Research Papers

Viscoelasticity of Tendons Under Transverse Compression

[+] Author and Article Information
C. Paul Buckley

Department of Engineering Science,
University of Oxford,
Parks Road,
Oxford OX1 3PJ, UK
e-mail: paul.buckley@eng.ox.ac.uk

S. T. Samuel Salisbury

Department of Engineering Science,
University of Oxford,
Parks Road,
Oxford OX1 3PJ, UK
e-mail: sam.salisbury@oxon.org

Amy B. Zavatsky

Department of Engineering Science,
University of Oxford,
Parks Road,
Oxford OX1 3PJ, UK
e-mail: amy.zavatsky@eng.ox.ac.uk

1Corresponding author.

Manuscript received March 3, 2016; final manuscript received July 26, 2016; published online August 18, 2016. Assoc. Editor: James C. Iatridis.

J Biomech Eng 138(10), 101004 (Aug 18, 2016) (8 pages) Paper No: BIO-16-1082; doi: 10.1115/1.4034382 History: Received March 03, 2016; Revised July 26, 2016

Tendons are highly anisotropic and also viscoelastic. For understanding and modeling their 3D deformation, information is needed on their viscoelastic response under off-axis loading. A study was made, therefore, of creep and recovery of bovine digital extensor tendons when subjected to transverse compressive stress of up to ca. 100 kPa. Preconditioned tendons were compression tested between glass plates at increasing creep loads. The creep response was anomalous: the relative rate of creep reduced with the increasing stress. Over each ca. 100 s creep period, the transverse creep deformation of each tendon obeyed a power law dependence on time, with the power law exponent falling from ca. 0.18 to an asymptote of ca. 0.058 with the increasing stress. A possible explanation is stress-driven dehydration, as suggested previously for the similar anomalous behavior of ligaments. Recovery after removal of each creep load was also anomalous. Relative residual strain reduced with the increasing creep stress, but this is explicable in terms of the reducing relative rate of creep. When allowance was made for some adhesion occurring naturally between tendon and the glass plates, the results for a given load were consistent with creep and recovery being related through the Boltzmann superposition principle (BSP). The tendon tissue acted as a pressure-sensitive adhesive (PSA) in contact with the glass plates: explicable in terms of the low transverse shear modulus of the tendons.

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Grahic Jump Location
Fig. 3

A double logarithmic plot of creep data (for clarity, only 1 in 200 of the data points are shown) for the same ten tests as shown in Fig. 2. The lines through the data points are linear regressions, over creep times 10 s–100 s.

Grahic Jump Location
Fig. 2

An example set of creep and recovery data for one of the tendons. Displacements are represented as the averaged strain 〈ε2〉y. Magnitudes of the corresponding applied creep stresses 〈σ2〉xc are as shown (in kPa).

Grahic Jump Location
Fig. 1

The representative race-track cross section shape, shown by Salisbury et al. [20] to approximate the shape of tendons after preconditioning in transverse compression. Along the axes of mirror symmetry AB and CD, principal axes 1, 2, and 3 are colinear with co-ordinate axes Ox, Oy, and Oz. The compression plates are shown hatched.

Grahic Jump Location
Fig. 4

Values of the coefficient A in the power law expression for the averaged strain during creep (Eq. (3)), fitted to all creep curves (from 10 s to 100 s) for all seven tendons, plotted versus the magnitude of the applied creep stress: −〈σ2〉xc. Each symbol refers to a different tendon.

Grahic Jump Location
Fig. 5

Values of the exponent n in the power law expression for the averaged strain during creep (Eq. (3)), fitted to all creep curves (from 10 s to 100 s) for all seven tendons, plotted versus the magnitude of the applied creep stress: −〈σ2〉xc. Symbols refer to the same tendons as in Fig. 4. Also shown (line) is an empirical curve least-squares fitted to the data points (Eq. (4)).

Grahic Jump Location
Fig. 7

Typical plots of the magnitude of tack stress −〈σ1〉xc versus the magnitude of applied creep stress −〈σ2〉xc, for four tendons (symbols, referring to the same tendons as in Figs. 46), as deduced from the residual strains remaining at a recovery time = 5tu. Also shown (lines) are linear regressions through each set of points.

Grahic Jump Location
Fig. 8

Typical plots of residual strain versus recovery time, for four magnitudes of applied creep stress shown (in kPa), for the tendon in Figs. 2 and 3. Also shown (lines) are the corresponding displacements calculated from Eq. (A3).

Grahic Jump Location
Fig. 6

The relative residual strain remaining after a recovery time of 5tu, following creep tests of duration tu ≈ 120 s, for all ten tests on each of the seven tendons, plotted versus the magnitude of the applied creep stress: −〈σ2〉xc. Symbols refer to the same tendons as in Figs. 4 and 5.



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