Struct Hencky

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

The Hencky elastic 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 $\mathbf{H}=\tfrac{1}{2}\ln(\mathbf{C})$.

Trait Implementations

impl<P> Constitutive<P> for Hencky<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 Hencky<P>

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

Formats the value using the given formatter.

impl<P> Elastic for Hencky<P>

where P: Parameters,

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

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

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

\mathcal{G}_{IJkL}(\mathbf{F}) = \mu\,\frac{\partial\ln C_{IJ}}{\partial F_{kL}} + \left(\kappa - \frac{2}{3}\,\mu\right)\delta_{ij}F_{kL}^{-T}

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<P> Solid for Hencky<P>

where P: Parameters,

fn bulk_modulus(&self) -> &Scalar

Returns the bulk modulus.

fn shear_modulus(&self) -> &Scalar

Returns the shear modulus.