A one-dimensional model for a narrow ribbon is derived from the plate theory of Kirchhoff by means of a power expansion in the width variable. The energy found coincides with the corrected Sadowsky’s energy. Furthermore, we derive the Euler-Lagrange equations and use them to study an equilibrium configuration of a twisted ribbon. Within this example we also describe how to construct the fine scale oscillations that develop in the deformed configuration.
Paroni, R., & Tomassetti, G. (2019). Macroscopic and Microscopic Behavior of Narrow Elastic Ribbons. JOURNAL OF ELASTICITY, 135(1-2), 409-433 [10.1007/s10659-018-09712-w].