DifFlexMM

Differentiable Flexible Mechanical Metamaterials

movie_s3_astronaut_light.mp4

🌅 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, 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 module.
• Ligament paramaters: energy functions can be defined in the energy module.
• Damping parameters: linear viscous damping as defined in the loading 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 data structure.

The main entry point of the simulator is the setup_dynamic_solver(...) in the dynamics 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).

🎯 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, Kagome	Quads, Kagome	Quads, Kagome
️🗡️	Splitting energy between different target locations	Quads	Quads	Quads
✨	Focusing multiple inputs at the same target location	Quads	Quads	Quads
️💫	Reprogramming focusing target via static pre-compression	Quads	Quads	Quads
🌟🛡️	Switching between focusing and protection task	Quads	Quads	Quads
🌀	Nonlinear motion conversion	Quads	Quads	Quads

💾 All data generated or used for the paper can be downloaded from . 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.
• Load and visualize experimental data using the notebooks in the 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

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

DifFlexMM with examples of solved design problems

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

pip install -e .

🤝 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 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:

@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},
}