A model for the anisotropic response of fibrous soft tissues using six discrete fibre bundles
KAUST Grant NumberKUK-C1-013-04
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AbstractThe 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.
CitationFlynn C, Rubin MB, Nielsen P (2011) A model for the anisotropic response of fibrous soft tissues using six discrete fibre bundles. International Journal for Numerical Methods in Biomedical Engineering 27: 1793–1811. Available: http://dx.doi.org/10.1002/cnm.1440.
SponsorsThis 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).