Nonlinear mechanical metamaterial cloaks

Inverse-design of nonlinear mechanical metamaterial cloaks

cloaked_spaghetto.mp4

🌅 Why nonlinear mechanical metamaterial cloaks?

We propose a design strategy that extends mechanical cloaking to the nonlinear regime, bypassing the limitations of traditional methods. By framing cloaking as a behavior-mimicking optimization problem—matching the nonlinear mechanical response of a reference system—we eliminate the need for explicit analytical solutions or transformation-based approaches. We solve this optimization using the differentiable simulation framework DifFlexMM, specialized here for cloaking applications. Besides accounting for large deformations and contact interactions, our approach brings different design challenges under the same behavior-mimicking formulation, such as shielding against external excitations and creating stress-free target regions.

🚁 Overview

This repository contains the full pipeline used in the paper to design and validate nonlinear mechanical cloaks with rigid units and elastic couplings. Key building blocks include:

• 🧩 Geometry parametrizations for cloaks and inclusions (mechanicalmetamaterialcloaks/geometry.py).
• 🎈 Elastic energy models for ligaments and interactions (mechanicalmetamaterialcloaks/energy.py).
• 💥 Differentiable dynamic solver for forward simulation (mechanicalmetamaterialcloaks/dynamics.py).
• 🧭 Loading, actuation, and boundary conditions (mechanicalmetamaterialcloaks/loading.py).
• 📈 Visualization utilities (mechanicalmetamaterialcloaks/plotting.py).

Problem definitions live in problems and are paired with notebooks that reproduce each cloaking task and experimental dataset.

📜 Paper

This repository contains all the code developed for the paper:

G. Bordiga, J.-G. Argaud, A. A. Watkins, V. Tournat, K. Bertoldi. Nonlinear Mechanical Metamaterial Cloaks. Advanced Functional Materials (2025).

Preprint: https://doi.org/10.48550/arXiv.2508.21277

🎯 Solved design problems

	Task description	Notebooks	Data 💾	Experiments 🧪	Video 🎥
🛡️	Blocking unwanted excitations (dynamic shielding)	Shielding Cloak size sweep	Cloaked Reference	Cloaked Reference	adfm73203-sup-0002-movies1.mp4
🫥	Stress-free regions	Stress-free circle	Stress-free	Stress-free	adfm73203-sup-0003-movies2.mp4
🕳️	Static cloaking of voids	Heart Cat Dolphin Shamrock Smile Kagome	Quads Reference Kagome	Reference Smile void	adfm73203-sup-0004-movies3.mp4
🧱	Static cloaking of rigid inclusions	Rigid inclusion	Rigid inclusion		heart_shaped_rigid_inclusion.mp4
🌊	Dynamic cloaking of voids	Quads	Quads		adfm73203-sup-0005-movies4.mp4

💾 Optimization and experimental data

Important

Install the package along with the examples to visualize the data and notebooks.

All data generated or used for the paper can be downloaded from . To access and visualize the data:

• Download the archive from Zenodo.
• Extract the contents into the root directory of the repository.
• Use the notebooks to load and visualize optimization results.
• Explore experimental results under exp.

Once the data is in place, the folder tree should look like this:

MechanicalMetamaterialCloaks/
├── data/
├── exp/
├── mechanicalmetamaterialcloaks/
├── notebooks/
├── out/
├── problems/
...

⬇️ Installation

MechanicalMetamaterialCloaks only

Assuming you have access to the repo and ssh keys are set up in your GitHub account, you can install the package with

pip install git+ssh://git@github.com/bertoldi-collab/MechanicalMetamaterialCloaks.git

MechanicalMetamaterialCloaks with examples

Clone the repository, cd into the root folder, and install with

pip install -e .

The code has been tested with Python 3.10–3.11 but may work with other versions once the proper dependencies are installed.

🤝 Contributing

Expand here

The dependency management of the project is done via poetry.

To get started:

• Install poetry.
• Clone the repository.
• cd into the root directory and run poetry install. This will create the poetry environment with all the necessary dependencies.
• If you are using VS Code, search for venv path in the settings and paste ~/.cache/pypoetry/virtualenvs in the venv path field. Then select the poetry environment as the Python environment for the project.

👥 Contributors

Contributor	Affiliation	Contributions
Giovanni Bordiga	Harvard University	Research design, simulation & optimization code, data analysis
Jean-Gabriel Argaud	MINES Paris – PSL Université / Harvard University	Simulation & optimization code, fabrication, experiments, data analysis
Audrey A. Watkins	Harvard University	Fabrication, experiments, data analysis
Vincent Tournat	Harvard University / Le Mans Université	Research design, experiments, data analysis
Katia Bertoldi	Harvard University	Research design, data analysis

📝 Citation

If you use this code in your research or anywhere, please cite the paper:

@article{bordiga2025nonlinear,
		title   = {Nonlinear Mechanical Metamaterial Cloaks},
		author  = {Bordiga, Giovanni and Argaud, Jean-Gabriel and Watkins, Audrey A. and Tournat, Vincent and Bertoldi, Katia},
		year    = {2025},
		journal = {Advanced Functional Materials},
		volume  = {36},
		number  = {28},
		pages   = {e22895},
		doi     = {10.1002/adfm.202522895},
}