Active filaments I: Curvature and torsion generation
Active filaments I: Curvature and torsion generation
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DOI：
10.1016/j.jmps.2022.104918
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发表时间：
2022-05-14
影响因子：
5.3
通讯作者：
Goriely, Alain
中科院分区：
文献类型：
--
作者：
Kaczmarski, Bartosz;Moulton, Derek E.;Goriely, Alain
在许多植物结构中，如静水臂、根和茎，材料的活性或生长部分取决于收缩或伸长的纤维。通过肌肉收缩或生长的激活，这些纤维将产生内应力，这些内应力通过获得内在扭转和弯曲的细丝而部分缓解。这一过程不仅是形态发生的基础，也是植物向性、植物固体激活以及象鼻和章鱼臂等消化器官的肌肉运动的基础。在这里，我们提供了一个一般的理论，链接在微观尺度上的任意纤维的激活，在宏观尺度上的曲率和扭转的产生。这个理论是通过从三维物体的全滞弹性描述降维到形态弹性克希霍夫杆而得到的。因此，它将嵌入纤维的几何形状和材料特性与杆的形状和刚度联系起来。该理论适用于螺旋缠绕在锥形和非锥形长丝的中心芯周围的纤维。
In many filamentary structures, such as hydrostatic arms, roots, and stems, the active or growing part of the material depends on contractile or elongating fibers. Through their activation by muscular contraction or growth, these fibers will generate internal stresses that are partially relieved by the filament acquiring intrinsic torsion and curvature. This process is fundamental in morphogenesis but also in plant tropism, nematic solid activation, and muscular motion of filamentary organs such as elephant trunks and octopus arms. Here, we provide a general theory that links the activation of arbitrary fibers at the microscale to the generation of curvature and torsion at the macroscale. This theory is obtained by dimensional reduction from the full anelastic description of three-dimensional bodies to morphoelastic Kirchhoff rods. Hence, it links the geometry and material properties of embedded fibers to the shape and stiffness of the rod. The theory is applied to fibers that are wound helically around a central core in tapered and untapered filaments.