From an important identity regarding the curl of a tensor we know that for a continuous, single-valued displacement field u , ∇ ∇ × × ( ∇ ∇ u ) = 0 . Since ∇ ∇ u = ε ε + W we have ∇ ∇ × × W = − − ∇ ∇ × × ε ε = − − ∇ ∇ w .