Micromechanically-motivated analysis of fibrous tissue

Collagen fibers are the main load bearing component in fibrous tissues. Systematic analyses of their structure and orientation are thus crucial for the development of material models that enable to predict the mechanical tissue response. To this end, biaxial tests at different stretch ratios were performed on two tissue samples of the medial layer extracted from a human aorta. The tissues were loaded in the circumferential and axial directions simultaneously. We develop here a micromechanical model which is based on structural parameters of collagen fibers that were extracted from second-harmonic generation images of the two samples. The tissue is modeled as a periodic six-layered laminate in which the individual layers are treated as periodic fibrous structures with one family of fibers. We make use of the Hill-Mandel theory in the context of periodic homogenization to determine the overall mechanical tissue response. Both the analytical and numerical models are able to capture the overall mechanical response of the two tissue samples using a straightforward representation of the tissue structure together with a limited set of material parameters. Up to 10% of strains the model captures the almost linear response of both tissue samples. Beyond that stretch level the stiffening of the tissues becomes more evident, especially in the circumferential direction. In cases where the axial stretch is larger than the circumferential stretch the predictions are somewhat stiffer, while a very good agreement is obtained when the circumferential stretch is dominant. The stiffening of one tissue sample was substantially larger than the other, implying that higher-order stiffening mechanisms may kick in at larger strains. Our sensitivity analyses reveal that the parameters of the material model and the fiber dispersion have a minor effect on the tissue response. The novel modeling approach has the potential to reduce the need of time-consuming experimental data of the mechanical behavior of fibrous tissues.