Stretchable Fibrous Materials with Different Micro-Geometries of Wavy Fibers

Abstract

The mechanical behavior of collagenous tissues crucially depends on the fibers’ micro-geometry. Herein, we systematically analyze this ubiquitous class of tissues. Finite element simulations of periodic cells enable us to relate the macroscopic tissue response to the mechanical processes of the underlying microstructure. We examine cells with a single thick fiber and cells with a bundle of seven thin fibers while keeping the fraction of the fiber substance identical in both cells. Models with shallow and wrinkled fibers are examined in both cases. Plane stress conditions are imposed, where the stretching direction is aligned with or inclined to the fiber direction. The latter mimics the loading state in the arterial wall. To even better mimic the physiological state, we superimpose a 10% prestretch in the transverse direction. Overall, the stress-stretch curves are bilinear with a low initial slope that converges into a steeper slope as the fibers straighten. This recruitment process becomes even more pronounced under aligned loading. Our expectation that the thick fiber model will be stiffer than the seven fibers bundle model due to its larger bending stiffness turned out to be inaccurate. Analysis of the stresses in the surrounding matrix material revealed that this counterintuitive occurrence is due to a through-matrix interaction between the fibers in the bundle.

Twenty years ago, I supervised a young graduate student, Ilia Hariton, who was about to complete his M.Sc. thesis. Ilia wished to continue his studies towards a Ph.D. in Biomechanics, and while we were discussing his options, we studied some of the recent works in this field. Among the most intriguing and advanced works we encountered were the ones by Gerhard and his colleagues. Since back then, I was rather new in the field of Biomechanics, I contacted Gerhard and offered him to join me and supervise Ilia’s work together. Although we have never met before, I received a warm and positive response. After a few emails, we decided to join forces and, in Gerhard’s words, to explore ‘a micro-mechanical constitutive approach to describe the mechanical behavior of biological soft tissues’. During our work, I found that Gerhard loves to work in the field of biomechanics, to collaborate, to explore new ideas, to share his knowledge with others, and to listen to them too. In fact, our work was a real fusion of our expertise in the fields of Biomechanics and Micromechanics. I am glad that twenty years afterward, Gerhard is creative than ever, and I am looking forward to his next contributions and our future collaboration.

Gal