Consider a deformation of a rectangular bar whose deformed

Question

Consider a deformation of a rectangular bar whose deformed geometry is given as

x₁ = αX₁, x₂ = βX₂, x₃ = βX₃

When the material is incompressible and St. Venant-Kirchhoff material properties are given as E = 600 MPa and ν = 0.49, write the expression of the S₁₁ component of the second Piola-Kirchhoff stress as a function of α.

In addition, write the expression of σ₁₁ of the Cauchy stress as a function of α. Plot S₁₁ and σ₁₁ in the range of α = [0.7 1.5].