= Saint Venant–Kirchhoff hyperelastic energy
{c}
{title2=$\mathcal W=\lambda(\operatorname{tr}E)^2/2+\mu\operatorname{tr}(E^2)$}
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.
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