In cylindrical polar coordinates ( r , θ θ , z ), the displacement vector can be written as u = u r e r + u θ θ e θ θ + u z e z The components of the strain tensor in a cylindrical coordinate system are given by: ε ε r r = ∂ ∂ u r ∂ ∂ r ε ε θ θ θ θ = 1 r ( ∂ ∂ u θ θ ∂ ∂ θ θ + u r ) ε ε z z = ∂ ∂ u z ∂ ∂ z ε ε r θ θ = 1 2 ( 1 r ∂ ∂ u r ∂ ∂ θ θ + ∂ ∂ u θ θ ∂ ∂ r − − u θ θ r ) ε ε θ θ z = 1 2 ( ∂ ∂ u θ θ ∂ ∂ z + 1 r ∂ ∂ u z ∂ ∂ θ θ ) ε ε z r = 1 2 ( ∂ ∂ u r ∂ ∂ z + ∂ ∂ u z ∂ ∂ r )