Growth under pressure: New metamaterial designed with counterintuitive property

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In the not-too-distant future, it may be

possible to 3-D print virtually anything. Consider standard printers,

which "synthesize" thousands of colors by using only three color

cartridges. By analogy, future 3-D printers may be capable of

synthesizing thousands of different material properties with a mere

handful of material cartridges.

This concept inspired a group of researchers from the Karlsruhe

Institute of Technology (KIT) in Germany and the French National Center

for Scientific Research to explore such development of one 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 which expands in size under hydrostatic pressure, even

though it's made up of material which normally shrinks under hydrostatic

pressure. In principle, there is no limit to the negative value this

material's effective compressibility can take.

"[O]ur poroelastic three-dimensional metamaterial, a human-made

composite material that exhibits properties not found in natural

materials, effectively expands upon increasing the hydrostatic pressure

of a surrounding gas or liquid," said Jingyuan Qu, a doctoral student

and researcher at KIT's Institute of Applied Physics and Institute of

Nanotechnology. "For most materials, the behavior is the exact opposite.

At first sight, a negative compressibility even appears to violate

fundamental laws of physics."

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


"Akin to a drum, these membranes will warp inward if the outside

pressure is larger than the pressure in the enclosed volume inside the

cross," Qu said. "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."

This is particularly intriguing work, Qu pointed out, because a

negative compressibility under static and unconstrained conditions is

generally forbidden by the laws of physics.

"It's unstable and violates energy conservation," Qu said. "The trick

of our 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, according to Qu. "This means that

the metamaterial's effective volume simply won't change," he said.

With the success of the structure's extensive modeling, the group has

already started to pursue the demanding task of demonstrating its


"We've calculated the behavior of the material using [engineering

simulation software], so the material has yet to be fabricated and

measured experimentally," Qu said. "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


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