TY - JOUR
T1 - A model for the anisotropic response of fibrous soft tissues using six discrete fibre bundles
AU - Flynn, Cormac
AU - Rubin, M. B.
AU - Nielsen, Poul
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This work was in part supported by the New Zealand Foundation for Research, Science and Technology, through grants NERF 139400 and NERF 9077/3608892. This publication is also based on work supported in part by Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2011/6/30
Y1 - 2011/6/30
N2 - The development of constitutive models of fibrous soft-tissues is a challenging problem. Many consider the tissue to be a collection of fibres with a continuous distribution function representing their orientations. A discrete fibre model is presented consisting of six weighted fibre-bundles. Each bundle is oriented such that it passes through opposing vertices of a regular icosahedron. A novel aspect is the use of simple analytical distribution functions to simulate undulated collagen fibres. This approach yields closed-form analytical expressions for the strain energy of the collagen fibre-bundle that avoids the sometimes costly numerical integration of some statistical distribution functions. The elastin fibres are characterized by a modified neo-Hookean type strain energy function which does not allow for fibre compression. The model accurately simulates biaxial stretching of rabbit-skin (error-of-fit 8.7), uniaxial stretching of pig-skin (error-of-fit 7.6), equibiaxial loading of aortic valve cusp (error-of-fit 0.8), and simple shear of rat septal myocardium (error-of-fit 8.9). It compares favourably with previous soft-tissue models and alternative methods of representing undulated collagen fibres. Predicted collagen fibre stiffnesses range from 8.0thinspaceMPa to 930MPa. Elastin fibre stiffnesses range from 2.0 kPa to 154.4 kPa. © 2011 John Wiley & Sons, Ltd.
AB - The development of constitutive models of fibrous soft-tissues is a challenging problem. Many consider the tissue to be a collection of fibres with a continuous distribution function representing their orientations. A discrete fibre model is presented consisting of six weighted fibre-bundles. Each bundle is oriented such that it passes through opposing vertices of a regular icosahedron. A novel aspect is the use of simple analytical distribution functions to simulate undulated collagen fibres. This approach yields closed-form analytical expressions for the strain energy of the collagen fibre-bundle that avoids the sometimes costly numerical integration of some statistical distribution functions. The elastin fibres are characterized by a modified neo-Hookean type strain energy function which does not allow for fibre compression. The model accurately simulates biaxial stretching of rabbit-skin (error-of-fit 8.7), uniaxial stretching of pig-skin (error-of-fit 7.6), equibiaxial loading of aortic valve cusp (error-of-fit 0.8), and simple shear of rat septal myocardium (error-of-fit 8.9). It compares favourably with previous soft-tissue models and alternative methods of representing undulated collagen fibres. Predicted collagen fibre stiffnesses range from 8.0thinspaceMPa to 930MPa. Elastin fibre stiffnesses range from 2.0 kPa to 154.4 kPa. © 2011 John Wiley & Sons, Ltd.
UR - http://hdl.handle.net/10754/597310
UR - http://doi.wiley.com/10.1002/cnm.1440
UR - http://www.scopus.com/inward/record.url?scp=80054981305&partnerID=8YFLogxK
U2 - 10.1002/cnm.1440
DO - 10.1002/cnm.1440
M3 - Article
VL - 27
SP - 1793
EP - 1811
JO - International Journal for Numerical Methods in Biomedical Engineering
JF - International Journal for Numerical Methods in Biomedical Engineering
SN - 2040-7939
IS - 11
ER -