  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.
