To continue our derivation, we substitute in the equilibrium equation ∂ ∂ σ σ i j ∂ ∂ x j + f i = 0 . Then ∫ ∫ V ( ∂ ∂ u i ∂ ∂ x j σ σ i j + u i ∂ ∂ σ σ i j ∂ ∂ x j ) d V = ∫ ∫ V ( ∂ ∂ u i ∂ ∂ x j σ σ i j − − u i f i ) d V