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Technical Brief

Studies on the Stress-Strain Relationship Bovine Cortical Bone Based on Ramberg–Osgood Equation

[+] Author and Article Information
N. K. Sharma

Department of Mechanical Engineering,
University of Saskatchewan,
Saskatoon, SK S7N5A9, Canada
e-mail: enksharma@yahoo.com

M. D. Sarker

Division of Biomedical Engineering,
University of Saskatchewan,
Saskatoon, SK S7N5A9, Canada
e-mail: mas921@mail.usask.ca

Saman Naghieh

Division of Biomedical Engineering,
University of Saskatchewan,
Saskatoon, SK S7N5A9, Canada
e-mail: san908@mail.usask.ca

Daniel X. B. Chen

Department of Mechanical Engineering,
University of Saskatchewan,
Saskatoon, SK S7N5A9, Canada;
Division of Biomedical Engineering,
University of Saskatchewan,
Saskatoon, SK S7N5A9, Canada
e-mail: xbc719@mail.usask.ca

1Corresponding author.

Manuscript received July 3, 2018; final manuscript received February 6, 2019; published online March 5, 2019. Assoc. Editor: Christian Puttlitz.

J Biomech Eng 141(4), 044507 (Mar 05, 2019) (5 pages) Paper No: BIO-18-1310; doi: 10.1115/1.4042901 History: Received July 03, 2018; Revised February 06, 2019

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).

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Figures

Grahic Jump Location
Fig. 1

Schematic diagram showing (a) whole bovine femur bone, (b) bone diaphysis obtained after removing the epiphyses ends of the femur and further division of diaphysis into three equal parts namely upper, middle and lower diaphysis, (c) division of each diaphysis part into four sections to obtain samples from each anatomic quadrant location, and (d) orientation of longitudinal and transverse specimens prepared for tensile test

Grahic Jump Location
Fig. 2

Longitudinal stress–strain curves for different locations of bone diaphysis

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Fig. 3

Transverse stress–strain curves for different locations of bone diaphysis

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Fig. 4

Longitudinal true stress–plastic strain curves for different locations of bone diaphysis

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Fig. 5

Transverse true stress–plastic strain curves for different locations of bone diaphysis

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Fig. 6

Linear fit of log (true plastic strain) versus log (true stress) curves for different locations of bone diaphysis in case of longitudinal direction of loading

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Fig. 7

Linear fit of log (true plastic strain) versus log (true stress) curves for different locations of bone diaphysis in case of transverse direction of loading

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