Struct Newtonian 

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

The Newtonian 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 rate of deformation is given by $\mathbf{D}=\tfrac{1}{2}(\mathbf{L}+\mathbf{L}^T)$ with $\mathbf{L}=\dot{\mathbf{F}}\cdot\mathbf{F}^{-1}$.

Fields

bulk_viscosity: Quantity<Viscosity>

The bulk viscosity $\zeta$.

shear_viscosity: Quantity<Viscosity>

The shear viscosity $\eta$.

Trait Implementations

impl Clone for Newtonian

fn clone(&self) -> Newtonian

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Newtonian

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

Formats the value using the given formatter.

impl Hyperviscous for Newtonian

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

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

impl Viscous for Newtonian

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

\boldsymbol{\sigma}(\mathbf{F},\dot{\mathbf{F}}) = 2\eta\mathbf{D}' + \zeta\,\mathrm{tr}(\mathbf{D})\mathbf{1}

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

\mathcal{V}_{ijkL}(\mathbf{F}) = \eta\,\delta_{ik}F_{jL}^{-T} + \eta\,\delta_{jk}F_{iL}^{-T} + \left(\zeta - \frac{2}{3}\,\eta\right)\delta_{ij}F_{kL}^{-T}

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

Returns the bulk viscosity.

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

Returns the shear viscosity.

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.

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

Calculates and returns the viscous second Piola-Kirchhoff stress.

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

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