Micromechanical models of helical superstructures in ligament and tendon fibers predict large Poisson's ratios

Abstract

Experimental measurements of the Poisson's ratio in tendon and ligament tissue greatly exceed the isotropic limit of 0.5. This is indicative of volume loss during tensile loading. The microstructural origin of the large Poisson's ratios is unknown. It was hypothesized that a helical organization of fibrils within a fiber would result in a large Poisson's ratio in ligaments and tendons, and that this helical organization would be compatible with the crimped nature of these tissues, thus modeling their classic nonlinear stress strain behavior. Micromechanical finite element models were constructed to represent crimped fibers with a super helical organization, composed of fibrils embedded within a matrix material. A homogenization procedure was performed to determine both the effective Poisson's ratio and the Poisson function. The results showed that helical fibril organization within a crimped fiber was capable of simultaneously predicting large Poisson's ratios and the nonlinear stress strain behavior seen experimentally. Parametric studies revealed that the predicted Poisson's ratio was strongly dependent on the helical pitch, crimp angle and the material coefficients. The results indicated that, for physiologically relevant parameters, the models were capable of predicting the large Poisson's ratios seen experimentally. It was concluded that helical organization within a crimped fiber can produce both the characteristic nonlinear stress strain behavior and large Poisson's ratios, while fiber crimp alone could only account for the nonlinear stress-strain behavior.

Fascicles from energy-storing tendons show an age-specific response to cyclic fatigue loading

“…In this study, we observed a significant decrease in rotation after FL in samples from young horses, suggesting that FL causes alterations to the helix structure. This is somewhat supported by the trend for decreased Poisson's ratios observed in samples from young horses; while the large Poisson's ratios observed may be owing to exudation of fluid from the fascicles [17], finite-element modelling has shown that the presence of helical substructures within tendon predicts large Poisson's ratios [45]. While the specific alterations that occur to the helix during FL are as yet unknown, it is possible that some of the characteristic sample lengthening observed during creep may occur as a result of straightening of the coil of the helix, such that helix pitch angle decreases.…”

Poisson's ratio of collagen fibrils measured by small angle X-ray scattering of strained bovine pericardium

“…For collagen in bovine pericardium, at low strain, the Poisson's ratio appears to have a very high value (15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27), but for strain above 0.09, the Poisson's ratio is in the range 2.1-2.8. For the total strain (from 0 to 0.25), the change in d-spacing and diameter gives 0 ¼ 2.1 6 0.7 (these values of 0 can be calculated from Fig.…”

“…15,16 Modeling of the crimp present in many collagen tissues, such a tendon and ligament or helical structure of the fibrils, has suggested that these features could explain much of the high Poisson's ratio of the tissue composed of collagen. 17 It has also been suggested that in tendon, the strain may be taken up by sliding of fibrils within the tendon rather than by extension of the collagen fibrils. 18 In leather, where there is very little crimp, the reorientation of fibrils may be an important mechanism for absorbing strain.…”

Tendon Fascicles Exhibit a Linear Correlation Between Poisson's Ratio and Force During Uniaxial Stress Relaxation

“…This suggests the presence of a helical organization within the fascicle. Micromechanical models of helical structures within tendon and ligament suggest the presence of helical twisting, which may be responsible for the large experimentally observed Poisson's ratios [33]. Evidence for helical organization has been reported in histological studies on tendon and ligament [34][35][36][37].…”