= Full frame indifference degenerates a quadratic small-strain energy
Write a quadratic small-strain energy as $\widetilde W(F)=Q(\operatorname{sym}(F-I))$ with $Q$ homogeneous of degree two. If it were fully frame indifferent, the rotation $R=\operatorname{diag}(1,-1,-1)$ would have zero energy. Quadratic homogeneity would then make every $F_s=I+s(R-I)$ have zero energy. At $s=1/4$, $F_s=\operatorname{diag}(1,1/2,1/2)$ has determinant $1/4$, yet zero energy. Thus a nondegenerate <linear elasticity> energy cannot also be used as a fully objective finite-deformation energy. Its invariance concerns infinitesimal rotations around the reference state.
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