Nov 17, 2017 | By Benedict

Engineers at Rice University and Brazil’s University of Campinas have created 3D printed schwarzites—mathematical structures named after their creator Hermann Schwarz—with complex curved geometries. The researchers envision buildings being made with the 3D printed structures.

(Image: Jeff Fitlow/Rice University)

If you need a demonstration of how 3D printing has radically changed science and engineering, look no further than these 3D printed schwarzites developed at Rice University. Schwarzites, lattice structures with negative Gaussian curvature, were first hypothesize in the 1880s by German scientist Hermann Schwarz. But until the dawn of 3D printing, there was no real means of making the complex structures a reality.

The 3D printed schwarzites developed by engineers from both Rice and Brazil's University of Campinas are designed with computer algorithms before being turned into tangible polymer models. The result is a strong yet compressible plastic structure that could be used to make nanoscale electronic devices, catalysts, molecular sieves, and battery components, as well as much larger structures like buildings and airplanes.

Before any 3D printing could begin, however, the engineers working on the schwarzite project had to devise a way to make them. That job was the responsibility of materials scientist Pulickel Ajayan and researchers from the University of Campinas in São Paulo, who carried out molecular dynamics simulations to more closely examine the bottom-up construction of schwarzites and find out what shapes would work best.

"The geometries of these are really complex,” commented Rice postdoctoral researcher Chandra Sekhar Tiwary. “Everything is curved, the internal surfaces have negative curvature, and the morphologies are very interesting. "Schwarzite structures are very much the same.”

(Image: Brandon Martin/Rice University)

While the engineers have only attempted to 3D print primitive and gyroid structures, which have periodic minimal surfaces, the team thinks that the 3D printed structures could have very practical uses because of their strength and other desirable mechanical properties.

“The theory shows that at the atomic scale, these materials can be very strong,” Tiwary said. “It turns out that making the geometry bigger with polymer gives us a material with a high load-bearing capacity.”

The deformation characteristics of the 3D printed schwarzites were also to the researchers’ liking, with Tiwary noting how the structures “are beautiful because if you apply force to one side, they deform slowly, layer by layer.”

This, the engineers believe, would be an extremely valuable characteristic of, say, a building, and the 3D printed schwarzites could feasibly be printed on a much larger scale to create full-size, schwarzite-walled buildings that would be safe even in extreme weather situations, for example.

(Image: Brandon Martin/Rice University)

In fact, the researchers were slight surprised at how well their schwarzites performed: during testing (of both the computer simulations and 3D printed models), both the primitive and gyroid structures transferred loads across the entire geometry of the structure, regardless of which side was compressed.

"It is a little surprising that some atomic-scale features are preserved in the printed structures," said Douglas Galvão, a professor at the University of Campinas. “We discussed that it would be nice if we could translate schwarzite atomic models into 3D printed structures. After some tentatives, it worked quite well.”

But that doesn’t mean the 3D printed schwarzites couldn’t potentially work even better. The researchers now plan to upgrade their 3D printers to more high-resolution machines in order to produce more effective schwarzites that are lighter and which could even be made with ceramic and metallic materials.

"There's no reason these have to be blocks," said Rice graduate student Peter Owuor. "We're basically making perfect crystals that start with a single cell that we can replicate in all directions.”

The researchers’ study, “Multiscale Geometric Design Principles Applied to 3D Printed Schwarzites,” has been published in Advanced Materials.



Posted in 3D Printing Application



Maybe you also like:


I.AM.Magic wrote at 11/20/2017 8:34:41 AM:

How does it compare to other cell structures?

Richard Pasillas wrote at 11/19/2017 5:03:40 AM:

Funny! We worked these structures way back in July 2014 but viewed their potential as flexible structures. While they worked successfully, the files were huge and print times were extensive. Can’t imagine what the numbers would be like in the scale of building structures.

Sad newd wrote at 11/18/2017 5:43:50 AM:

These guys forgot to do very important and essential thing in research called "literature review" " The researchers now plan to upgrade their 3D printers to more high-resolution machines in order to produce more effective schwarzites that are lighter and which could even be made with ceramic and metallic materials." A simple google search or even google images search for "triply periodic minimal surfaces" will do the job. This is sad by all means to the scientific community. The sadest part is that it is published in advanced materials, and it went through.

Schwartz wrote at 11/18/2017 5:05:24 AM:

Check out this website, this guy is doing them out of steel, also at the microscal

Minimal surfaces wrote at 11/18/2017 5:03:10 AM:

Reigniting the wheel. Congratulations

Leave a comment:

Your Name:


Subscribe us to Feeds twitter facebook   

About provides the latest news about 3D printing technology and 3D printers. We are now six years old and have around 1.5 million unique visitors per month.

News Archive