= Solution
In three dimensions, the general rank-two <isotropic tensor> is $a\delta_{ij}$ and the general rank-three <tensor> invariant under proper rotations is $b\epsilon_{ijk}$. Here $\delta$ is the <Kronecker delta> and $\epsilon$ the <Levi-Civita symbol>. The latter is orientation-sensitive: an ordinary third-rank <tensor> invariant under all orthogonal transformations is zero instead. This distinction does not change the stress conclusion.
For an isotropic material, the constitutive <tensor> must consequently have $A_{ijk}=b\epsilon_{ijk}$ in the proper-rotation convention. Hence $\sigma_{ij}=b\epsilon_{ijk}B_k=-\sigma_{ji}$. Mechanical stress in the model is also symmetric, so $\sigma_{ij}=-\sigma_{ij}$ and every component vanishes. Thus \b[nonzero stress linear in the field requires anisotropic material coefficients]. This is the <isotropic linear magnetostriction vanishes> restriction, not a claim that all higher-order <magnetostriction> is impossible in isotropic materials.
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