= Lamé parameters from hyperelastic energy Hessian
{c}
{title2=$\lambda=\rho_0W_{A_{11}A_{22}}(I),\quad\mu=\rho_0W_{A_{12}A_{12}}(I)$}
At a stress-free natural reference state, an objective <isotropic> <hyperelastic material> with energy $W$ per unit mass has $\rho_0[W(I+H)-W(I)]=\lambda(\operatorname{tr}e)^2/2+\mu e:e+O(|H|^3)$, where $e=\operatorname{sym}H$. Twice differentiating gives the displayed <Lamé parameters> and the usual <elastic stiffness tensor>. A prestressed reference requires initial-stress corrections.
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