Step 1: Recognize the process family.
The question is describing metal forming operations like forging, rolling, and extrusion, where a shape change happens by pushing or squeezing metal, not by cutting it away or melting and recasting it. Because the mass and volume stay the same before and after, this rules out machining and casting right away, and points us toward a deformation based process.
Step 2: Separate elastic behaviour from plastic behaviour.
Every metal first stretches or compresses a little elastically when a load is applied, and that part is fully recoverable, the metal springs back the instant the load is removed. If the process only used elastic deformation, the shape change would vanish and nothing permanent would be produced, which contradicts the idea of metal being displaced from one location to another in a lasting way.
Step 3: Confirm why plastic deformation fits.
Once the applied stress crosses the material's yield point, the metal flows permanently, atoms slip past one another along crystal planes, and the new shape stays even after the load is taken off. This permanent, volume conserving flow of material is exactly plastic deformation, and it is the working principle behind forging, rolling and extrusion.
\[ \boxed{\text{Plastic deformation}} \]