Consider a simple shear deformation of a square whose deformed geometry is given as
x1 = X1 + aX2, x2= X2, x3 = X3
When the material is incompressible Mooney-Rivlin hyperelastic material with A10 = 80 MPa and A01 = 20 MPa, write the expression of the S12 component of the second Piola-Kirchhoff stress as a function of α.
In addition, write the expression of σ12 of the Cauchy stress as a function of α. Plot S12 and σ12 in the range of α = [0.0, 1.5].