: Understand the thermodynamic consistency required for physically realistic material laws. Constitutive Modeling
Tools like Mathematica or Maple are excellent for checking your work. You can input the strain energy functions provided in the book and use the software to derive the Cauchy stress tensors.
Derive the material (Lagrangian) tangent modulus $\mathbbC = 2 \frac\partial S\partial C$ for a compressible Neo-Hookean material with strain-energy function $\Psi = \frac\mu2(I_1 - 3) - \mu \ln J + \frac\lambda2(\ln J)^2$.