A new strain energy function for the hyperelastic modelling of ligaments and tendons based on fascicle microstructure

TL;DR

This paper introduces a novel strain energy function for hyperelastic modeling of ligaments and tendons based on fibril microstructure, providing a more accurate fit to experimental data than existing models.

Contribution

The paper develops a new strain energy function derived from fibril crimp angle distributions, with parameters directly measurable through experiments, improving modeling accuracy.

Findings

The new model better fits human patellar tendon stress-strain data.

Average relative error with the new model is 0.053, significantly lower than 0.57 with HGO.

Average absolute error with the new model is 0.12 MPa, compared to 0.31 MPa for HGO.

Abstract

A new strain energy function for the hyperelastic modelling of ligaments and tendons based on the geometrical arrangement of their fibrils is derived. The distribution of the crimp angles of the fibrils is used to determine the stress-strain response of a single fascicle, and this stress-strain response is used to determine the form of the strain energy function, the parameters of which can all potentially be directly measured via experiments - unlike those of commonly used strain energy functions such as the Holzapfel-Gasser-Ogden (HGO) model, whose parameters are phenomenological. We compare the new model with the HGO model and show that the new model gives a better match to existing stress-strain data for human patellar tendon than the HGO model, with the average relative error in matching this data when using the new model being 0.053 (compared with 0.57 when using the HGO model), and the average absolute error when using the new model being 0.12 MPa (compared with 0.31 MPa when using the HGO model).