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1)Derive the energy form and its linearization of a Mooney-Rivlin hyperelastic material using the perturbed Lagrangian method

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

3)Derive the 3*3 [D] matrix in Eq. (3.147) for a two-dimensional Mooney- Rivlin material with three material parameters (A₁₀, A₀₁, and K). Use the perturbed Lagrangian method for near-incompressibility.