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The stiffness (aka. tangent modulus of the stress) can be represented as a symmetric 6-by-6 matrix, i.e. it has 21 independent components in the most general case. In the linear case, this matrix is constant, whereas in the non-linear case it depends on the current state of deformation. The following questions addresses both the linear and the non-linear case.

  1. Is there any material with a dense stiffness matrix? By this I mean that none of the entries are zero.
  2. If so, is there any material for which all the 21 components are independent of each other?
  3. If the answer to 2. is no, then which material has the most independent components?

I want to explicitly include meta-materials as possible candidates, i.e. structures with homogenizable mechanical response functions.

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    $\begingroup$ Fully anisotropic materials have their normal and shear modes of deformation coupled. That coupling occurs in most materials (even though the coupling factors may be small). The simplified material models we use are only approximations of that behavior inspired by the symmetries of perfect crystals. $\endgroup$ – Biswajit Banerjee Oct 11 at 22:18

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