A model for the anisotropic response of fibrous soft tissues using six discrete fibre bundles

Abstract

Abstract 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 930 MPa. Elastin fibre stiffnesses range from 2.0 kPa to 154.4 kPa. Copyright © 2011 John Wiley & Sons, Ltd.