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

Shearer, Tom (2014) A new strain energy function for the hyperelastic modelling of ligaments and tendons based on fascicle microstructure. Journal of Biomechanics, 48. pp. 290-297. ISSN 0021-9290

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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 0.12MPa (compared with 0.31MPa when using the HGO model).

Item Type: Article
Uncontrolled Keywords: Ligaments; Tendons; Strain energy function; Microstructure; Crimp angle distribution
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 74 Mechanics of deformable solids
MSC 2010, the AMS's Mathematics Subject Classification > 92 Biology and other natural sciences
PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 40 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID MECHANICS > 46 Continuum mechanics of solids
Depositing User: Dr Tom Shearer
Date Deposited: 02 Oct 2015
Last Modified: 20 Oct 2017 14:13
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2394

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