Deformation/Fracture from Impact What equations predict the deformation from two objects colliding? Such as dropping a heavy ball onto a plate of metal. Source references would help, I havent found much anything yet.
 A: 
What equations predict the deformation from two objects colliding?

There are two possible types of deformation: Elastic and inelastic. For a perfectly elastic collision, the deformations of the two objects are totally recoverable so that the total kinetic energy before and and after the collision is the same. For source references, look up "perfectly elastic collision". To determine the amount of elastic deformation of each object, which would equal the elastic potential energy of each object, you can treat the two objects as ideal springs.
However, all real collisions at the macroscopic level are at least partially inelastic. Meaning there is some permanent deformation of one or more colliding objects such that the permanent deformation energy equals the loss of macroscopic kinetic energy of the objects. The coefficient of restitution of the collision, which is the ratio of the final to initial relative speed of the two objects after they collide, can be used to determine the loss of kinetic energy. Look up "Coefficient of Restitution".
So for your example of dropping a heavy ball on a plate of metal, the energy lost to permanent deformation of the combination of the ball and plate would equal the kinetic energy of the ball just prior to impact with the metal plate,  minus the kinetic energy of the ball immediately after impact with the metal plate, assuming the metal plate remains stationary.
Hope this helps.
