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].