Struct SaintVenantKirchhoff 

pub struct SaintVenantKirchhoff {
    pub bulk_viscosity: Quantity<Viscosity>,
    pub shear_viscosity: Quantity<Viscosity>,
}

The Saint Venant-Kirchhoff viscous fluid constitutive model.

Parameters

• The bulk viscosity $\zeta$.
• The shear viscosity $\eta$.

External variables

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

Internal variables

• None.

Notes

• The Green-Saint Venant strain rate $\dot{\mathbf{E}}$ follows from $\mathbf{E}=\tfrac{1}{2}(\mathbf{C}-\mathbf{1})$.

Fields

bulk_viscosity: Quantity<Viscosity>

The bulk viscosity $\zeta$.

shear_viscosity: Quantity<Viscosity>

The shear viscosity $\eta$.

Trait Implementations

impl Clone for SaintVenantKirchhoff

fn clone(&self) -> SaintVenantKirchhoff

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for SaintVenantKirchhoff

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

Formats the value using the given formatter.

impl Hyperviscous for SaintVenantKirchhoff

fn viscous_dissipation( &self, deformation_gradient: &DeformationGradient, deformation_gradient_rate: &DeformationGradientRate, ) -> Result<Quantity<Dissipation>, ConstitutiveError>

\psi(\mathbf{F},\dot{\mathbf{F}}) = \eta\,\mathrm{tr}(\dot{\mathbf{E}}^2) + \frac{1}{2}\left(\zeta - \frac{2}{3}\,\eta\right)\mathrm{tr}(\dot{\mathbf{E}})^2

impl Viscous for SaintVenantKirchhoff

fn viscous_second_piola_kirchhoff_stress( &self, deformation_gradient: &DeformationGradient, deformation_gradient_rate: &DeformationGradientRate, ) -> Result<SecondPiolaKirchhoffStress, ConstitutiveError>

\mathbf{S}(\mathbf{F},\dot{\mathbf{F}}) = 2\eta\dot{\mathbf{E}}' + \zeta\,\mathrm{tr}(\dot{\mathbf{E}})\mathbf{1}

fn viscous_second_piola_kirchhoff_rate_tangent_stiffness( &self, deformation_gradient: &DeformationGradient, _: &DeformationGradientRate, ) -> Result<SecondPiolaKirchhoffRateTangentStiffness, ConstitutiveError>

\mathcal{W}_{IJkL}(\mathbf{F}) = \eta\,\delta_{JL}F_{kI} + \eta\,\delta_{IL}F_{kJ} + \left(\zeta - \frac{2}{3}\,\eta\right)\delta_{IJ}F_{kL}

fn bulk_viscosity(&self) -> Quantity<Viscosity>

Returns the bulk viscosity.

fn shear_viscosity(&self) -> Quantity<Viscosity>

Returns the shear viscosity.

fn viscous_cauchy_stress( &self, deformation_gradient: &DeformationGradient, deformation_gradient_rate: &DeformationGradientRate, ) -> Result<CauchyStress, ConstitutiveError>

Calculates and returns the viscous Cauchy stress.

fn viscous_cauchy_rate_tangent_stiffness( &self, deformation_gradient: &DeformationGradient, deformation_gradient_rate: &DeformationGradientRate, ) -> Result<CauchyRateTangentStiffness, ConstitutiveError>

Calculates and returns the rate tangent stiffness associated with the viscous Cauchy stress.

fn viscous_first_piola_kirchhoff_stress( &self, deformation_gradient: &DeformationGradient, deformation_gradient_rate: &DeformationGradientRate, ) -> Result<FirstPiolaKirchhoffStress, ConstitutiveError>

Calculates and returns the viscous first Piola-Kirchhoff stress.

fn viscous_first_piola_kirchhoff_rate_tangent_stiffness( &self, deformation_gradient: &DeformationGradient, deformation_gradient_rate: &DeformationGradientRate, ) -> Result<FirstPiolaKirchhoffRateTangentStiffness, ConstitutiveError>

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