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

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