A stochastic model of stroma: interweaving variability and compressed fibril exclusion

Abstract

Hyperelastic constitutive models of the human stroma accounting for the stochastic architecture of the collagen fibrils and particularly suitable for computational applications are discussed. The material is conceived as a composite where a soft ground matrix is embedded with collagen fibrils characterized by non-homogeneous spatial distributions typical of reinforcing stromal lamellae. A multivariate probability density function of the spatial distribution of the fibril orientation is used in the formulation of the lamellar branching observed on the anterior third of the stroma, selectively excluding the contribution of compressed fibrils. The physical reliability and the computational robustness of the model are enhanced by the adoption of a second order statistics approximation of the average structure tensors typically employed in fiber reinforced models.