There are a lot of different things that can happen, based on material and lattice structures temperature, etc.

If it's elastically deformed and released, the stored energy snaps it back into place.

If you deform and hold it, the stored energy can cause the lattice structure to shift over time in a process called ratcheting in order to permanently deform. Increased temperature speeds up the process.

If you go past elasticity, then you can think of the material acting like ice flows moving around past one another, though on a macro scale, it tends to act like a really stiff taffy, depending on the ductile nature.

It can even change the lattice structure from one kind to another, giving it properties of the same material in those alternative lattice structures.