Given a continuous, single-valued displacement field u and the corresponding infinitesimal strain tensor ε ε , we have (see Tensor derivative (continuum mechanics)) ∇ ∇ × × ε ε = e i j k ε ε l j , i e k ⊗ ⊗ e l = 1 2 e i j k [ u l , j i + u j , l i ] e k ⊗ ⊗ e l Since a change in the order of differentiation does not change the result, u l , j i = u l , i j . Therefore e i j k u l , j i = ( e 12 k + e 21 k ) u l , 12 + ( e 13 k + e 31 k ) u l , 13 + ( e 23 k + e 32 k ) u l , 32 = 0 Also 1 2 e i j k u j , l i = ( 1 2 e i j k u j , i ) , l = ( 1 2 e k i j u j , i ) , l = w k , l Hence ∇ ∇ × × ε ε = w k , l e k ⊗ ⊗ e l = ∇ ∇ w