Hyperelastic

Arruda-Boyce – The Arruda-Boyce hyperelastic constitutive model.
Fung – The Fung hyperelastic constitutive model.
Gent – The Gent hyperelastic constitutive model.
Mooney-Rivlin – The Mooney-Rivlin hyperelastic constitutive model.
Neo-Hookean – The Neo-Hookean hyperelastic constitutive model.
Saint Venant-Kirchhoff - The Saint Venant-Kirchhoff hyperelastic constitutive model.

Functions

Conspire.helmholtz_free_energy_density — Function

helmholtz_free_energy_density(
    model::ArrudaBoyce,
    F
) -> Float64

\[a(\mathbf{F}) = \frac{3\mu N_b\gamma_0}{\eta_0}\left[\gamma\eta - \gamma_0\eta_0 - \ln\left(\frac{\eta_0\sinh\eta}{\eta\sinh\eta_0}\right) \right] + \frac{\kappa}{2}\left[\frac{1}{2}\left(J^2 - 1\right) - \ln J\right]\]

source

helmholtz_free_energy_density(model::Fung, F) -> Float64

\[a(\mathbf{F}) = \frac{\mu - \mu_m}{2}\left[\mathrm{tr}(\mathbf{B}^* ) - 3\right] + \frac{\mu_m}{2c}\left(e^{c[\mathrm{tr}(\mathbf{B}^* ) - 3]} - 1\right)\]

source

helmholtz_free_energy_density(model::Gent, F) -> Float64

\[a(\mathbf{F}) = -\frac{\mu J_m}{2}\,\ln\left[1 - \frac{\mathrm{tr}(\mathbf{B}^* ) - 3}{J_m}\right] + \frac{\kappa}{2}\left[\frac{1}{2}\left(J^2 - 1\right) - \ln J\right]\]

source

helmholtz_free_energy_density(
    model::MooneyRivlin,
    F
) -> Float64

\[a(\mathbf{F}) = \frac{\mu - \mu_m}{2}\left[\mathrm{tr}(\mathbf{B}^* ) - 3\right] + \frac{\mu_m}{2}\left[I_2(\mathbf{B}^*) - 3\right] + \frac{\kappa}{2}\left[\frac{1}{2}\left(J^2 - 1\right) - \ln J\right]\]

source

helmholtz_free_energy_density(
    model::NeoHookean,
    F
) -> Float64

\[a(\mathbf{F}) = \frac{\mu}{2}\left[\mathrm{tr}(\mathbf{B}^*) - 3\right] + \frac{\kappa}{2}\left[\frac{1}{2}\left(J^2 - 1\right) - \ln J\right]\]

source

helmholtz_free_energy_density(
    model::SaintVenantKirchhoff,
    F
) -> Float64

\[a(\mathbf{F}) = \mu\,\mathrm{tr}(\mathbf{E}^2) + \frac{1}{2}\left(\kappa - \frac{2}{3}\,\mu\right)\mathrm{tr}(\mathbf{E})^2\]

source