Derive the energy form and its linearization of a

Question

1. Derive the energy form and its linearization of a Mooney-Rivlin hyperelastic material using the perturbed Lagrangian method. Use a mixed variable r = [u^T, p]^T.

2. Derive the 3 X 3 [D] matrix in Eq. (3.147) for a two-dimensional MooneyRivlin material with three material parameters (A₁₀, A₀₁, and K). Use the penalty method for near-incompressibility.