Considering a 2D fourth-order tensor $C_{IJKL}$ which can be represented in Voigt notation as: $$ C_{IJKL} = \begin{bmatrix}C_{1111}&C_{1122}&C_{1112}\\ C_{2211}&C_{2222}&C_{2212}\\ C_{1211}&C_{1222}&C_{1212}\end{bmatrix} $$ and an asymmetric 2nd-order tensor $l_{mM}$ where: $$ l_{mM}= \begin{bmatrix} l_{11}&l_{12}\\ l_{21}&l_{22} \end{bmatrix} $$ We have two equations as below: $$ Q_{mMnN} = C_{MJNL}l_{mJ}l_{nL} $$ and $$ Q_{mMnN} = C_{MNKL}\delta_{mn}(l_{kK}l_{kL}-1) $$ How one can write above equations in matrix form? In general, what is happening in those equations?
2026-03-27 00:10:32.1774570232
Conversion of fourth-order tensor multiplication from indices notation to matrix form
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