Comparison of constitutive models of arterial layers with distributed collagen fibre orientations

Several constitutive models have been proposed for description of mechanical behaviour of soft tissues containing collagen fibres. The model with aligned fibres is modified in this paper to take the dispersion of fibre orientations into account through angular integration and it is compared with the model that is defined through generalized structure tensor. The paper is focused on the effect of fibre dispersion on the resulting stress-strain behaviour predicted by both models analyzed. Analytical calculations are used for the comparison of the mechanical behaviour under a specific biaxial tension mode. The two models have been implemented into commercial finite element code ANSYS via user subroutines and used for numerical simulation resulting in a non-homogeneous stress field. The effects of the fibre dispersion predicted by both models being compared differ significantly, e.g., the resulting stress difference between both models is lower than 10% only in the case of extremely small dispersion of collagen fibres orientation (κ< (0.01 to 0.03)). These results are consistent with those of other related literature. The applicability of the model defined through the generalized structure tensor is discussed.