We made crumple zones in class. The aim was to keep a marble on the trolley even after a crash. The brick wall caused the front to deform. You can argue by energy that the deformation uses up energy that would otherwise have been transferred as kinetic. But we used a momentum argument. Same mass and speed meant same change in momentum as the trolley came to a stop. But the crumpling means that it takes a longer time to stop. There is a smaller rate of change of momentum and thus a smaller force.
I did like the following design!
