A new strain energy function for modelling ligaments and tendons whose fascicles have a helical arrangement of fibrils

TL;DR

This paper introduces a new strain energy function for modeling ligaments and tendons with helical fibril arrangements, accurately fitting experimental data and revealing how fibril structure influences mechanical behavior.

Contribution

A novel constitutive law for hyperelastic modeling of helical fascicle arrangements in ligaments and tendons, validated against experimental data and used to analyze structural effects.

Findings

The model fits human patellar tendon data with 9.8% average error.

Shear stresses are much lower than uniaxial stresses at the same strain.

Fibril and fascicle helix angles significantly influence tendon stiffness.

Abstract

A new strain energy function for the hyperelastic modelling of ligaments and tendons whose fascicles have a helical arrangement of fibrils is derived. The stress-strain response of a single fascicle whose fibrils exhibit varying levels of crimp throughout its radius is calculated and used to determine the form of the strain energy function. The new constitutive law is used to model uniaxial extension test data for human patellar tendon and is shown to provide an excellent fit, with the average relative error being 9.8%. It is then used to model shear and predicts that the stresses required to shear a tendon are much smaller than those required to uniaxially stretch it to the same strain level. Finally, the strain energy function is used to model ligaments and tendons whose fascicles are helical, and the relative effects of the fibril helix angle, the fascicle helix angle and the fibril crimp variable are compared. It is shown that they all have a significant effect; the fibril crimp variable governs the non-linearity of the stress-strain curve, whereas the helix angles primarily affect its stiffness. Smaller values of the helix angles lead to stiffer tendons; therefore, the model predicts that one would expect to see fewer helical sub-structures in stiff positional tendons, and more in those that are required to be more flexible.