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

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.