# Investigating the compaction of open ring stacks through real and numerical experiments

Emile Hohnadel, Tomohiko G Sano, Toshiyuki Kawata, Thibaut Métivet, Florence Bertails-Descoubes

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Emile Hohnadel, Tomohiko G Sano, Toshiyuki Kawata, Thibaut Métivet, Florence Bertails-Descoubes. Investigating the compaction of open ring stacks through real and numerical experiments. European Solid Mechanics Conference ESMC 2022, Jul 2022, Galway, Ireland. hal-03962464

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Submitted on 30 Jan 2023

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<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Investigating the compaction of open ring stacks through real and nu-
merical experiments

Emile Hohnadel<fnref n="1" />*, Tomohiko G. Sano<fnref n="2" />*, Toshiyuki Kawata<fnref n="2" />, Thibaut Metivet<fnref n="1" />, Florence Bertails-Descoubes<fnref n="1" />

E-mail: emile.hohnadel@inria.fr

E-mail: sano@mech.keio.ac.jp

Keywords: Thin elastic rods, frictional contact, simulation, mechanical metamaterials, snap-fits

<figure><img src="image_2.png" /><figcaption>Fig. 1: Left: Our experimental set-up with 30 open rings. Center: Simulation of our set-up scaled up to 300 open rings. Right: Stress-strain plot from our simulation, for 5 consecutive compression cycles.</figcaption></figure>

We investigate the mechanical response of a stack of bidimensional flexible open rings subject to
compression cycles, by the means of experiments and simulations. To perform reliable and scalable
simulations, we build a numerical model based on an unclamped version of the 2D super-helix [1]
for open thin elastic rods, coupled to frictional contact constraints [2]. We carefully validate this
numerical model, first against theoretical predictions given by the analysis of a single ring snap
fit [3], second by comparing numerical and experimental results for an assembly of rings of moderate
size (30 rings). Our excellent prediction results allow us to rely on the simulator for investigating the
mechanical behaviour of a large collection of (300) randomly stacked rings, depending on their
opening angle and their friction coefficient. In particular, we find that such a system, which acts as a
disordered mechanical metamaterial, can absorb and store mechanical energy upon compression in
a controlled fashion, exploiting large displacement and rearrangement of rings, snap-fits, and friction.

References

[1] F. Bertails, B. Audoly, M.-P. Cani, B. Querleux, F. Leroy, J.-L. Lévêque, "Super-Helices for Predicting the Dynamics of Natural Hair", ACM Transactions on Graphics, 25:3: 1180-1187, 2006.

[2] G. Daviet, F. Bertails-Descoubes, L. Boissieux, "A hybrid iterative solver for robustly capturing Coulomb friction in hair dynamics", ACM Transactions on Graphics, 30, Article 139: 1-12, 2011.

[3] K. Yoshida, H. Wada, "Mechanics of a Snap Fit", Physical Review Letters, 125, 194301, 2020.

<footnote n="1">¹ *Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK, Grenoble, France*</footnote>

<footnote n="2">² Department of Mechanical Engineering, Keio University, Yokohama, Japan</footnote>

<footnote>* These authors contributed equally to this work</footnote>