Trait Elastic

pub trait Elastic
where
    Self: Solid,
{
    // Provided methods
    fn cauchy_stress(
        &self,
        deformation_gradient: &DeformationGradient,
    ) -> Result<CauchyStress, ConstitutiveError> { ... }
    fn cauchy_tangent_stiffness(
        &self,
        deformation_gradient: &DeformationGradient,
    ) -> Result<CauchyTangentStiffness, ConstitutiveError> { ... }
    fn first_piola_kirchhoff_stress(
        &self,
        deformation_gradient: &DeformationGradient,
    ) -> Result<FirstPiolaKirchhoffStress, ConstitutiveError> { ... }
    fn first_piola_kirchhoff_tangent_stiffness(
        &self,
        deformation_gradient: &DeformationGradient,
    ) -> Result<FirstPiolaKirchhoffTangentStiffness, ConstitutiveError> { ... }
    fn second_piola_kirchhoff_stress(
        &self,
        deformation_gradient: &DeformationGradient,
    ) -> Result<SecondPiolaKirchhoffStress, ConstitutiveError> { ... }
    fn second_piola_kirchhoff_tangent_stiffness(
        &self,
        deformation_gradient: &DeformationGradient,
    ) -> Result<SecondPiolaKirchhoffTangentStiffness, ConstitutiveError> { ... }
}

Required methods for elastic constitutive models.

Provided Methods

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

Calculates and returns the Cauchy stress.

\boldsymbol{\sigma} = J^{-1}\mathbf{P}\cdot\mathbf{F}^T

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

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

\mathcal{T}_{ijkL} = \frac{\partial\sigma_{ij}}{\partial F_{kL}} = J^{-1} \mathcal{G}_{MNkL} F_{iM} F_{jN} - \sigma_{ij} F_{kL}^{-T} + \left(\delta_{jk}\sigma_{is} + \delta_{ik}\sigma_{js}\right)F_{sL}^{-T}

fn first_piola_kirchhoff_stress( &self, deformation_gradient: &DeformationGradient, ) -> Result<FirstPiolaKirchhoffStress, ConstitutiveError>

Calculates and returns the first Piola-Kirchhoff stress.

\mathbf{P} = J\boldsymbol{\sigma}\cdot\mathbf{F}^{-T}

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.

\mathcal{C}_{iJkL} = \frac{\partial P_{iJ}}{\partial F_{kL}} = J \mathcal{T}_{iskL} F_{sJ}^{-T} + P_{iJ} F_{kL}^{-T} - P_{iL} F_{kJ}^{-T}

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

Calculates and returns the second Piola-Kirchhoff stress.

\mathbf{S} = \mathbf{F}^{-1}\cdot\mathbf{P}

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.

\mathcal{G}_{IJkL} = \frac{\partial S_{IJ}}{\partial F_{kL}} = \mathcal{C}_{mJkL}F_{mI}^{-T} - S_{LJ}F_{kI}^{-T} = J \mathcal{T}_{mnkL} F_{mI}^{-T} F_{nJ}^{-T} + S_{IJ} F_{kL}^{-T} - S_{IL} F_{kJ}^{-T} -S_{LJ} F_{kI}^{-T}

Implementors

impl Elastic for ArrudaBoyce

impl Elastic for Fung

impl Elastic for Gent

impl Elastic for conspire::constitutive::solid::hyperelastic::Hencky

impl Elastic for MooneyRivlin

impl Elastic for NeoHookean

impl Elastic for conspire::constitutive::solid::hyperelastic::SaintVenantKirchhoff

impl Elastic for AlmansiHamel

impl Elastic for conspire::constitutive::solid::elastic::Hencky

impl Elastic for conspire::constitutive::solid::elastic::SaintVenantKirchhoff

impl<C1, C2> Elastic for Additive<C1, C2>

where C1: Elastic, C2: Elastic,

impl<C1, C2> Elastic for Multiplicative<C1, C2>

where C1: Elastic, C2: Elastic,

impl<const N: usize> Elastic for Yeoh<N>