Struct SethHillLagrangian 

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

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

pub fn exponent(&self) -> Scalar

Returns the exponent.

Trait Implementations

impl Clone for SethHillLagrangian

fn clone(&self) -> SethHillLagrangian

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for SethHillLagrangian

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

Formats the value using the given formatter.

impl Elastic for SethHillLagrangian

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

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

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

\mathcal{G}_{IJkL}(\mathbf{F}) = \mu\,\frac{\partial C_{IJ}^{m/2}}{\partial F_{kL}} + \lambda\,\delta_{IJ}F_{kM}C_{ML}^{m/2-1}

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 SethHillLagrangian

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.