Struct AlmansiHamelLagrangian 

pub struct AlmansiHamelLagrangian {
    pub bulk_modulus: Quantity<Stress>,
    pub shear_modulus: Quantity<Stress>,
}

The Lagrangian Almansi-Hamel elastic solid constitutive model.

Parameters

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

External variables

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

Internal variables

• None.

Notes

• The Lagrangian Almansi-Hamel strain measure is given by $\mathbf{E}=\tfrac{1}{2}(\mathbf{1}-\mathbf{C}^{-1})$.
• This is the Lagrangian counterpart of the Eulerian Almansi-Hamel model.

Fields

bulk_modulus: Quantity<Stress>

The bulk modulus $\kappa$.

shear_modulus: Quantity<Stress>

The shear modulus $\mu$.

Trait Implementations

impl Clone for AlmansiHamelLagrangian

fn clone(&self) -> AlmansiHamelLagrangian

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for AlmansiHamelLagrangian

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

Formats the value using the given formatter.

impl Elastic for AlmansiHamelLagrangian

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

\mathbf{S}(\mathbf{F}) = 2\mu\mathbf{E}' + \kappa\,\mathrm{tr}(\mathbf{E})\mathbf{1}

fn second_piola_kirchhoff_tangent_stiffness( &self, deformation_gradient: &DeformationGradient, ) -> Result<SecondPiolaKirchhoffTangentStiffness, ConstitutiveError>

\mathcal{G}_{IJkL}(\mathbf{F}) = \mu\left[F_{Ik}^{-1}C_{LJ}^{-1} + C_{IL}^{-1}F_{Jk}^{-1}\right] + \lambda\,\delta_{IJ}F_{Mk}^{-1}C_{ML}^{-1}

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

Calculates and returns the Cauchy stress.

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

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

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.

impl Solid for AlmansiHamelLagrangian

fn bulk_modulus(&self) -> Quantity<Stress>

Returns the bulk modulus.

fn shear_modulus(&self) -> Quantity<Stress>

Returns the shear modulus.

fn jacobian<I, J>( &self, deformation_gradient: &DeformationGradientGeneral<I, J>, ) -> Result<Scalar, ConstitutiveError>

Calculates and returns the Jacobian.