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I saw in a scientific paper that if a medium is too anisotropic, it becomes like a layered meduim and I don't know why. So my question is the following: Why more level (degree) of anisotropy of the elasticity tensor (matrix) $C(\mathbf{x})$, means that the corresponding medium tends to a layered medium?

PS: the level of anisotropy of the medium can be defined as the distance between the tensor $C(\mathbf{x})$ and the equivalent isotropic tesnor $C_{eqv}^{iso}(\mathbf{x})$.

Many thanks in advance

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    $\begingroup$ I don't know why either, since I regard anisotropy (of the crystal structure, say) as quite distinct from a layered medium (where I would expect interfaces). Things perhaps get blurred at graphitic-like structures, but even so... $\endgroup$
    – Jon Custer
    Jul 27, 2017 at 13:43

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The paper may be making the point that the highest degree of anisotropy is achieved when two dissimilar materials are arranged in a bonded layered configuration.

Consider a layered structure of equal thicknesses of rubber and steel, perfectly bonded, where the layering occurs along the 3-direction. If I pull on the material in the 3-direction, I'm going to measure an effective stiffness of twice the stiffness of rubber. (If this is not intuitive, please refer to the rule of mixtures.) If I pull on the material in any combination of the 1- and 2-directions, however, I'll measure an effective stiffness of half the stiffness of steel.

This is an enormous degree of anisotropy, with the stiffness varying by many orders of magnitude depending on the loading direction, originating from the layered configuration. By contrast, other configurations with the same components don't exhibit this same degree of anisotropy; for example, randomly dispersed small chunks of steel encased in rubber would compose an approximately isotropic material.

Thus, the reasoning that increasing anisotropy leads to a layered composite is backwards. In engineering, we don't have a direct knob for anisotropy; we do have a direct knob for a manufacturing process that produces bonded layers. However, in nature, if you observe a highly anisotropic material, it is reasonable to posit a layered configuration, and even to deduce the orientation of the layers. Perhaps this is the point the authors were trying to make.

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  • $\begingroup$ Thank you very much for your detailed answer and clarifications. It helped me a lot. $\endgroup$ Jul 28, 2017 at 9:31

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