Great questions Robin! I'll answer your questions in reverse.

1) Helmets typically have two parts to them: an outer shell made of polycarbonate and a body made of polystyrene foam. The foam body is relatively soft and can absorb a lot of energy, but is vulnerable to being punctured or cut. The outer shell is relatively hard and protects the foam, but does not absorb much of an impact. When an impact occurs, the shell helps to spread the force evenly over the entire helmet, rather than have it be totally localized to the impact site.

2) Bicycle helmets are tested by filling them with 11 pounds of lead and dropping them at 14 miles per hour. This corresponds to about 100 Joules of energy. When an impact does occur, the soft part of the helmet is typically permanently crushed, so if another impact occurs it won't be able to absorb as much energy. For this reason it is important to replace your bike helmet after a crash.

3) Studies have found that wearing a helmet reduces the rate of injury by 60-80%. This is a pretty significant decrease in risk, but no helmet is perfect!

Different types of helmets are made from different materials and can protect from different hazards. For example, hard hats protect the head from falling objects, are made of a polymer material called high-density polyethylene and can withstand a 2.2 lbs heavy and pointy object dropped from 8 ft above onto the helmet. Bicycle helmets are made out of a polycarbonate shell over expanded polystyrene foam and protect the head from impacts. The polycarbonate shell is supposed to crack on an impact and distributes the energy of the impact over the polystyrene foam. This foam then compresses while absorbing the energy and protecting the head.

In contrast, military helmets like the Advanced Combat Helmet (ACH), used by the U.S. Army, are made of Kevlar fiber. They can protect the head from bullets, shrapnel, and explosions. It is hard to estimate the exact energy this helmet can absorb. For example, the value depends on the distance of the helmet to the explosion and the relative orientation of the helmet towards the blast. In order words, if the blast hits the helmet from the top or from the side. However, a very rough estimation can be obtained using the tensile strength of the helmet. This is a measure for how much pressure can be applied to the helmet materials before it breaks. The ACH has a tensile strength of 7400 Mega Pascal and an area of 516 cm².

Using these values, it can be estimated that the helmet can withstand a force of 381 Mega Newton distributed over the area of the helmet. If this force is applied over the thickness of the helmet of 8.4 mm, this equals an energy of 3.2 Mega Joule that is needed to break the helmet. 1 Kg of the explosive TNT stores an energy of 4.6 Mega Joule. This means that the helmet can withstand the energy of an explosion of about 0.7 Kg of TNT in direct contact with the helmet while assuming that the helmet will absorb all the energy of the explosion.

In a real scenario, the explosive would be further away from the helmet and only a small fraction of the energy of the explosion would be absorbed by the helmet, which means that it can withstand a larger explosion. However, even if the material of the helmet withstands the blast, the human head can still be hurt from the impact of the blast.