A group of researchers from the Karlsruhe Institute of Technology (KIT) in Germany and the French National Center for Scientific Research, inspired by evolving 3-D printing capability, set out to explore the development of a mechanical property called effective static compressibility. As they now report in Applied Physics Letters, from AIP Publishing, by using a single cartridge it's possible to print a metamaterial that expands in size under hydrostatic pressure, even though it's made up of material that normally shrinks under hydrostatic pressure. In principle, there is no limit to the negative value this material's effective compressibility can take.

At the heart of the group's design for the metamaterial structure is a hollow, 3-D cross structure with circular membranes at each end of the cross.

According to researchers, these membranes will warp inward if the outside pressure is larger than the pressure in the enclosed volume inside the cross. By properly connecting these membranes via bars, and by using eight such three-dimensional crosses within one unit cell, it's possible to obtain an isotropic effective volume increase upon increasing the pressure—a negative effective compressibility.

The work is interesting because, according to researchers, a negative compressibility under static and unconstrained conditions is generally forbidden by the laws of physics. The trick of the structure is that the volume you can see increases upon increasing the surrounding pressure, whereas the volume enclosed by the 3-D printed material—a quantity that you don't perceive directly—decreases and makes the structure both stable and physical.

One of the metamaterial structure's special properties is a zero negative effective compressibility, which means that the metamaterial's effective volume simply won't change.

With the success of the structure's extensive modeling, the group has already started to pursue the demanding task of demonstrating its fabrication.

Researchers have calculated the behavior of the material using engineering simulation software, so the material has yet to be fabricated and measured experimentally. Fabrication is a demanding case for 3-D laser nanoprinting because the necessary concealed inner volumes haven't previously been achieved.

Making such a metamaterial would probably not be possible with conventional machining techniques, which tend to remove material to build a structure. With an additive technique like 3-D printing, however, fabricating concealed structures and enclosed volumes becomes possible making this an ideal way to create negative compressibility metamaterials.