# J-shaped stress-strain diagram of collagen fibers: Frame tension of triangulated surfaces with fixed boundaries

## TL;DR

This study uses Monte Carlo simulations of two triangulated surface models to investigate the J-shaped stress-strain diagram of collagen fibers, revealing the importance of directional collagen degrees of freedom in this nonlinear behavior.

## Contribution

It demonstrates that Finsler geometry modeling captures collagen's directional effects, providing insights beyond traditional Helfrich-Polyakov models.

## Key findings

- FG model explains the J-shape with collagen directionality
- HP model cannot reproduce the J-shaped diagram
- Finsler geometry offers a coarse-grained interaction picture

## Abstract

We present Monte Carlo data of the stress-strain diagrams obtained using two different triangulated surface models. The first is the canonical surface model of Helfrich and Polyakov (HP), and the second is a Finsler geometry (FG) model. The shape of the experimentally observed stress-strain diagram is called J-shaped. Indeed, the diagram has a plateau for the small strain region and becomes linear in the relatively large strain region. Because of this highly non-linear behavior, the J-shaped diagram is far beyond the scope of the ordinary theory of elasticity. Therefore, the mechanism behind the J-shaped diagram still remains to be clarified, although it is commonly believed that the collagen degrees of freedom play an essential role. We find that the FG modeling technique provides a coarse-grained picture for the interaction between the collagen and the bulk material. The role of the directional degrees of freedom of collagen molecules or fibers can be understood in the context of FG modeling. We also discuss the reason for why the J-shaped diagram cannot (can) be explained by the HP (FG) model.