Struct AlmansiHamel

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

The Almansi-Hamel viscoelastic constitutive model.

Parameters

• The bulk modulus $\kappa$.
• The shear modulus $\mu$.
• 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 Almansi-Hamel strain measure is given by $\mathbf{e}=\tfrac{1}{2}(\mathbf{1}-\mathbf{B}^{-1})$.

Trait Implementations

impl<P> Constitutive<P> for AlmansiHamel<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 AlmansiHamel<P>

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

Formats the value using the given formatter.

impl<P> ElasticHyperviscous for AlmansiHamel<P>

where P: Parameters,

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

Calculates and returns the viscous dissipation.

\phi(\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

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

Calculates and returns the dissipation potential.

fn minimize_uniaxial( &self, deformation_gradient_rate_11: impl Fn(Scalar) -> Scalar, integrator: impl Explicit<DeformationGradientRate, DeformationGradientRates>, time: &[Scalar], ) -> Result<(Times, DeformationGradients, DeformationGradientRates), IntegrationError>

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

fn root_uniaxial( &self, deformation_gradient_rate_11: impl Fn(Scalar) -> Scalar, integrator: impl Explicit<DeformationGradientRate, DeformationGradientRates>, time: &[Scalar], ) -> Result<(Times, DeformationGradients, DeformationGradientRates), IntegrationError>

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

impl<P> Solid for AlmansiHamel<P>

where P: Parameters,

fn bulk_modulus(&self) -> &Scalar

Returns the bulk modulus.

fn shear_modulus(&self) -> &Scalar

Returns the shear modulus.

impl<P> Viscoelastic for AlmansiHamel<P>

where P: Parameters,

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

Calculates and returns the Cauchy stress.

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

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

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

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

Calculates and returns the first Piola-Kirchhoff stress.

fn 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 first Piola-Kirchhoff stress.

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

Calculates and returns the second Piola-Kirchhoff stress.

fn 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 second Piola-Kirchhoff stress.

impl<P> Viscous for AlmansiHamel<P>

where P: Parameters,

fn bulk_viscosity(&self) -> &Scalar

Returns the bulk viscosity.

fn shear_viscosity(&self) -> &Scalar

Returns the shear viscosity.