1.I.6B

Write down the general isotropic tensors of rank 2 and 3 .

According to a theory of magnetostriction, the mechanical stress described by a second-rank symmetric tensor $\sigma_{i j}$ is induced by the magnetic field vector $B_{i}$. The stress is linear in the magnetic field,

$\sigma_{i j}=A_{i j k} B_{k},$

where $A_{i j k}$ is a third-rank tensor which depends only on the material. Show that $\sigma_{i j}$ can be non-zero only in anisotropic materials.

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