  The Discrete elastic rod method (Bergou et al., 2008) is a numerical method
for simulating slender elastic bodies. It works by representing the center-line
as a polygonal chain, attaching two perpendicular directors to each segment,
and defining discrete stretching, bending and twisting deformation measures and
a discrete strain energy. Here, we investigate an alternative formulation of
this model based on a simpler definition of the discrete deformation measures.
Both formulations are equally consistent with the continuous rod model. Simple
formulas for the first and second gradients of the discrete deformation
measures are derived, making it easy to calculate the Hessian of the discrete
strain energy. A few numerical illustrations are given. The approach is also
extended to inextensible ribbons described by the Wunderlich model, and both
the developability constraint and the dependence of the energy of the strain
gradients are handled naturally.
