Are there solid materials that begin as isotropic materials (i.e. isotropic elastic parameters) in their natural (i.e. unstressed) state, but that become anisotropic under sufficient stress/strain? What would it take to modify an existing material with isotropic elastic properties to have anisotropic elastic properties?

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    $\begingroup$ While googling a little bit I found that there exists indeed (elastic) stress-induced anisotropy on solid materials and granular materials, some of the literature focuses on 'rocks' (just like that). I didn't read the papers so I dont know the mechanism behind this phenomenon, but there's definitely info online to read about. $\endgroup$
    – user190081
    Nov 3, 2018 at 14:22
  • $\begingroup$ @user190081. That’s great! Sometimes just knowing what terms to search for helps a lot! :) $\endgroup$
    – Paul
    Nov 3, 2018 at 16:56

1 Answer 1



Deformation induced anisotropy is ubiquitous in materials, whether they are metals, polymers, foams, soils, rocks etc. A typical example is any rolled metal product.


If you wish to deal only with purely elastic deformations, you have to define what elastic properties mean and how you will measure these properties.

Suppose that you are interested only in small-strain elasticity in a single crystal, perfectly annealed and free of defects. If you deform the crystal, do the elastic properties of the crystal change depending on the direction of deformation? Keep in mind that no solid material is truly isotropic except for some glasses.

Assume that the speed of propagation of a wave in a particular direction of the crystal is a proxy for the elastic properties of the crystal in that direction. When you compress the crystal, the atomic spacing decreases and the wave takes a shorter time to travel, i.e., the elastic modulus increases in that direction and the crystal anisotropy increases. However, the induced anisotropy is small and not permanent. See, for example, https://www.sciencedirect.com/science/article/pii/0041624X63900039 and the Acousto-elastic effect.

Any permanent anisotropy requires an increase in entropy via plastic dissipation, microcrack growth etc.

For induced anisotropy in bulk metallic glasses, see https://www.sciencedirect.com/science/article/pii/S1359646211001072

  • $\begingroup$ OP is asking about induced anisotropy under elastic deformation, a rolled metal product has anisotropy because it grains have been plastically deformed. $\endgroup$
    – user190081
    Nov 5, 2018 at 16:35
  • $\begingroup$ @user190081: I don't read the question that way. Perhaps better to ask the OP? The OP asks about elastic moduli post deformation, not elastic deformations. $\endgroup$ Nov 5, 2018 at 20:09
  • $\begingroup$ Maybe OP meant something else, but it is completely clear from the the title of the question that he is asking: Can isotropic materials become anisotropic under elastic deformation? $\endgroup$
    – user190081
    Nov 5, 2018 at 20:28
  • $\begingroup$ @user190081: I see. Missed that detail. $\endgroup$ Nov 5, 2018 at 20:54

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