Voigt bound ($a^{\ast }⪯⟨a⟩$)

An affine trial temperature in the minimum-energy principle gives the upper tensor bound by the volume-averaged local conductivity. For an isotropic two-phase composite, $a^{\ast }\le p_1{a}_1+p_2{a}_2$. The same uniform-field variational idea supplies the familiar corresponding elastic upper bound.