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My textbook says that the magnitude of strain produced is the same whether the stress is tensile or compressive. So the Young's modulus, which is the ratio of (tensile or compressive) stress to the longitudinal strain, should be the same for both compressive and tensile stress.

However, my textbook gives the Young's Modulus Of Bone for Tensile stress as 16 x 10^9 N/m^2 and for Compressive Stress as 9 x 10^9 N/m^2.

Since the Young's Moduli for other substances have been given only one value for both tensile and compressive stress, I was wondering if Bone is a special case, and if so, why?

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2 Answers 2

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Well-defined, solid continuum materials generally have the same compressive and tensile Young's moduli.

The reason is that the elastic moduli measure slight displacements from an energy minimum, typically representing the equilibrium spacing of atoms balanced between attraction and repulsion. All smooth energy minima look like symmetric parabolas close up. Thus, the restoring forces from symmetric slight compression and tension are nearly identical, and so are the corresponding Young's moduli.

What about bone? Bone is a biological material with a variety of compositions and some degree of porosity. The description "bone" is too ambiguous: What bone, from what animal? Was the same material used for both the compressive and tensile tests? How did the researchers correct for the discrepancy between the measured cross-sectional area and the actual material area, given the porosity? And in particular, did the compressive displacement involve slight atomic shifting only, or did some of the struts forming the porous cells buckle, an effect that wouldn't occur in tension? (Differences in compressive and tensile behavior in such porous materials is discussed in Gibson's & Ashby's Cellular Materials.)

For these reasons, I'd expect nearly identical compressive and tensile Young's moduli in most engineering materials (solid ceramics, metals, polymers below the glass transition temperature) but am not very surprised to see different experimental results for an entry labeled simply "bone." I would agree with you (in contrast to the other answer, which I think deeply confuses stiffness and strength) that bone is a special case in this context.

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  • $\begingroup$ 'All smooth energy minima look like symmetric parabolas close up'. It is a good point.+1 $\endgroup$ Feb 11, 2022 at 17:55
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Ceramics usually are like that, large difference between compression and tension. Same for nanotubes, fiber based materials in general, bulk glass. Bone is like that too.

Few materials are the same in compression and tension. Metals, some crystals. but those are more stable and easy to measure. So we have more information about them. Probably this is why measuring just one property became popular.

But I would say materials with different compression and tension characteristics are more common in practice.

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    $\begingroup$ "Ceramics usually are like that, large difference between compression and tension." Citation, please. Remember that the context is stiffness, not strength. $\endgroup$ Feb 11, 2022 at 17:20
  • $\begingroup$ @Chemomechanics phys.libretexts.org/Bookshelves/Classical_Mechanics/… and a simple thought experiment with it: ceramic breaks after certain strain (size change), in both directions. But ceramic is much weaker in tension. So for the same strain stress will be lower in tension. Therefore Young modulus is smaller. It would be hard to make a material that has such a large strength difference as ceramic has, but same young modulus, in tension and compression $\endgroup$ Feb 11, 2022 at 17:35
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    $\begingroup$ Your link (“For many materials, Young’s Modulus is the same when the material is under tension and compression,” with a single Young’s modulus given for tension and compression of a ceramic) says the opposite of what you’re claiming. You’re still confusing stiffness with strength. $\endgroup$ Feb 11, 2022 at 18:20
  • $\begingroup$ @Chemomechanics "... There are some important exceptions. Concrete and stone ...". And concrete is ceramic. And even basic Young modulus definition should be sufficient. $\endgroup$ Feb 11, 2022 at 18:27
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    $\begingroup$ Sure—concrete is a synthetic nonuniform aggregate with some degree of porosity. I note elsewhere that such materials (I’ll include sedimentary rock) can show asymmetry in stiffness; still, I maintain that it’s useful to understand why stiffness symmetry generally appears in uniform solids. Since you’re claiming that ceramics usually have very different tensile and compressive Young’s moduli, I’d like to see a reference table from the literature. $\endgroup$ Feb 11, 2022 at 18:51

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