超弾性
Φ ^ ( α C ) = Φ [ ( d e t α C ) − 1 3 ( α C ) ] = Φ [ ( α 3 d e t C ) − 1 3 ( α C ) ] = Φ [ ( d e t C ) − 1 3 C ] = Φ ^ ( C ) {\displaystyle {\hat {\Phi }}(\alpha {\boldsymbol {C}})=\Phi [(\mathrm {det} \,\alpha {\boldsymbol {C}})^{-{\frac {1}{3}}}(\alpha {\boldsymbol {C}})]=\Phi [(\alpha ^{3}\mathrm {det} \,{\boldsymbol {C}})^{-{\frac {1}{3}}}(\alpha {\boldsymbol {C}})]=\Phi [(\mathrm {det} \,{\boldsymbol {C}})^{-{\frac {1}{3}}}{\boldsymbol {C}}]={\hat {\Phi }}({\boldsymbol {C}})}
ここで、 I I I C = d e t C {\displaystyle III_{C}=\mathrm {det} \,{\boldsymbol {C}}} を用いた。