Statistical approach for a continuum description of damage evolution in soft collagenous tissues

We propose a statistical approach to describe microscopic damage evolution in soft collagenous tissues such as arterial walls. The damage model extends a framework published by Balzani et al. (2012), Comput. Methods Appl. Mech. Engrg., 213-216:139-151, by postulating specific damage functions that result from the fibers' microstructure. Statistical distributions of three different microscopic quantities such as proteoglycan orientation, fibril length parameters and ultimate proteoglycan stretch are considered. The resulting stress-stretch response is compared with experimental data obtained from uniaxial tension tests given in the literature. In particular, the individual statistical distributions are analyzed in regard to their ability to capture the distinct softening hysteresis observed when subjecting soft tissues to cyclic loading in the supra-physiological domain. Details regarding the algorithmic implementation are provided, and the applicability of the model within a finite element framework is shown by simulating the overexpansion of simplified atherosclerotic arteries.