# Modelling a Feather as a Strongly Anisotropic Elastic Shell

Jean Jouve, Victor Romero, Rahul Narain, Laurence Boissieux, Theodore

Kim, Florence Bertails-Descoubes

► To cite this version:

Jean Jouve, Victor Romero, Rahul Narain, Laurence Boissieux, Theodore Kim, et al. Modelling a Feather as a Strongly Anisotropic Elastic Shell. ESMC 2025 - 12th European Solid Mechanics Conference, Jul 2025, Lyon, France. pp.1-29. hal-05230404

HAL Id: hal-05230404

https://hal.science/hal-05230404v1

Submitted on 29 Aug 2025

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Distributed under a Creative Commons Attribution 4.0 International License
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# Modelling a Feather as a Strongly Anisotropic Elastic Shell

**Jean Jouve**<fnref n="1" />, **Victor Romero**<fnref n="1" />, **Rahul Narain**<fnref n="2" />, **Laurence Boissieux**<fnref n="1" />, **Theodore Kim**<fnref n="3" />, **Florence Bertails-Descoubes**<fnref n="1" />

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<footnote n="1">¹ Université Grenoble Alpes, INRIA, CNRS, GrenobleINP</footnote>

<footnote n="2">² Indian Institute of Technology Delhi</footnote>

<footnote n="3">³ Yale University</footnote>
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~ $10^3$ feathers
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# Intricate multi-scale structure

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# Intricate multi-scale structure

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# Shell Model

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## Stretching

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## Bending

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## Fracture & Healing

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# Shell Model

## Stretching

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## Bending

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## Fracture & Healing

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# In-plane characterization

<figure><img src="image_22.png" /><figcaption>2 cm</figcaption></figure>
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# In-plane characterization

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# In-plane characterization

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# In-plane characterization

Transverse

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Longitudinal

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# In-plane characterization

Transverse

× 10⁻²

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Longitudinal

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Very small displacement
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# In-plane characterization
Transverse

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## Longitudinal

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# Anisotropic shell model

We use ArcSim [Narain, 2012] as a base simulation Software

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# Anisotropic shell model

We use ArcSim [Narain, 2012] as a base simulation Software

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$$ \begin{bmatrix} \sigma_{xx} \\ \sigma_{yy} \\ \sigma_{xy} \end{bmatrix} = \begin{bmatrix} E_{xx} & 0 & 0 \\ 0 & E_{yy} & 0 \\ 0 & 0 & E_{xy} \end{bmatrix} \begin{bmatrix} \epsilon_{xx} \\ \epsilon_{yy} \\ \epsilon_{xy} \end{bmatrix} $$
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# Anisotropic shell model

We use ArcSim [Narain, 2012] as a base simulation Software

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$$ \begin{bmatrix} \sigma_{xx} \\ \sigma_{yy} \\ \sigma_{xy} \end{bmatrix} = \begin{bmatrix} E_{xx} & 0 & 0 \\ 0 & E_{yy} & 0 \\ 0 & 0 & E_{xy} \end{bmatrix} \begin{bmatrix} \epsilon_{xx} \\ \epsilon_{yy} \\ \epsilon_{xy} \end{bmatrix} \quad \sim 10^4 \rightarrow \text{Numerical Locking} $$

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# Anisotropic shell model

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Two ingredients:
- Mesh alignment
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# Anisotropic shell model

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Two ingredients:

- Mesh alignment

- Edge constraint
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# Anisotropic shell model

$$ \begin{bmatrix} \sigma_{xx} \\ \sigma_{yy} \\ \sigma_{xy} \end{bmatrix} = \begin{bmatrix} E_{xx} & 0 & 0 \\ 0 & E_{yy} & 0 \\ 0 & 0 & E_{xy} \end{bmatrix} \quad \begin{bmatrix} \epsilon_{xx} \\ \epsilon_{yy} \\ \epsilon_{xy} \end{bmatrix} $$

Two ingredients:

- Mesh alignment

- Edge constraint

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# Parameter Identification?

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# Parameter Identification?

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# Micro-scale model

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Barbs Density: $d \sim 0.16 \pm 0.03$

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Numerical model*
for calibration
and validation

* Experimentally Validated, see the paper

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# Calibration Macro-scale model

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# Validation Macro-scale model

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Barbs orientation (degrees)
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# Shearing Stiffness

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# Validation Macro-scale Model

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Both models capture
well the deformed
geometry
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# « Fracture » of feathers

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# « Fracture » of feathers

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# Conclusions

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* **Experimental mechanical characterization** of Feathers.

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* **Numerical implementation of an anisotropic model** capable of dealing with numerical locking.

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* **Numerical Model based on the structure of feathers for calibration and validation.**

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* **Validation** of numerical results.

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Thank you

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Code and data for **feather-shell** are available at
https://gitlab.inria.fr/elan-public-code/feather-shell.git

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