Multistability of free spontaneously-curved anisotropic strips

TL;DR

This paper analyzes the multistability of anisotropic elastic strips with spontaneous curvature, revealing conditions for bistability and tristability based on curvature and stiffness properties, and extends existing shell multistability theory.

Contribution

It provides a comprehensive theoretical framework for understanding multistability in anisotropic strips with spontaneous curvature, including new stability criteria and the possibility of tristability.

Findings

Strips with positive spontaneous curvature are always bistable.

Negative spontaneous curvature strips are bistable only under certain conditions.

Anisotropic strips can be tristable when bending rigidity is small.

Abstract

Multistable structures are objects with more than one stable conformation, exemplified by the simple switch. Continuum versions are often elastic composite plates or shells, such as the common measuring tape or the slap bracelet, both of which exhibit two stable configurations: rolled and unrolled. Here we consider the energy landscape of a general class of multistable anisotropic strips with spontaneous Gaussian curvature. We show that while strips with non-zero Gaussian curvature can be bistable, strips with positive spontaneous curvature are always bistable, independent of the elastic moduli, strips of spontaneous negative curvature are bistable only in the presence of spontaneous twist and when certain conditions on the relative stiffness of the strip in tension and shear are satisfied. Furthermore, anisotropic strips can become tristable when their bending rigidity is small. Our study complements and extends the theory of multistability in anisotropic shells and suggests new design criteria for these structures.