Methods | Part IB, 2004

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 σij\sigma_{i j} is induced by the magnetic field vector BiB_{i}. The stress is linear in the magnetic field,

σij=AijkBk,\sigma_{i j}=A_{i j k} B_{k},

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

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