# Snapping of elastic strips with controlled ends

## TL;DR

This paper analyzes the snapping behavior of elastic strips with controlled boundary conditions, introducing a universal snap surface that predicts critical conditions for snapping, validated by experiments and simulations, with applications in energy harvesting and robotics.

## Contribution

It develops an analytical framework using Euler's elastica to identify stable configurations and defines a universal snap surface for elastic strips with controlled ends.

## Key findings

- Universal snap surface accurately predicts snapping conditions.
- Experimental and simulation results confirm theoretical predictions.
- Insights into elastic energy release useful for impulsive motion optimization.

## Abstract

Snapping mechanisms are investigated for an elastic strip with ends imposed to move and rotate in time. Attacking the problem analytically via Euler's elastica and the second variation of the total potential energy, the number of stable equilibrium configurations is disclosed by varying the kinematics of the strip ends. This result leads to the definition of a `universal snap surface', collecting the sets of critical boundary conditions for which the system snaps. The elastic energy release at snapping is also investigated, providing useful insights for the optimization of impulsive motion. The theoretical predictions are finally validated through comparisons with experimental results and finite element simulations, both fully confirming the reliability of the introduced universal surface. The presented analysis may find applications in a wide range of technological fields, as for instance energy harvesting and jumping robots.