= Effective elastic energy
{title2=$W^{\mathrm{eff}}(E)=|\Omega|^{-1}\inf_{u=Ex}\int_\Omega W(\operatorname{sym}\nabla u,x)\,dx$}
The <effective elastic energy> is the minimum averaged <strain energy density> under prescribed affine boundary <displacement>. For differentiable stable elastic response without <body force>, varying the prescribed mean <strain> gives $DW^{\mathrm{eff}}(E)=\langle\sigma\rangle$. The result follows by <integration by parts>, because the interior variation with zero boundary data does no work against an equilibrated <stress tensor>.
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