Technical Briefs

The Influence of Fiber Orientation on the Equilibrium Properties of Neutral and Charged Biphasic Tissues

[+] Author and Article Information
Thomas Nagel, Daniel J. Kelly

Trinity Centre for Bioengineering, Mechanical and Manufacturing Engineering, School of Engineering, Trinity College, Dublin 2, Ireland

At small strains the compressive modulus K relates the volumetric strain e=trϵ to the hydrostatic pressure p=1/3trσ: p=Ke.

J Biomech Eng 132(11), 114506 (Oct 27, 2010) (7 pages) doi:10.1115/1.4002589 History: Received May 11, 2010; Revised September 13, 2010; Posted September 21, 2010; Published October 27, 2010; Online October 27, 2010

Constitutive models facilitate investigation into load bearing mechanisms of biological tissues and may aid attempts to engineer tissue replacements. In soft tissue models, a commonly made assumption is that collagen fibers can only bear tensile loads. Previous computational studies have demonstrated that radially aligned fibers stiffen a material in unconfined compression most by limiting lateral expansion while vertically aligned fibers buckle under the compressive loads. In this short communication, we show that in conjunction with swelling, these intuitive statements can be violated at small strains. Under such conditions, a tissue with fibers aligned parallel to the direction of load initially provides the greatest resistance to compression. The results are further put into the context of a Benninghoff architecture for articular cartilage. The predictions of this computational study demonstrate the effects of varying fiber orientations and an initial tare strain on the apparent material parameters obtained from unconfined compression tests of charged tissues.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

Fiber angle throughout the depth of the tissue defining the Benninghoff architecture (Eq. 12)

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Figure 2

(a) Axial Cauchy stress with respect to actual or reference strain. (b) Axial Cauchy stress with respect to applied or apparent strain (relative to FS configuration).

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Figure 3

Sample geometry in the FS state: height (h), radius (r). and volume (V). “Benn.” stands for Benninghoff architecture. Isotropic means no fiber architecture.

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Figure 4

Axial Cauchy stress σzz over axial strain ϵzzFS for (a) uncharged and (b) charged materials. In the case of the Benninghoff architecture (“Benn.”), ϵzzFS=0 represents the point where full contact with the loading platen is established. The average total stress value is therefore not zero.

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Figure 5

(a) Swelling pressure Δπ over axial strain ϵzzFS (5a). (b) Matrix stress σ33E=σ33+Δπ over axial strain ϵzzFS. “Benn.” stands for Benninghoff architecture.

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Figure 6

Apparent Poisson’s ratio ν over axial strain ϵzzFS for (a) uncharged and (b) charged materials. “Benn.” stands for Benninghoff architecture.

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Figure 7

Nominal Young’s modulus Enom over axial strain ϵzzFS for (a) uncharged and (b) charged materials. (c) Incremental Young’s modulus Einc over axial strain ϵzzFS for the charged tissue. “Benn.” stands for Benninghoff architecture.

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Figure 8

Nominal Young’s modulus after including an offset strain Etare over axial strain ϵzzFS for the charged material. “Benn.” stands for Benninghoff architecture.



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