Modeling the tensile behavior of human Achilles tendon

Uniaxial quasi-static tensile stress, σ, versus strain, ε, data were obtained from 29 cadaveric Achilles tendons (donor ages: 36 to 100 years), at a strain rate of either 10 or 100%/s. These results were then used in modeling the elastic component of the tensile deformational behavior of this tissue. Two approaches were taken. In the first, it was shown that the following constitutive relation provided an excellent fit to the elastic section of the σ−ε curve,

σ=Cεexp[Dε+Fε²],

with C, D and F being material constants, whose values for the present dataset were found to be C = 2.00 ± 0.99, D = 0.089 ± 0.087 and F = −0.0047 ± 0.0095. The values of these coefficients were not statistically significantly affected by either donor age or test strain rate.

In the second approach, the value of the modulus of elasticity of a filamentary polymer matrix composite material was computed as a function of various combinations of values of the modulus of elasticity of the fiber, the modulus of elasticity of the matrix, and angle of orientation of the principal material axes with respect to the reference coordinate axes (θ) for a fiber volume fraction of 0.6 and a material Poisson's ratio of 0.4. By comparing these results with the experimentally-obtained values of the tangent modulus of elasticity of the tendons (defined as the slope of the linear section of the post-toe zone in the σ−ε plot), and assuming that the tendon may be idealized as a filamentary polymer matrix composite material, the suggestion is made that the winding angle of the fibers (collagen fibrils) in the tendon (taken to be equal to θ) is about 6°.