It's straight up not physically possible to make a javelin head that is soft enough to bend *after* impact, while also being strong enough to penetrate a shield.
The weapon does not necessarily have to bend on impact, also because if it did bend on impact it would risk not crossing the shield as it should and would not hit the enemy.
The pilim must bend after penetrating the shield.
And nowhere is it written that he has to do it by harnessing the forces and energies due to the impact and the speed of impact.
These are interpretations that do not take into account the dynamics of the clashes, situations and times that the soldiers have to act.
Let's imagine the scene:
After the pilum crosses the shield (and if it hits the enemy, so much the better) the target, if left unharmed, tries to extract it, but the hooks (when there are), the shape of the tip and the discomfort of the movements (also due to at the excitement of the moment, there is a Roman at 15 meters running towards him) they do not allow it and begins to move it with force, perhaps rotating it around the fulcrum (the hole in the shield).
If the metal meets the following conditions:
1) the impact force applied along its length does not generate bending and allows it to break through wooden shields.
Considering that they were throwing from a not too great distance, the accuracy in the throw and the target that raised the shield in the direction of the incoming pilum, gave angles of impact such that the forces acting on the axis of the pilum were as much parallel to the axis as possible. same.
2) fixed a fulcrum and fixed the resistances linked to the constraints (the constraint forces generated during an attempt to bring the tip towards the entry hole and the subsequent non-exit from the hole) and applied a force orthogonal to the axis of the metal rod (always trying to get it out), it would have to bend.
In those few seconds, our target of the example ends up bending the pilum, because he cannot be precise in removing it as his gaze goes from the shield to the Romans, from the Romans to the shield and sees that the Romans are first at 20 meters, then at 15, then at 10, while he with all his strength tries to get that damned javelin out.
So the metal must be such as not to bend on impact (forces generally parallel to the axis), but to bend subsequently IF there are forces applied not parallel to the axis (guy who wants to extract it) and resistances (the wood of the shield, maybe even the arm or part of the body of the soldier that prevents the tip from rotating and moving, the fact of keeping the shield on the ground to extract the pilum means that the ground does not rotate the part penetrated into the shield).
only a slight bend is needed to "make the draw tedious" and make the target decide to throw the shield, because while he tries to draw, there is a Roman 15 meters running towards him.
There were probably different variants of the pilum over time, but the laws of physics prevent any of them from bending the way they do in most people's imagination.
The problem is when the laws of physics are applied to support a thesis.
If it is said that the metal must bend as a result of the energies and momentum due to the impact(longitudinal foces), then I agree that the pilum either bends and does not break through the shield, or it breaks through the shield and does not bend.
But if the metal has to bend as a result of the attempt to extract the pilum (trasversal forces), then the forces involved and their directions are not those due to the impact, but rather the man's attempt to extract the pilum from the shield (which in itself would be already complicated even if it did not bend).
If the one who has to remove the pilum has the shield on his left arm and tries to remove it with his right, trying not to lower his guard too much, he ends up applying orthogonal forces to the pilum axis, which could bend it.
In any case, the goal is not: "the pilum must bend at all costs", but "let's make the extraction of the pilum more tedious and time-consuming".
If it bends by means of the forces due to extraction ,? well, the enemy throws the shield.
If it bends on hitting a rock? well, the enemy won't throw it back at me.