Zhou Zicong, Lai Pik-Yin, Joós Béla
Department of Physics and Graduate Institute of Life Sciences, Tamkang University, Tamsui, Taiwan 251, Republic of China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 May;71(5 Pt 1):052801. doi: 10.1103/PhysRevE.71.052801. Epub 2005 May 20.
We derive the general shape equations in terms of Euler angles for a uniform elastic rod with spontaneous torsion and curvatures and subjected to external force and torque. Our results based on an analytic formalism show that the extension of a helical rod may undergo a one-step discontinuous transition with increasing stretching force. This agrees quantitatively with experimental observations for a helix in a chemically defined lipid concentrate. The larger the twisting rigidity, the larger the jump in the extension. The effect of torque on the jump is, however, dependent on the value of the spontaneous torsion. In contrast, increasing the spontaneous torsion encourages the continuous variation of the extension. An "over-collapse" behavior is observed for the rod with asymmetric bending rigidity, and an intrinsic asymmetric elasticity under twisting force is found.
我们推导了具有自发扭转和曲率且受到外力和扭矩作用的均匀弹性杆的欧拉角形式的一般形状方程。我们基于解析形式主义的结果表明，随着拉伸力的增加，螺旋杆的伸长可能会经历一步不连续转变。这与在化学定义的脂质浓缩物中螺旋的实验观察结果在数量上相符。扭转刚度越大，伸长的跳跃就越大。然而，扭矩对跳跃的影响取决于自发扭转的值。相比之下，增加自发扭转会促使伸长的连续变化。对于具有不对称弯曲刚度的杆，观察到了“过度坍塌”行为，并且发现了扭转力下的固有不对称弹性。
