Struct Hencky

pub struct Hencky {
    pub bulk_modulus: Scalar,
    pub shear_modulus: Scalar,
}

The Hencky hyperelastic constitutive model.

Parameters

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

External variables

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

Internal variables

• None.

Notes

• The Hencky strain measure is given by $\mathbf{h}=\tfrac{1}{2}\ln(\mathbf{B})$.

Fields

bulk_modulus: Scalar

The bulk modulus $\kappa$.

shear_modulus: Scalar

The shear modulus $\mu$.

Trait Implementations

impl Debug for Hencky

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

Formats the value using the given formatter.

impl Elastic for Hencky

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

\boldsymbol{\sigma}(\mathbf{F}) = \frac{2\mu}{J}\,\mathbf{h}' + \frac{\kappa}{J}\,\mathrm{tr}(\mathbf{h})\mathbf{1}

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

\mathcal{T}_{ijkL}(\mathbf{F}) = \frac{\mu}{J}\left[\frac{\partial\ln B_{ij}}{\partial F_{kL}} - \frac{2}{3}\,\delta_{ij}F_{kL}^{-T} - 2h_{ij}'F_{kL}^{-T}\right] + \frac{\kappa}{J}\left[1 - \mathrm{tr}(\mathbf{h})\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.

impl Hyperelastic for Hencky

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

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

impl Solid for Hencky

fn bulk_modulus(&self) -> &Scalar

Returns the bulk modulus.

fn shear_modulus(&self) -> &Scalar

Returns the shear modulus.