Ok - this is a moderately tough question which I can't figure out. So I am trying to work on a simplified model to start with. I imagine a solid, very massive impenetrable object. I have a tube or any long object which can exhibit some elastic behavior and also plastic behavior. If the tube hits the much larger massive object at slow speed I reason that it pretty much just stops dead in it's track - tiny bit of bounce but a low low restitution constant. Above a certain speed, when the tube hit the wall, the force required to cause plastic deformation is exceeded and so the tube is crushed. The high the speed the more it gets crushed. Now, finally getting to the question: If I measure the deceleration of the tube, at the end of the tube, furthest from the wall, so the end that is not being crushed, what equation can I use to calculate the deceleration? It seems like it is at least a first or maybe second order differential equation because the tube's length is not constant and hence its center of gravity is shifting towards the rear. Also there must be a point where it slows down to a point where it no longer has enough momentum to cause plastic deformation. But I am just not quite sure where to start. Cheers and thanks for reading.