1.1 [25 points] (Hyperelastic material) Using the results derived in homework 4 and the material properties listed in Table 3.7 of the Allen Bower book, plot graphs showing the e1-directional Cauchy (left panel) and nominal (right panel) stresses as a function of stretch ratio for each of (a) a Neo-Hookean material; (b) a Mooney-Rivlin material; (c) the Arruda-Boyce material and (c) the Ogden material when subjected to uniaxial tension (0.5 < < 2).
2.1. [25 points] Repeat problem 1.1. for biaxial tension (plot stresses in the e1-direction only).
3.1 [20 points] (Viscoelastic material – Maxwell model) Given a viscoelastic material, we impose constant stress 0 at t = 0. Derive the constitutive equation using the Maxwell model (i.e., express strain as a function of stiffness k, damping factor , time t, and given stress 0).
4.1 [10 points] (Viscoelastic material – Maxwell model) Plot the strain of this viscoelastic material as a function of time t (0 to 600 s), given 0 = 1 MPa, k = 0.1 GPa, and = 20 GPa-s. Which behavior does this model represent, retarded elastic behavior or steady-state creep behavior?
5.1 [20 points] (Viscoelastic material – Maxwell model) Given a viscoelastic material, we impose constant strain 0 at t = 0. Derive the constitutive equation using the Maxwell model (i.e., express stress as a function of stiffness k, damping factor , time t, and given stress 0).
