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With the right Cauchy-Green deformation tensor $C=F^{T}F$, the Green-Lagrange strain tensor measures the change in the material metric. Since ${\dot{E}}^{(2)}=F^{T}DF$, its work-conjugate stress and strain partner is the second Piola-Kirchhoff stress tensor $F^{-1}\tau F^{-T}$. The formula follows by cycling factors in $T:{\dot{E}}^{(2)}$, not by identifying nominal and symmetric material stress.

This objective isotropic constitutive model uses the Green-Lagrange strain tensor $E=(A^{\mathsf{T}}A-I)/2$. It reproduces linear elasticity at small strain. Under simple shear $A=[(1,q,0{)}^{\mathsf{T}},e_2,e_3]$, its longitudinal nominal stress is $(\lambda +2\mu )q^2/2$. Nonuniform finite shear therefore generates longitudinal acceleration, even though the corresponding infinitesimal transverse mode is uncoupled.