Buche-Silberstein model
- class BucheSilberstein(method, nondimensional_link_stiffness, number_of_links)
The Buche-Silberstein hyperelastic constitutive model.
Helmholtz method for both the Helmholtz free energy and the equilibrium distribution.
Gibbs-Legendre method for both the Helmholtz free energy and the equilibrium distribution.
Gibbs-Legendre for the Helmholtz free energy and a Gaussian equilibrium distribution.
- nondimensional_link_stiffness
The nondimensional stiffness of each link in a chain.
- number_of_links
The number of links in a chain.
- uniaxial_tension(stretch)
The nondimensional Cauchy stress as a function of stretch in uniaxial tension,
\[\beta\sigma_{11}/n = 2\pi\int_0^\infty r\,dr\int_0^\infty dz\,P^\mathrm{eq}(\gamma_0)\,\frac{\eta(\gamma)}{\gamma}\,\left(2z^2-r^2\right),\]where \(\gamma=\sqrt{z^2+r^2}\) and \(\gamma_0=\sqrt{\left(z/F_{11}\right)^2+F_{11}r^2}\).
- Parameters:
stretch (numpy.ndarray) – The applied stretch \(F_{11}\).
- Returns:
The nondimensional Cauchy stress \(\beta\sigma_{11}/n\).
- Return type:
numpy.ndarray
- equibiaxial_tension(stretch)
The nondimensional Cauchy stress as a function of stretch in equibiaxial tension,
\[\beta\sigma_{11}/n = 2\pi\int_0^\infty r\,dr\int_0^\infty dz\,P^\mathrm{eq}(\gamma_0)\,\frac{\eta(\gamma)}{\gamma}\,\left(r^2-2z^2\right),\]where \(\gamma=\sqrt{z^2+r^2}\) and \(\gamma_0=\sqrt{\left(F_{11}^2z\right)^2+\left(r/F_{11}\right)^2}\).
- Parameters:
stretch (numpy.ndarray) – The applied stretch \(F_{11}\).
- Returns:
The nondimensional Cauchy stress \(\beta\sigma_{11}/n\).
- Return type:
numpy.ndarray