As the name says, only with the prototype, the workpiece is created. It must exist before it can be re-shaped. Only solid objects can be re-shaped, and in fact only those which are sufficiently malleable. Thus e.g., lamellar-graphite cast iron does not lend itself to bending.
So, a material can be allow itself to be bent, it may break (cast iron) or it may return to its original shape when the bending force is removed, this is called elasticity. Basically, the amount of force applied for the re-shaping, depends on the elasticity limits. Re-shaping is a matter of overcoming these limits.
The reason for this, is the attraction force of the atoms to each other. They are separated from each other through the linear shifting in the crystal lattice. Should the distance still be too small or if the attracting forces are strong enough, it could return to the initial situation. Otherwise, the atoms moving away, find themselves in the area of others. The distortion then remains.
The same as in the milling of steel, bending can be carried out in a cold or a warm state. The latter exploits the lower connecting forces of a warm material with less resistance to bending, to reduce the forces necessary to carry out the bend. One speaks of a working temperature which is higher than the recrystallization temperature.
Apart from the material-type and it's temperature, the bending forces also depend on the cross-section of the material and on the individual pressure points. The resistance to bending also has directly to do with resistance to tension and pressure. Mostly, it is proportional to at least one of the two.
Whether it's a pipe or a solid material, when being bent, there is always an inside layer, which is being compressed and an outer layer, which is being stretched. Between the two, is the so-called neutral fibre. This can be used to determine the original length of, e.g., a piece of flat steel before it was bent, i.e., if the radius is not too small.
Have a look at the long pipe in the foreground. In this case, the neutral fibre is more recognizable from above. This is clearly marked by the continuous welding bead. Because welding beads are not suitable for deforming, they are used as little as possible as neutral fibres.
In vehicle manufacturing, apart from the coachwork area, the bending of piping is predominant, since solid material, as far as solidity is concerned, is simply too heavy. In the above picture, you can see one type of pipe-bending, where keeping an even cross-section is not that important. On the other hand, in the picture below, is a pipe which has presumably, been partially widened through hydro shaping using water pressure. 05/14