I am trying to understand how an anvil might best be made. An anvil requires two essential characteristics: enough hardness to not be deformed under the blows of the hammer, but as little rebound and spring as possible. It is not good if the hammer bounces off the work. Ideally we want the work to absorb as much energy as possible from the hammer and be a "dead blow". Note that here I am speaking of a blacksmith's anvil, but the same principles apply to large, machine-driven power forges as well.
In the old days anvils were made from wrought iron, welded together in several large chunks. The shapes of these pieces was considered a valuable trade secret by anvil makers. Later, around 1850, it became the practice to weld a slab of steel about 3/4" thick on top of the anvil to make it harder and more resistant to deformation than plain wrought iron. Red hot steel is a somewhat plastic material, but it will wear away at wrought iron eventually and form divots and creases that require the anvil to be painstakingly resurfaced. Around 1900 the wrought iron was dispensed with entirely, due to expense, and replaced with cast iron and today anvils are either cast iron with steel tops or in some cases are solid cast steel.
The old wrought iron anvils are still sought after and fetch a premium price from blacksmiths. I cannot tell much of a difference myself, but supposedly they have a better feel than cast iron anvils. The ring of the hammer is definitely different on both. In fact, even anvils of the same style will have a different ring.
My question is how to understand (1) what causes rebound and (2) what theory should be applied to govern the design of an anvil to minimize rebound.