Hyperelasticity

Consider the rod shown subjected to the distributed loading $l_x.$ Perform hyperelastic analysis of the tensile test for
(a) logarithmic material model,
(b) Mooney–Rivlin material model,
(c) Ogden material model.

Hyperelastic compressible material.

(a) Logarithmic description of the deformation, linear constitutive relations with parameters $E=1.265717\text{ MPa},$ $\nu=0.49789.$

(b) Mooney–Rivlin material model with parameters $C_1=165{,}391\text{ Pa,}$ $C_2=46{,}211\text{ Pa},$ $\kappa=10^8\text{ Pa}.$

(c) Ogden material model with parameters $\alpha_1=1.3,$ $\mu_1=0.63\text{ MPa},$ $\alpha_2=5,$ $\mu_2=0.0012\text{ MPa},$ $\alpha_3=−2,$ $\mu_3=-0.01\text{ MPa},$ $\kappa=10^8\text{ Pa}.$

Statically determinate.

$l_x=0.4\text{ MPa}.$

• Logarithmic formulation, BEAM56H1
• Mooney–Rivlin material model, BEAM56H2
• Ogden material model, BEAM56H3