Table 1 Cauchy stress for special cases of stress states
From: Non-contact experimental methods to characterise the response of a hyper-elastic membrane
Stress state | Stretch ratios | Neo-Hookean | Mooney-Rivlin |
|---|---|---|---|
Equi-bi-axial | λ 1=λ 2=λ | \(\sigma _{1} = \sigma _{2} = 2C_{1}\left (\lambda ^{2}-\frac {1}{\lambda ^{4}}\right)\) | \(\sigma _{1} = \sigma _{2} = 2\left (\lambda ^{2} - \frac {1}{\lambda ^{4}} \right) \left (C_{1} + C_{2}\lambda ^{2} \right)\) |
|  | \(\lambda _{3} = \frac {1}{\lambda ^{2}}\) | σ 3=0 | σ 3=0 |
Uni-axial | λ 3=λ | σ 1=σ 2=0 | σ 1=σ 2=0 |
| Â | \(\lambda _{1} = \lambda _{2} = \frac {1}{\sqrt {\lambda }}\) | \(\sigma _{3} = 2C_{1}\left (\lambda ^{2} - \frac {1}{\lambda }\right)\) | \(\sigma _{3} = 2\left (\lambda - \frac {1}{\lambda ^{2}} \right) \left (C_{1} \lambda + C_{2} \right)\) |