An element of an elastic body is subjected to a three-dimensional stress system σₓ , σᵧ , and σ. show that, if the direct strains in the directions x, y, and z are εₓ, εᵧ, and ε, then
σₓ = λe + 2Geₓ, σᵧ = λe + 2Geᵧ , σ = λe + 2G
Where
λ = vE / (1 + v)(1-2v) and e = εₓ + εᵧ + ε
the volumetric strain.