= Incremental elastic moduli
{title2=$c_{\alpha i\beta j}=W_{,A_{i\alpha}A_{j\beta}}$}
= Incremental elastic modulus
{synonym}
For unconstrained <hyperelastic material>, the <Hessian> of the <strain energy density> gives $\delta N_{\alpha i}=c_{\alpha i\beta j}\delta A_{j\beta}$. Commuting the second derivatives gives major symmetry $c_{\alpha i\beta j}=c_{\beta j\alpha i}$. These material-coordinate moduli linearize about a finite base deformation; they need not have the minor symmetries of a small-strain <elastic stiffness tensor>. Material constraints require their additional reaction increments and admissibility equations.
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