Isotropic linear magnetostriction vanishes ($A_{ijk}=b{ϵ}_{ijk},{\sigma }_{ij}=A_{ijk}{B}_k=0$)

Under proper rotations a third-rank isotropic tensor is proportional to the Levi-Civita symbol. Its contraction with a field vector is antisymmetric in the two stress indices. A physical symmetric stress therefore vanishes in this linear constitutive model. Under the full orthogonal group an ordinary isotropic third-rank tensor is already zero; the orientation-sensitive Levi-Civita tensor requires the usual pseudotensor distinction.