Topology and materials design
Why does the Eiffel tower not fall down?

The key answer: topology. Topology helps us figure out out how different parts of an object are connected to each other. In other words, it describes the object’s architecture.

It’s precisely their architecture that sets how structural materials act: why the Eiffel tower doesn’t fall over, why bones don’t spontaneously break, and why a table is the perfect place to put your coffee cup.

The logical next step: using topology as a design tool for structural materials.

How does that work? Here’s a short primer:

Topological polarization dictates where a simple structure is floppy, and where it’s stiff. Just like electrical polarization localizes negative and positive charges.

From 2014 to 2015, I had the pleasure of working with Vincenzo Vitelli and Jayson Paulose at Leiden University. Building on seminal work by Charlie Kane and Tom Lubensky, we investigated how to use topological polarization to design a structure’s locally hard and soft spots.

Our work showed that this idea doesn’t just work in a computer model, but in real, three-dimensional structures. And beyond simple bars and hinges, we found out how to use different mechanical elements to harness the same effects– see the video below.

Topology is a powerful tool for materials design.