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https://github.com/bertoldi-collab/difflexmm
Differentiable Flexible Mechanical Metamaterials
https://github.com/bertoldi-collab/difflexmm
automatic-differentiation differentiable-physics inverse-design mechanical-metamaterials metamaterial-design nonlinear-dynamics nonlinear-optimization nonlinear-waves
Last synced: about 6 hours ago
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Differentiable Flexible Mechanical Metamaterials
- Host: GitHub
- URL: https://github.com/bertoldi-collab/difflexmm
- Owner: bertoldi-collab
- License: mit
- Created: 2024-02-26T06:29:00.000Z (9 months ago)
- Default Branch: main
- Last Pushed: 2024-10-30T19:42:35.000Z (17 days ago)
- Last Synced: 2024-10-30T20:30:26.220Z (17 days ago)
- Topics: automatic-differentiation, differentiable-physics, inverse-design, mechanical-metamaterials, metamaterial-design, nonlinear-dynamics, nonlinear-optimization, nonlinear-waves
- Language: Jupyter Notebook
- Homepage:
- Size: 38.2 MB
- Stars: 11
- Watchers: 1
- Forks: 2
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# DifFlexMM
[](https://github.com/bertoldi-collab/DifFlexMM/actions/workflows/python_tests.yml)
[](https://doi.org/10.1038/s41563-024-02008-6)
[](https://doi.org/10.5281/zenodo.12823471)
[](https://arxiv.org/abs/2403.08078)
[](https://github.com/bertoldi-collab/DifFlexMM/blob/main/LICENSE)
[](https://hits.seeyoufarm.com)
**Dif**ferentiable **Flex**ible **M**echanical **M**etamaterials
https://github.com/user-attachments/assets/8e966e96-13d4-439b-a0cb-d7dff115e7e1
## 🌅 Why DifFlexMM?
🚀 The goal of this framework is to push the boundary of designable dynamic behaviors achievable by nonlinear mechanical metamaterials.
🤖 Through the power of differentiable simulations, the framework removes the typical limitations of metamaterial design e.g. periodicity, intuition-based design, manual tuning, single-task design, etc., and enables the automated discovery of non-periodic, multi-functional, and reprogrammable metamaterials in the nonlinear dynamic regime.
## 🚁 Overview
This repository provides a fully differentiable dynamic design framework for 2D flexible mechanical metamaterials i.e. a network of rigid units connected by flexible ligaments.
The main physical ingredients of the model are:
- 🥌 Rigid-body kinematics of the units.
- 🎈 Elastic ligaments modeled by customizable energy functions.
- 💥 Energy-based contact interactions between rigid units.
With these ingredients, flexible mechanical metamaterials define a rich space of nonlinear dynamic behaviors that can be navigated by the framework.
🔭 From a high-level perspective, the framework facilitates the construction of the mapping between design parameters and the desired behavior of the metamaterial system.
By leverging [JAX](https://github.com/google/jax), this complex mapping is implemented in a differentiable fashion, thus allowing gradients to flow through the entire dynamic simulation.
In particular, differentiability is provided with respect to:
- Geometric paramaters: arbitrary parametrizations can be defined in the [`geometry`](difflexmm/geometry.py) module.
- Ligament paramaters: energy functions can be defined in the [`energy`](difflexmm/energy.py) module.
- Damping parameters: linear viscous damping as defined in the [`loading`](difflexmm/loading.py) module.
- Driving parameters: arbitrary driving functions can be applied to any degree of freedom.
- Loading parameters: arbitrary loading functions can be applied to any degree of freedom.
- Initial conditions: initial positions and velocities of the system.
- and any other paramater present in the [`ControlParams`](difflexmm/utils.py#L145-L163) data structure.
The main entry point of the simulator is the [`setup_dynamic_solver(...)`](difflexmm/dynamics.py#L60) in the [`dynamics`](difflexmm/dynamics.py) module.
This function takes all the fixed mappings (geometry, energy, loading, etc.) and returns a differentiable function that simulates the metamaterial dynamics.
Arbitrary forward problems can be defined by chaining this simulator function with any desired objective function.
