Overcurvature induced multistability of linked conical frusta: How a `bendy straw' holds its shape

TL;DR

This paper investigates how geometry and internal stress lead to multiple stable configurations in linked conical shells, similar to bendy straws, revealing design principles for reconfigurable structures.

Contribution

It identifies the roles of geometrical parameters and internal pre-stress in achieving multistability in linked conical frusta, supported by experimental and mechanical modeling.

Findings

Geometry tuning induces axial bistability.

Internal pre-stress enables bent state stability.

Curvature analysis explains stability mechanisms.

Abstract

We study the origins of multiple mechanically stable states exhibited by an elastic shell comprising multiple conical frusta, a geometry common to reconfigurable corrugated structures such as `bendy straws'. This multistability is characterized by mechanical stability of axially extended and collapsed states, as well as a partially inverted `bent' state that exhibits stability in any azimuthal direction. To understand the origin of this behavior, we study how geometry and internal stress affect the stability of linked conical frusta. We find that tuning geometrical parameters such as the frustum heights and cone angles can provide axial bistability, whereas stability in the bent state requires a sufficient amount of internal pre-stress, resulting from a mismatch between the natural and geometric curvatures of the shell. We analyze the latter effect through curvature analysis during deformation using X-ray computed tomography (CT), and with a simple mechanical model that captures the qualitative behavior of these highly reconfigurable systems.