= Isotropic elasticity on tensor components
{title2=$P=(3\alpha+\beta+\gamma)T,\quad S=(\beta+\gamma)W,\quad A=(\beta-\gamma)V$}
The rank-four law $c_{ijkl}=\alpha\delta_{ij}\delta_{kl}+\beta\delta_{ik}\delta_{jl}+\gamma\delta_{il}\delta_{jk}$ sends a strain array to $P_{ij}=\alpha\delta_{ij}T_{kk}+\beta T_{ij}+\gamma T_{ji}$. Applying the <scalar, symmetric-traceless and axial tensor decomposition> gives the displayed independent actions on the three components. The inverse requires all relevant coefficients nonzero. Restricting to a <symmetric second-rank tensor> eliminates the axial part and gives $P_{ij}=\alpha\delta_{ij}T_{kk}+(\beta+\gamma)T_{ij}$. Without that symmetry restriction the two-parameter form is not generally valid.
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