1.1 (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 ο¬ 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 < ο¬ < 2).
2.1. Repeat problem 1.1. for biaxial tension (plot stresses in the e1-direction only).
3.1Β (Viscoelastic material β Maxwell model) Given a viscoelastic material, we impose constant stress ο³0 at t = 0. Derive the constitutive equation using the Maxwell model (i.e., express strain ο₯ as a function of stiffness k, damping factor ο¨, time t, and given stress ο³0).
4.1Β (Viscoelastic material β Maxwell model) Plot the strain of this viscoelastic material as a function of time t (0 to 600 s), given ο³0 = 1 MPa, k = 0.1 GPa, and ο¨ = 20 GPa-s. Which behavior does this model represent, retarded elastic behavior or steady-state creep behavior?
5.1 (Viscoelastic material β Maxwell model) Given a viscoelastic material, we impose constant strain ο₯0 at t = 0. Derive the constitutive equation using the Maxwell model (i.e., express stress ο³ as a function of stiffness k, damping factor ο¨, time t, and given stress ο₯0).
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