Struct Fung

pub struct Fung<'a> { /* private fields */ }

The Fung hyperelastic constitutive model.¹

Parameters

• The bulk modulus $\kappa$.
• The shear modulus $\mu$.
• The extra modulus $\mu_m$.
• The exponent $c$.

External variables

• The deformation gradient $\mathbf{F}$.

Internal variables

• None.

Notes

• The Fung model reduces to the Neo-Hookean model when $\mu_m\to 0$ or $c\to 0$.

---

1. Y.C. Fung, Am. J. Physiol. 213, 1532 (1967). ↩

Trait Implementations

impl<'a> Constitutive<'a> for Fung<'a>

fn new(parameters: Parameters<'a>) -> Self

Constructs and returns a new constitutive model.

fn jacobian( &self, deformation_gradient: &DeformationGradient, ) -> Result<Scalar, ConstitutiveError>

Calculates and returns the Jacobian.

impl<'a> Debug for Fung<'a>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<'a> Elastic<'a> for Fung<'a>

fn cauchy_stress( &self, deformation_gradient: &DeformationGradient, ) -> Result<CauchyStress, ConstitutiveError>

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

fn cauchy_tangent_stiffness( &self, deformation_gradient: &DeformationGradient, ) -> Result<CauchyTangentStiffness, ConstitutiveError>

\begin{aligned}
\mathcal{T}_{ijkL}(\mathbf{F}) =
\,& \frac{1}{J^{5/3}}\left[\mu + \mu_m\left(e^{c[\mathrm{tr}(\mathbf{B}^* ) - 3]} - 1\right)\right]\left(\delta_{ik}F_{jL} + \delta_{jk}F_{iL} - \frac{2}{3}\,\delta_{ij}F_{kL} - \frac{5}{3} \, B_{ij}'F_{kL}^{-T} \right)
\\
&+ \frac{2c\mu_m}{J^{7/3}}\,e^{c[\mathrm{tr}(\mathbf{B}^* ) - 3]}B_{ij}'B_{km}'F_{mL}^{-T} + \frac{\kappa}{2} \left(J + \frac{1}{J}\right)\delta_{ij}F_{kL}^{-T}
\end{aligned}

fn first_piola_kirchhoff_stress( &self, deformation_gradient: &DeformationGradient, ) -> Result<FirstPiolaKirchhoffStress, ConstitutiveError>

Calculates and returns the first Piola-Kirchhoff stress.

fn first_piola_kirchhoff_tangent_stiffness( &self, deformation_gradient: &DeformationGradient, ) -> Result<FirstPiolaKirchhoffTangentStiffness, ConstitutiveError>

Calculates and returns the tangent stiffness associated with the first Piola-Kirchhoff stress.

fn second_piola_kirchhoff_stress( &self, deformation_gradient: &DeformationGradient, ) -> Result<SecondPiolaKirchhoffStress, ConstitutiveError>

Calculates and returns the second Piola-Kirchhoff stress.

fn second_piola_kirchhoff_tangent_stiffness( &self, deformation_gradient: &DeformationGradient, ) -> Result<SecondPiolaKirchhoffTangentStiffness, ConstitutiveError>

Calculates and returns the tangent stiffness associated with the second Piola-Kirchhoff stress.

fn solve( &self, applied_load: AppliedLoad, ) -> Result<(DeformationGradient, CauchyStress), ConstitutiveError>

Solve for the unknown components of the Cauchy stress and deformation gradient under an applied load.

impl<'a> Hyperelastic<'a> for Fung<'a>

fn helmholtz_free_energy_density( &self, deformation_gradient: &DeformationGradient, ) -> Result<Scalar, ConstitutiveError>

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)

impl<'a> Solid<'a> for Fung<'a>

fn bulk_modulus(&self) -> &Scalar

Returns the bulk modulus.

fn shear_modulus(&self) -> &Scalar

Returns the shear modulus.