
M.
, and
Kharaziha
,
M.
,
2017
, “
Combinational Processing of 3D Printing and Electrospinning of Hierarchical Poly(Lactic Acid)/Gelatin-Forsterite Scaffolds as a Biocomposite: Mechanical and Biological Assessment
,”
Mater. Des.
,
133
, pp.
128
135
.
17.
Naghieh
,
S.
,
Reihany
,
A.
,
Haghighat
,
A.
,
Foroozmehr
,
E.
,
Badrossamay
,
M.
, and
Forooghi
,
F.
,
2016
, “
Fused Deposition Modeling and Fabrication of a Three-Dimensional Model in Maxillofacial Reconstruction
,”
Regen. Reconstr. Restor.
,
1
(
3
), pp.
139
144
.http://journals.sbmu.ac.ir/tripleR/article/view/12543/10652
18.
Naghieh
,
S.
,
Karamooz Ravari
,
M. R. R.
,
Badrossamay
,
M.
,
Foroozmehr
,
E.
, and
Kadkhodaei
,
M.
,
2016
, “
Numerical Investigation of the Mechanical Properties of the Additive Manufactured Bone Scaffolds Fabricated by FDM: The Effect of Layer Penetration and Post-Heating
,”
J. Mech. Behav. Biomed. Mater.
,
59
, pp.
241
250
.
19.
Yan
,
J.
,
Mecholsky
,
J. J.
, Jr.
, and
Clifton
,
K. B.
,
2007
, “
How Tough is Bone? Application of Elastic–Plastic Fracture Mechanics to Bone
,”
Bone
,
40
(
2
), pp.
479
484
.
20.
Sharma
,
N. K.
,
Pal
,
R.
,
Sehgal
,
D. K.
, and
Pandey
,
R. K.
,
2014
, “
Application of Elastic-Plastic Fracture Mechanics to Determine the Locational Variation in Fracture Properties of Cortical Bone
,”
Mater. Perform. Charact.
,
3
(
3
), pp.
429
447
.
21.
Sharma
,
N. K.
,
Sehgal
,
D. K.
, and
Pandey
,
R. K.
,
2011
, “
Orientation Dependence of Elastic-Plastic Fracture Toughness and Micro-Fracture Mechanism in Cortical Bone
,”
Eng. Lett.
,
19
(
4
), pp. 304–309.https://www.researchgate.net/publication/286569221_Orientation_Dependence_of_Elastic-plastic_Fracture_Toughness_and_Micro-fracture_Mechanism_in_Cortical_Bone
22.
Sharma
,
N. K.
,
Sehgal
,
D. K.
, and
Pandey
,
R. K.
,
2011
, “
Effect of Orientation on Elastic-Plastic Fracture Toughness of Cortical Bone
,”
World Congress on Engineering
, London, July 6–8, pp.
2298
2302
.https://www.researchgate.net/publication/286569077_Effect_of_Orientation_on_Elastic-plastic_Fracture_Toughness_of_Cortical_Bone
23.
Saxena
,
A.
,
1998
,
Nonlinear Fracture Mechanics
, CRC Press, Boca Raton, FL, pp.
1
13
.
24.
Perez
,
N.
,
2004
,
Plastic Fracture Mechanics in: Fracture Mechanics
,
Springer
, Boston, MA, pp.
147
172
.
25.
Ramberg
,
W.
, and
Osgood
,
W. R.
,
1943
, “
Description of Stress-Strain Curves by Three Parameters
,” National Advisory Committee for Aeronautics, Technical Note No.
902
.http://www.apesolutions.com/spd/public/NACA-TN902.pdf
26.
Ritchie
,
R. O.
,
Koester
,
K. J.
,
Ionova
,
S.
,
Yao
,
W.
,
Lane
,
N. E.
, and
Ager
,
J. W.
,
2008
, “
Measurement of the Toughness of Bone: A Tutorial With Special Reference to Small Animal Studies
,”
Bone
,
43
(
5
), pp.
798
812
.
27.
Sharma
,
N. K.
,
Nayak
,
J.
,
Sehgal
,
D. K.
, and
Pandey
,
R. K.
,
2012
, “
Studies on Post-Yield Behavior of Cortical Bone
,”
Appl. Mech. Mater.
,
232
, pp. 157–161.
28.
Broek
,
D.
,
1989
,
The Practical Use of Fracture Mechanics
,
Kluwer Academic Publishers
,
Dordrecht, The Netherlands
, pp.
88
122
.
You do not currently have access to this content.