Bendability parameter for twisted ribbons to describe longitudinal wrinkling and delineate the near-threshold regime

Abstract

We propose a dimensionless bendability parameter, $\epsilon^{-1} = [\left(h/W\right)^2 T^{-1}]^{-1}$ for wrinkling of thin, twisted ribbons with thickness $h$, width $W$, and tensional strain $T$. Bendability permits efficient collapse of data for wrinkle onset, wavelength, critical stress, and residual stress, demonstrating longitudinal wrinkling's primary dependence on this parameter. This new parameter also allows us to distinguish the highly bendable range ($\epsilon^{-1} > 20$) from moderately bendable samples ($\epsilon^{-1} \in (0,20]$). We identify scaling relations to describe longitudinal wrinkles that are valid across our entire set of simulated ribbons. When restricted to the highly bendable regime, simulations confirm theoretical near-threshold (NT) predictions for wrinkle onset and wavelength.