Voigt elastic approximation ($W_V(E)=⟨W(E,x)⟩$)

The Voigt elastic approximation assumes uniform strain. Differentiating its averaged strain energy density gives the averaged local stress. For linear elasticity the predicted elastic stiffness tensor is $C_V=⟨C⟩$. The uniform strain is an admissible affine displacement trial field, so this gives an upper elastic energy bound for convex local energy.