Figure 2
From: Twist-to-bend ratio: an important selective factor for many rod-shaped biological structures
Evolution of the phase field in terms of maximising minimal flexural rigidity Dmin and minimising torsional rigidity Dz, (\({\sigma }_{1}=-\,{\sigma }_{2}=1,{\sigma }_{3}=0\)). (a) Evolution of the shape of the phase field with respect to torsional rigidity Dz (vertical axis) and flexural rigidity Dmin (horizontal axis). (b) Evolution of the shape of the phase field with respect to the twist-to-bend ratio Dmin/Dz and pseudo-time t. The development of a deep central groove leads to a noticeable reduction in torsional rigidity, see (a) and thus to a first strong increase in the ratio, see (b). The flexural rigidity is then greatly increased by a widening of the central groove, (a) leading to another markedly increase in the twist-to-bend ratio. These two effects ultimately form the characteristic U-shaped ___domain. The numerical steady state is effected by the chosen artificial boundary conditions and is not considered in the comparison to plant morphology.
