Warning: attempt at internally-consistent handwaving.
Based on answers clarifying what asker is trying to achieve, I see only one explanation: Make it susceptible to acceleration.
Normal materials are concerned with force, not acceleration, and break apart if applied force is greater than for example it's tensile strength. This material is different: no matter what force is applied, it becomes relatively fragile when it accelerates (this is "the big lie", rest is derived from this quality). Even accelerating, it can easily outperform ordinary materials, but it's the strongest when it's still or moving at constant speed, easily defeating bullets made of same material.
In practice, this means that it's great for construction, or perfect for armours and non-moving parts of weapons (like barrels, but not locks, at least not without extreme redesign) but terrible for blades, bullets or shells: 9 mm bullet weights about 100 grams and is moving at 400 m/s giving it momentum of 40 kg*m/s, same as 80 kg human moving at 0.5 m/s. During impact, bullet is subject to extreme deceleration while it transfers almost all of it's momentum to wearer, wearer on the other hand is only slightly affected - bullet becomes much more fragile than armour and shatters.
This means, that humans wearing such armour are completely immune to small arms fire, and any "indestructible" projectile lighter than target (assuming target isn't anchored in any way) will shatter and has to rely on other properties than penetration to make a kill (120mm Abrams cannon: ~8 kg projectile, 1700 m/s, after impact 80 kg wearer would be sent flying at ~150 m/s, which without liquid breathing should kill him anyway, but shell is subjected to almost 10 times higher acceleration than armour), which means that "indestructible" projectile has no advantage over normal projectile.
In practice, this remarkable property would have very interesting impact on modern battlefield: armoured infantry becomes immune to shrapnel and small arms fire, airburst bombs and artillery become completely ineffective because ground itself protects from acceleration/deceleration. The main way to kill infantry is to use projectiles and explosions intended to send them flying, killing them within armour. Infantry on the other hand is most likely equipped with some means to quickly anchor themselves to the ground/surrounding for increased protection when located in exposed or otherwise dangerous spot. As technology develops, increased weight of powered armour becomes a great boon, in addition, anchors can easily become part of armour, deploying automatically when radar detects incoming fire (same as anti-missile systems used on modern tanks). The only sure way to kill, is to use shell heavier than target, while target is in air or space.
Edit to explore effects a bit more:
Tanks become effectively immune to any regular weapons, but are not cost effective compared to infantry, infantry on the other hand is completely immune to regular weapons wielded by other infantry, this heavily changes infantry tactics:
- use flamethrowers to cook them alive
- hand to hand combat to subdue enemy and either physically kick out of borders, or drown/bury alive (could take a while if internal oxygen tanks become regular part of armour)
- Weaponise whatever production process is used to shape this material
- much higher reliance on flash-bangs and other means to incapacitate enemy while you are getting close to pry him out of his armour
- Flame-throwers (again)
- charges (mines, bombs, precision shells and missiles) designed to flip tank around, taking it out of action without destroying it
- Weapons intended to take out cameras, and obscure vision ports, rendering tank inoperable (smoke bombs? guided double warhead tar-and-feathers missiles?) and let infantry take it all the way down with flamthrowers.
In practice that removes tanks from battlefield, because increase in protection over infantry is not worth costs and loss in versatility and mobility, unless tanks can carry weapons that CAN damage this material while same weapons are impractical for infantry. For example, tanks could use laser/plasma weapons which are too big even for powered armours (something about fusion chamber sizes and energy requirement necessitating use of reactors?) but can penetrate this astounding material.
The way I see it, end result is a mess where infantry fights each other in melee and literally dismantles tanks if let close, while tanks rule supreme in open terrain.
Hmm, it's not actually THAT different.