Fiber distributed hyperelastic modeling of biological tissues

In view of a more realistic description of the spatial distribution of the collagen fibers in soft biological tissues, for example the human cornea, we propose a material model alternative to the one based on generalized structure tensors, proposed by Gasser et al. (2006). We assume that the strain energy function depends on the mean value and on the variance of the pseudo-invariant I4 of the distribution of the fibers. Indeed, the mean value was the only term considered in the original generalized structure tensor model. We derive the expression of the stress and of the consistent tangent stiffness of the new model and compare its mechanical response with the one of the original model for standard uniaxial, shear and biaxial tests. The comparisons are made with reference to the response of the exact fiber dispersed model, based on the direct integration of the contribution of the fibers