Struct NeoHookean

pub struct NeoHookean<P> { /* private fields */ }

The Neo-Hookean hyperelastic constitutive model.¹

Parameters

• The bulk modulus $\kappa$.
• The shear modulus $\mu$.

External variables

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

Internal variables

• None.

---

1. R.S. Rivlin, Philos. Trans. R. Soc. London, Ser. A 240, 459 (1948). ↩

Trait Implementations

impl<P> Constitutive<P> for NeoHookean<P>

where P: Parameters,

fn new(parameters: P) -> Self

Constructs and returns a new constitutive model.

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

Calculates and returns the Jacobian.

impl<P: Debug> Debug for NeoHookean<P>

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

Formats the value using the given formatter.

impl<P> Elastic for NeoHookean<P>

where P: Parameters,

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

\boldsymbol{\sigma}(\mathbf{F}) = \frac{\mu}{J}\,{\mathbf{B}^*}' + \frac{\kappa}{2}\left(J - \frac{1}{J}\right)\mathbf{1}

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

\mathcal{T}_{ijkL}(\mathbf{F}) = \frac{\mu}{J^{5/3}}\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{\kappa}{2} \left(J + \frac{1}{J}\right)\delta_{ij}F_{kL}^{-T}

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 root( &self, applied_load: AppliedLoad, ) -> Result<DeformationGradient, OptimizeError>

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

impl<P> Hyperelastic for NeoHookean<P>

where P: Parameters,

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

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]

fn minimize( &self, applied_load: AppliedLoad, ) -> Result<DeformationGradient, OptimizeError>

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

impl<P> Solid for NeoHookean<P>

where P: Parameters,

fn bulk_modulus(&self) -> &Scalar

Returns the bulk modulus.

fn shear_modulus(&self) -> &Scalar

Returns the shear modulus.