Consider a simple shear deformation of a square whose deformed geometry is given as
x1= X1 + αX2, x2 = X2, x3 = X3
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 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].