An anisotropic discrete fibre model based on a generalised strain invariant with application to soft biological tissues

This paper presents a discrete fibre model for soft biological tissues, which is based on a generalised strain invariant. Non-linear strain energy functions of this generalised invariant model the non-linear response of the soft tissue. Six fibre bundles are orientated such that they pass through opposing vertices of a regular icosahedron. The fibre bundles are weighted in order to characterise the anisotropic nature inherent in most soft tissues. A significant advantage of the generalised strain approach is that the fibre bundle weights are pure measures of the anisotropy of the simulated soft tissue. It is shown that the weights can be used to define an approximate continuous orientation distribution function of the fibres within the tissue. The proposed model accurately simulated uniaxial tensile loading of pig skin (Error 16.6%), biaxial stretching of rabbit skin (Error 12.0%), simple shear of septal myocardium (Error 13.4%), and the equibiaxial loading of fresh and fixed aortic valve cusps (Error 1.9% and 0.9%, respectively). The predicted fibre orientations are in general agreement with measurements in the literature.