SIAM News Blog

Design Tools for Metamaterials Bring Humans Into the Loop

By Jillian Kunze

Figure 1. A diagram illustrating metamaterials as machines. Figure courtesy of Alexandra Ion.
The democratization of three-dimensional (3D) printing has allowed the development of metamaterials—materials with unique abilities like changeable volume, tunable shock absorption, and locally varying elasticity—to flourish. “The definition I prefer for mechanical metamaterials is that they are artificial structures with unusual properties that originate in their geometry, rather than in the specific material they are made of,” Alexandra Ion of Carnegie Mellon University said. “To surpass traditional materials, you want to think of making geometric structures that have some kind of interesting properties.” Metamaterials are made up of many cells that work together — a single cell on its own will not have the same properties.

During a minisymposium presentation at the 2022 SIAM Annual Meeting, Ion explored different aspects of designing metamaterials with humans in the loop. “The question for me was ‘Wait, what else can they do?’” Ion said. She wanted to take a different perspective and think of metamaterials more like machines, in that the structure embeds functionality and reacts to simple input with complex behavior (see Figure 1). There are several different types of functionality to consider: robotic movement, computational capabilities, communication with users, and mass fabrication (in the future, once technology allows). All of these functionalities are governed by the ability to create complex geometry.

Figure 2. A 3D-printed metamaterial door knob that includes both rigid and shearing cells to create the desired type of movement. Figure courtesy of Alexandra Ion.
The first area that Ion discussed was analog metamaterials with actuation, in that the structure allows the material to implement complex motion. She provided an example of a doorknob that incorporates the ability to turn a handle into the structure of the metamaterial (see Figure 2). Her research lab creates these kinds of metamaterials by breaking the form of an object down into a grid with many cells: both rigid cells and shearing cells, the latter of which allow for continuous directional movement. Other examples of items that can be made as analog metamaterials with actuation include pliers and a pantograph that copies a drawing as a user makes it.

To help bring more people into the loop for developing these kinds of metamaterials, Ion’s group built software that can run in an internet browser and which iterates over a design to create a good metamaterial structure for a particular object. Though contemplating the full range of metamaterial abilities is quite a broad topic, approaching it from a human-computer interaction angle enables many different people to contribute unique ideas. Giving humans fast and simple tools to explore potential metamaterial structures provides the opportunity to develop creative designs to people with different experience levels.

Since designing metamaterials is quite difficult, the inverse design tool that Ion described helps tell the user where to place rigid and shearing cells in order to create the movement that they desire. This can be a challenging discrete optimization problem, since there are numerous discrete cells and a huge search space. In order to make searching easier, Ion’s group modeled unique mechanics with a constraint graph; operating on this constraint graph rather than a cell grid reduces the search space by quite a bit.

Figure 3. A metamaterial door lock that employs combinational logic. Figure courtesy of Alexandra Ion.
The next focus of the talk was metamaterials that are digital in the sense that they have two states and do not lose energy when triggered. Such metamaterials can be used for decision-making by employing combinational logic that computes an output to change the metamaterial. One example application is a door lock (see Figure 3). Putting multiple bistable springs in a row allows for signal transmission, so that logic gates can be made out of a metamaterial. Developing a material with tiny actuators everywhere could potentially lead to even more complex patterns.

For the metamaterial functionality of interfacing with the user or the environment, Ion provided an example of shoe treads that can configure in different ways to work with different ground surfaces and activities. The treads’ simple cell design allows for a variety of textures.

Moving along to the easy fabrication of metamaterials, Ion described redesigning metamaterials to be manufacturable by laser cutting, meaning that they must unroll to the plane. Laser cutters are a much faster method of manufacturing than 3D printing. This enables simple fabrication for end-users, allows for hands-on learning, and could potentially lead to mass fabrication in industry. Making metamaterials more practical in this way increases the chances that they will be utilized in the real world.

Figure 4. A metamaterial teddy bear made out of laser-cut paper loops. Figure courtesy of Alexandra Ion.
Particularly, Ion explained how her group laser cut paper into shapes with hooks that can form loops, which can then be combined to make volumetric metamaterials (see Figure 4). These shape-based objects work well as an educational tool. The research group created a design algorithm that uses an inverse design loop to fill a shape with paper ruffles that intersect with the shape’s outline. The tool can then export the result for laser cutting, and users reconfigure the laser-cut paper into the desired shape after fabrication. Moving forward, Ion’s group is very interested in stiffness optimization of such cuttable metamaterials. 

Ion concluded her talk by reminding the audience that geometry is key for all of these metamaterial applications. “Ask the question, how far can you push it?” Ion said. “How far can you go?”

More information, videos, and publications can be found on the Interactive Structures Lab website

  Jillian Kunze is the associate editor of SIAM News


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