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

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.

References in corpus (6)

• Monte Carlo study of multiply crosslinked semiflexible polymer networks
• Nonlinear Elasticity, Fluctuations and Heterogeneity of Nematic Elastomers
• Finsler geometry modeling and Monte Carlo study of 3D liquid crystal elastomer
• Universal behavior of crystalline membranes: crumpling transition and Poisson ratio of the flat phase
• Possible effects of tilt order on phase transitions of a fixed connectivity surface model
• Internal phase transition induced by external forces in Finsler geometric model for membranes

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