Asymmetric Bending Boundary Layer: the $\lambda$-test

TL;DR

This paper studies the mechanics of asymmetric ribbons under tension, revealing a universal binding angle related to bending stiffness and introducing the $\lambda$-test for membrane characterization.

Contribution

It introduces the $\lambda$-test, a novel visual technique to measure membrane properties, and challenges the assumption of negligible bending stiffness in thin shells at high tension.

Findings

Binding angle as a macroscopic signature of bending stiffness.

Universal non-linear rotational response independent of asymmetry ratio.

The $\lambda$-test enables simple mechanical characterization of membranes.

Abstract

We investigate the mechanics of two asymmetric ribbons bound at one end and pulled apart at the other ends. We characterize the elastic junction near the bonding and conceptualize it as a bending boundary layer. While the size of this junction decreases with the pulling force, we observe the surprising existence of the binding angle as a macroscopic signature of the bending stiffnesses. Our results thus challenge the standard assumption of neglecting bending stiffness of thin shells at large tensile loading. In addition, we show how the rotational response of the structure exhibits a non-linear and universal behavior regardless of the ratio of asymmetry. Leveraging the independence of the binding angle to the pulling force, we finally introduce the $\lambda$-test -- a visual measurement technique to characterize membranes through simple mechanical coupling.