Keep in mind that the material system is in place for far more than just metals. It would be silly to have metals following a completely different system from other things, and probably wouldn't work, at any rate.
Wouldn't be completely different. It's just that metals tend to have one single yield strength that's applicable no matter how and where force is applied, except when the shape of the object changes it (which will happen with stuff made of anything).
Which means that the yield strengths across the board for metals should usually be the same, while most rocks will have a much higher compressive strength than tensile, etc.
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But Yield (Strength), Fracture, and Elasticity would seem to be the relevant variables, although it doesn't give you enough information to know what should happen after Yield is exceeded but before Fracture is reached.
Elasticity tells you that. And the difference between yield and fracture strength allows fairly good guesstimation of the elongation % at break.
And yes, stress * strain is one way to arrive at energy. The main other ones are force * distance and mass * velocity^2.
Really, I think elasticity should mainly come into play for durability, not so much for effectiveness. If your weapon is made of very soft material, it doesn't matter whether it bounces back or stays dented, it's not going to be very effective. Rubber hammer vs. wax hammer. The rubber one lasts longer, but neither hits as hard as a steel one. Elasticity would mainly matter for armor. Inelastic armor would dent and stay dented, which could exaberate a wound. On the other hand, that could be a subset of item condition; wearing a dented piece of armor aggravates injuries under it, whether the dent and the injury happened at the same time or not.
But anyway, yield strength (of the relevant type if applicable), brittleness, and hardness should tell you everything relevant about a material, for the purposes of what gives first, and how it gives, when things are whacked together. Add in elasticity to determine durability, too. And I guess brittleness could be determined either by comparing yield to fracture strength (brittle materials fracture when they yield, or very shortly after), instead of an impact test. But still, impact yield is generally expressed in energy, because force alone tells you nothing about how rapidly the force is applied.