= Baker-Ericksen inequalities
{c}
{title2=$(\sigma_i-\sigma_j)(v_i-v_j)>0\quad(v_i\ne v_j)$}
For a smooth objective isotropic <hyperelastic material>, the strict Baker-Ericksen inequalities require larger distinct <principal stretches> to have larger <principal stresses>. For $W=\Phi(v_1,v_2,v_3)$ and $J=v_1v_2v_3$, $\sigma_i=J^{-1}v_i\Phi_i$. The strict convention implies every stress-free state has equal stretches: if $v_i\ne v_j$ but both stresses are zero, the displayed product would vanish. Thus a <natural state of a hyperelastic material> has $F=vQ$, $v>0$, $Q\in SO(3)$. A weak non-strict inequality alone does not imply this rigidity.
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