In order to describe the large bending of a flexible thin rod under the assumption of small strain, a new theory is developed based on the Cosserat elasticity. Two dimensionless parameters ω_αρ (α= 1, 2) are presented to distinguish between large and small bends, where ω_α are the bending curvatures and ρ is the characteristic radius of cross-sections. The bending is defined as small if ω_αρ ≪ 1. On the contrary, the bending should be treated as a large one. In the case of large bending, torsion and bending are coupled. The equations given in the theory can be reduced to the Kirchhoff’ form when the bending becomes small. In a sense, the new theory can be seen as an extension of Kirchhoff's rod theory. The size effect is accounted for.

为了描述在细应变假设下挠性细杆的大弯曲，基于Cosserat弹性提出了一种新的理论。两个无量纲参数ω _α ρ（α= 1，2）呈现大和小的弯曲，来区分其中ω _α是弯曲的曲率和ρ是横截面的特征半径。弯曲被定义为小，如果ω _α ρ«1。相反，弯曲应作为一个大一个处理。在大弯曲的情况下，扭转和弯曲是耦合的。当弯曲变小时，可以将理论中给出的方程简化为Kirchhoff'形式。从某种意义上说，新理论可以看作是基尔霍夫棒理论的延伸。尺寸效应被考虑。