Flexible thin rods with large bending

Abstract

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 ωαρ (α= 1, 2) are presented to distinguish between large and small bends, where ωα are the bending curvatures and ρ is the characteristic radius of cross-sections. The bending is defined as small if ωαρ ≪ 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.