## 📜 Paper
This repository contains all the code developed for the paper:
[G. Bordiga, E. Medina, S. Jafarzadeh, C. Boesch, R. P. Adams, V. Tournat, K. Bertoldi. Automated discovery of reprogrammable nonlinear dynamic metamaterials. _Nature Materials_. (2024).](https://doi.org/10.1038/s41563-024-02008-6)
## 🎯 Solved design problems
The framework has been used to design a variety of mechanical metamaterials with different functionalities.
| | Task/tasks description | Notebooks | Data 💾 | Video |
| --- | --- | --- | --- | --- |
| 🌟 | Focusing energy at a single target location | [Quads](notebooks/quads_focusing_3dp_pla_shims.ipynb), [Kagome](notebooks/kagome_focusing_3dp_pla_shims.ipynb) | [Quads](data/quads_focusing_3dp_pla_shims), [Kagome](data/kagome_focusing_3dp_pla_shims) | [Quads](https://github.com/bertoldi-collab/DifFlexMM/assets/16863374/ff76f0bc-463d-49c4-83bb-278f301af246), [Kagome](https://github.com/bertoldi-collab/DifFlexMM/assets/16863374/537a6e32-c62d-4fdc-8a9d-e4762fda8a21) |
| ️🗡️ | Splitting energy between different target locations | [Quads](notebooks/quads_energy_splitting_3dp_pla_shims.ipynb) | [Quads](data/quads_energy_splitting_3dp_pla_shims) | [Quads](https://github.com/user-attachments/assets/7b8ea46b-ccde-4f3f-8c04-e4f9015d62e5) |
| ✨ | Focusing multiple inputs at the same target location | [Quads](notebooks/quads_focusing_multi_input_3dp_pla_shims.ipynb) | [Quads](data/quads_focusing_multi_input_3dp_pla_shims) | [Quads](https://github.com/bertoldi-collab/DifFlexMM/assets/16863374/fda885c3-ffd6-4b67-a19e-ad59d5f52a96) |
| ️💫 | Reprogramming focusing target via static pre-compression | [Quads](notebooks/quads_focusing_switching_static_tuning_3dp_pla_shims.ipynb) | [Quads](data/quads_focusing_switching_static_tuning_3dp_pla_shims) | [Quads](https://github.com/bertoldi-collab/DifFlexMM/assets/16863374/5fa5cd61-f7dc-44b4-824c-6929818e7755) |
| 🌟🛡️ | Switching between focusing and protection task | [Quads](notebooks/quads_focusing_vs_protection_static_tuning_3dp_pla_shims.ipynb) | [Quads](data/quads_focusing_vs_protection_static_tuning_3dp_pla_shims) | [Quads](https://github.com/bertoldi-collab/DifFlexMM/assets/16863374/ad4f9811-e623-4867-af42-c36ee31bcfbb) |
| 🌀 | Nonlinear motion conversion | [Quads](notebooks/quads_spin_3dp_pla_shims.ipynb) | [Quads](data/quads_spin_3dp_pla_shims) | [Quads](https://github.com/bertoldi-collab/DifFlexMM/assets/16863374/9aa2bbc9-cbe0-4896-8c83-ce67f2c61af3) |
💾 All data generated or used for the paper can be downloaded from [](https://doi.org/10.5281/zenodo.12823471).
To access and visualize the data:
- Extract `data.zip` in the root directory of the repository.
- Load and visualize optimization results for all the solved problems using the provided [notebooks](notebooks).
- Load and visualize experimental data using the notebooks in the [exp](exp) folder.
## ⬇️ Installation
### DifFlexMM only
Assuming you have access to the repo and ssh keys are set up in your GitHub account, you can install the package with
```bash
pip install git+ssh://[email protected]/bertoldi-collab/DifFlexMM.git
```
### DifFlexMM with examples of solved design problems
Clone the repository, `cd` into the `DifFlexMM` folder, and install with
```bash
pip install -e .
```
## 🤝 Contributing
Expand here
The dependency management of the project is done via [poetry](https://python-poetry.org/docs/).
To get started:
- Install [poetry](https://python-poetry.org/docs/).
- 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 vscode, search for `venv path` in the settings and paste `~/.cache/pypoetry/virtualenvs` in the `venv path` field. Then select the poetry enviroment as python enviroment for the project.
## 📝 Citation
If you use this code in your research or anywhere, please cite the paper:
```bibtex
@article{bordiga_2024,
title = {Automated Discovery of Reprogrammable Nonlinear Dynamic Metamaterials},
author = {Bordiga, Giovanni and Medina, Eder and Jafarzadeh, Sina and B{\"o}sch, Cyrill and Adams, Ryan P. and Tournat, Vincent and Bertoldi, Katia},
year = {2024},
journal = {Nature Materials},
volume = {23},
number = {11},
pages = {1486--1494},
issn = {1476-4660},
doi = {10.1038/s41563-024-02008-6},
}
```