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 an incompressible Mooney-Rivlin hyperelastic material with A₁₀ = 80 MPa and A₀₁ = 20 MPa, 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].