In everyday experience, when you stretch something it gets thinner and when you compress it gets thicker. A new class of materials called auxetic materials behave in the opposite way. Here’s a quote from the ScienceDaily:

When a usual material is, for example, hit by a ball, the material “flows” outward from the impact zone making the point of impact weaker. However, in auxetic materials, the matter “flows” inward, thus strengthening this zone. Such materials would be advantageous for bulletproof vests. Auxetic materials also provide interesting possibilities for medical technology. The introduction of implants such as stents to hold open blood vessels would be easier if, under pressure, the device would get thinner instead of thicker in the perpendicular direction.

ScienceDaily: Unusual Rods Get Thicker When Stretched, Thinner When Compressed