= Elastic stiffness tensor
{title2=$\sigma_{ij}=c_{ijpq}\partial_pu_q$}
An <elastic stiffness tensor> maps a small <displacement gradient tensor> to the <stress tensor>. Minor symmetries in each index pair ensure symmetric <stress> and dependence only on symmetric <strain>; major symmetry $c_{ijpq}=c_{pqij}$ follows from an <elastic energy> and underlies reciprocity. Stability requires positive <elastic energy> on nonzero strains. In an isotropic material, $c_{ijpq}=\lambda\delta_{ij}\delta_{pq}+\mu(\delta_{ip}\delta_{jq}+\delta_{iq}\delta_{jp})$, with <Lamé parameters> $\lambda,\mu$.
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