Imagine picking up a lump of material and squeezing it, only to have it expand. The more you squeeze it, the more it expands, and to compress it, you have to stretch it back out. This is totally backwards from the way the world should work, but a new class of mechanical metamaterials could make it possible.
The way this new metamaterial would work is by taking advantage of interactions between four groups of molecules arranged in a line. The two innermost groups are weakly attracted to each other, and while they're bonded, they hold the outermost groups (which are more strongly attracted to each other) apart.
If you pull on the material, you break apart the weak inner bond, the outermost groups snap closer together, and the material shrinks. On the other hand, if you squeeze the material, you can bring the innermost groups close enough together to reform their weak bond, forcing the outermost groups apart and causing the material to expand again. Here's a little diagram of how it's set up:
This behavior is called "negative compressibility," and if you're having trouble wrapping your brain around how it works, the researchers working on this stuff (Zachary Nicolaou and Adilson Motter of Northwestern University) have these two examples of a practical application of their new metamaterial, showing how a tension force causes the material to compress:
This is all theoretical work so far, so no samples of this stuff exist yet, but the researchers are already thinking ahead to all kinds of futuristically cool potential uses for it, from the development of new actuators and new types of body armor, to deployable space structures and squishily expanding blobs that can stop superheroes dead in their tracks.