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Research Papers

Non-Linear Model for Compression Tests on Articular Cartilage

[+] Author and Article Information
Alfio Grillo

Department of Mathematical Sciences
“G.L. Lagrange,”
Politecnico di Torino,
Corso Duca degli Abruzzi 24,
Torino 10124, Italy
e-mail: alfio.grillo@polito.it

Amr Guaily

Engineering Mathematics
and Physics Department,
Cairo University,
Cairo University Road, Giza 12613, Egypt
e-mail: a.guaily@eng.cu.edu.eg

Chiara Giverso

MOX - Department of Mathematics,
Politecnico di Milano and Fondazione CEN,
P.za Leonardo da Vinci, 32,
Milan 20133, Italy
e-mail: chiara.giverso@polimi.it

Salvatore Federico

Department of Mechanical
and Manufacturing Engineering,
The University of Calgary,
2500 University Drive NW,
Calgary, AB T2N1N4, Canada
e-mail: salvatore.federico@ucalgary.ca

1Corresponding author.

Manuscript received December 22, 2014; final manuscript received March 31, 2015; published online June 2, 2015. Assoc. Editor: Pasquale Vena.

J Biomech Eng 137(7), 071004 (Jul 01, 2015) (8 pages) Paper No: BIO-14-1638; doi: 10.1115/1.4030310 History: Received December 22, 2014; Revised March 31, 2015; Online June 02, 2015

Hydrated soft tissues, such as articular cartilage, are often modeled as biphasic systems with individually incompressible solid and fluid phases, and biphasic models are employed to fit experimental data in order to determine the mechanical and hydraulic properties of the tissues. Two of the most common experimental setups are confined and unconfined compression. Analytical solutions exist for the unconfined case with the linear, isotropic, homogeneous model of articular cartilage, and for the confined case with the non-linear, isotropic, homogeneous model. The aim of this contribution is to provide an easily implementable numerical tool to determine a solution to the governing differential equations of (homogeneous and isotropic) unconfined and (inhomogeneous and isotropic) confined compression under large deformations. The large-deformation governing equations are reduced to equivalent diffusive equations, which are then solved by means of finite difference (FD) methods. The solution strategy proposed here could be used to generate benchmark tests for validating complex user-defined material models within finite element (FE) implementations, and for determining the tissue's mechanical and hydraulic properties from experimental data.

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References

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Figures

Grahic Jump Location
Fig. 1

Volume ratio J versus the normalized radial coordinate R/Rext. The curves are plotted for values of the normalized time t/tu = 0, 1, . . . ,10.

Grahic Jump Location
Fig. 2

Radial component PcrR of the constitutive part of the first Piola–Kirchhoff stress tensor of the solid phase, normalized to the material parameter α0, versus the normalized radial coordinate R/Rext. The curves are plotted for values of the normalized time t/tu = 0, 1, . . . ,10.

Grahic Jump Location
Fig. 3

Volume ratio J versus the normalized axial coordinate Z/H. The curves are plotted for values of the normalized time t/tu = 0, 1, . . . ,10.

Grahic Jump Location
Fig. 4

Axial component PczZ of the constitutive part of the first Piola–Kirchhoff stress tensor of the solid phase, normalized to the value α0(0) of the material parameter α0 at Z = 0, versus the normalized axial coordinate Z/H. The curves are plotted for values of the normalized time t/tu = 0, 1, . . . ,10.

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