Abstract

Nowadays, the 3D ultrastructure of a fibrous tissue can be reconstructed in order to visualize the complex nanoscale arrangement of collagen fibrils including neighboring proteoglycans even in the stretched loaded state [1]. In particular, experimental data of collagen fibers in human artery layers have shown that the fibers are not symmetrically dispersed [2]. In addition, it is known that collagen fibers are cross-linked and the density of cross-links in arterial tissues has a stiffening effect on the associated mechanical response. A first attempt to characterize this effect on the elastic response is presented and the influence of the cross-link density on the mechanical behavior in uniaxial tension is shown [3]. A recently developed extension of the model that accounts for dispersed fibers connected by randomly distributed cross-links is outlined [4]. A simple shear test focusing on the sign of the normal stress perpendicular to the shear planes (Poynting effect) is analyzed. In [5] it was experimentally observed that, in contrast to rubber, semi-flexible biopolymer gels show a tendency to approach the top and bottom faces under simple shear. This so-called negative Poynting effect and its connection with the cross-links as well as the fiber and cross-link dispersion is also examined.

References

[1] A. Pukaluk et al.: An ultrastructural 3D reconstruction method for observing the arrangement of collagen fibrils and proteoglycans in the human aortic wall under mechanical load. Acta Biomaterialia, 141:300-314, 2022.

[2] G.A. Holzapfel et al.: Modelling non-symmetric collagen fibre dispersion in arterial walls. Journal of the Royal Society Interface, 12:20150188, 2015.

[3] G.A. Holzapfel and R.W. Ogden: An arterial constitutive model accounting for collagen content and cross-linking. Journal of the Mechanics and Physics of Solids, 136:103682, 2020.

[4] S. Teichtmeister and G.A. Holzapfel: A constitutive model for fibrous tissues with cross-linked collagen fibers including dispersion – with an analysis of the Poynting effect. Journal of the Mechanics and Physics of Solids, 164:104911, 2022.

[5] P.A. Janmey et al.: Negative normal stress in semiflexible biopolymer gels. Nature Materials, 6:48–51, 2007.