Pitch Controls the Flexibility of Helical Ribbons

TL;DR

This study investigates how the pitch of micro-helical ribbons made from ultra-thin PMMA influences their mechanical stiffness, revealing a transition from twisting to bending regimes and confirming the model with experimental data.

Contribution

It provides new experimental insights into the role of helix pitch and cross-section geometry on the mechanical properties of micro-helices, supported by analytical modeling.

Findings

Helical ribbons stiffen with increasing pitch.

A transition from twisting to bending dominates at different pitches.

Experimental results agree with existing elastic strip models.

Abstract

Helical objects are often implemented in electronic or mechanical micro-systems, requiring a precise understanding of their mechanical properties. While helices formed by cylindrical filaments have been intensely investigated, little is known about the role of the cross-section of the filament at the basis of the helical shape. We study experimentally the force-extension response of micro-helices fabricated from ultra-thin PMMA ribbons. Leveraging newly achieved control on the helix geometry, the influence of the helical pitch is quantified and a significant stiffening of the helical ribbons with increasing pitch is highlighted. Two phenomena are identified: a mechanical transition from a regime dominated by twisting of the ribbon at small pitch to a bending-dominated regime at high pitch and a purely geometrical effect, specific to helical ribbons. Excellent agreement is found with a previously established analytical model of inextensible elastic strips.