Energy can be stored by materials in many ways. In terms of a crossbow, energy is stored by the physical change in shape of the object. As you push on it, it bends, and so a force is applied over a distance. As you release it, it unbends itself and applies a lot of force to do so, returning that energy.
To store more energy, you need to either bend it farther or make it push back harder. By thickening an object, you trade off these two aspects. Wood also doesn’t return anywhere near 100% off the energy you put in.
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