Elastic beams or rods in two and three dimensions produce smooth curves by minimizing the strain energy due to classical Euler-Bernoulli bending and Saint-Venant torsion subject to constraints on the arc length and end positions and orientations.However it is possible to postulate other strain energy measures. In this paper we describe a strain energy measure which is the sum of the square of the rate of change of curvature and the square of the product of the curvature and the Frenet torsion.
Adriaenssens, S., Malek, S., Miki, M., & Williams, C. J. K. (2013). Generating smooth curves in 3 dimensions by minimizing higher order strain energy measures. International Journal of Space Structures, 28(3-4), 119-126. https://doi.org/10.1260/0266-3511.28.3-4.119