Struct SethHillEulerian 

pub struct SethHillEulerian {
    pub bulk_modulus: Quantity<Stress>,
    pub shear_modulus: Quantity<Stress>,
    pub exponent: Scalar,
}

The Eulerian Seth-Hill elastic solid constitutive model.^1,2

Parameters

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

External variables

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

Internal variables

• None.

Notes

• The Eulerian Seth-Hill strain measure is given by $\mathbf{e}^{(m)} = \tfrac{1}{m}(\mathbf{V}^m - \mathbf{1})$.
• The model reduces to the hyperelastic Hencky model when $m=0$.
• The model reduces to the elastic Saint Venant-Kirchhoff model when $m=2$.
• The model reduces to the Eulerian Almansi-Hamel model when $m=-2$.
• This is the Eulerian counterpart of the Lagrangian Seth-Hill model.

---

1. B.R. Seth, Generalized Strain Measure with Applications to Physical Problems, AD0266913 (1961). ↩

2. R. Hill, J. Mech. Phys. Solids 16, 229 (1968). ↩

Fields

bulk_modulus: Quantity<Stress>

The bulk modulus $\kappa$.

shear_modulus: Quantity<Stress>

The shear modulus $\mu$.

exponent: Scalar

The exponent $m$.

Implementations

impl SethHillEulerian

pub fn exponent(&self) -> Scalar

Returns the exponent.

Trait Implementations

impl Clone for SethHillEulerian

fn clone(&self) -> SethHillEulerian

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for SethHillEulerian

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

Formats the value using the given formatter.

impl Elastic for SethHillEulerian

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

\boldsymbol{\sigma}(\mathbf{F}) = \frac{2\mu}{J}\,\mathbf{e}^{(m)}{}' + \frac{\kappa}{J}\,\mathrm{tr}\big(\mathbf{e}^{(m)}\big)\mathbf{1}

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

\mathcal{T}_{ijkL}(\mathbf{F}) = \frac{\mu}{J}\,\frac{\partial B_{ij}^{m/2}}{\partial F_{kL}} + \frac{\lambda}{J}\,\delta_{ij}B_{kM}^{m/2-1}F_{ML} - \sigma_{ij}F_{kL}^{-T}

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.

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

Calculates and returns the second Piola-Kirchhoff stress.

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

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

impl Solid for SethHillEulerian

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.