# Hysteretic slit-snapping and multistability in buckled beams with partial cuts

## TL;DR

Adding partial cuts to elastic beams allows precise control over their snapping behavior, enabling multiple stable shapes and advanced mechanical functions.

## Contribution

The study introduces a general method to control elastic instabilities using partial cuts, enabling programmable multistability and snapping transitions.

## Key findings

- Slit-beams exhibit tristability under compression due to hysteretic slit-snapping.
- Multislit beams demonstrate quadstability, multistep snapping, and zero-compression tristability.
- The approach enables programmable mechanical metamaterials with memory and sequential behavior.

## Abstract

Elastic instabilities such as buckling and snapping have evolved into a powerful design principle, enabling memory, sequential shape morphing, and computing in metamaterials and devices. Modifying the postbuckling configurations or their snapping transitions would greatly expand design possibilities, yet general principles for controlling elastic instabilities are lacking. Here, we show that adding a partial cut, or slit, to a flexible beam enables precise control of postbuckling behavior: Under compression, slit-beams first buckle and then snap, leading to tristability within the hysteretic regime. A truss model explains these phenomena by uncovering the interplay of geometric and slit-induced nonlinearities. Leveraging these insights, we realize multislit beams with programmable behavior, unlocking a vast design space featuring giant hysteresis, quadstability, multistep snapping, tristability at zero compression, and compression-induced snapping between left- and right-buckled states. Our strategy is general, simple to design and implement, and enables mechanical metamaterials and devices with advanced memory and sequential behavior.

Partial cuts in buckling elastic beams create controllable snapping transitions and multiple stable shapes.