A Corrected Sadowsky Functional for Inextensible Elastic Ribbons

The classical theory of ribbons, developed by Sadowsky and Wunderlich, has recently received renewed attention. Here, by means of \(\varGamma\)-convergence, we re-examine the derivation of the limit energy of an inextensible, isotropic, elastic strip as the width goes to zero. We find that this rigorously derived functional agrees with the classical Sadowsky functional only for “large” curvature of the centerline of the strip.