In spherical coordinates ( r , θ θ , ϕ ϕ ), the displacement vector can be written as u = u r e r + u θ θ e θ θ + u ϕ ϕ e ϕ ϕ The components of the strain tensor in a spherical 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 ϕ ϕ ϕ ϕ = 1 r sin ⁡ ⁡ θ θ ( ∂ ∂ u ϕ ϕ ∂ ∂ ϕ ϕ + u r sin ⁡ ⁡ θ θ + u θ θ cos ⁡ ⁡ θ θ ) 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 ϕ ϕ = 1 2 r ( 1 sin ⁡ ⁡ θ θ ∂ ∂ u θ θ ∂ ∂ ϕ ϕ + ∂ ∂ u ϕ ϕ ∂ ∂ θ θ − − u ϕ ϕ cot ⁡ ⁡ θ θ ) ε ε ϕ ϕ r = 1 2 ( 1 r sin ⁡ ⁡ θ θ ∂ ∂ u r ∂ ∂ ϕ ϕ + ∂ ∂ u ϕ ϕ ∂ ∂ r − − u ϕ ϕ r )