Trait Elastic

pub trait Elastic<'a>
where
    Self: Solid<'a>,
{
    // 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> { ... }
    fn solve(
        &self,
        applied_load: AppliedLoad,
    ) -> Result<(DeformationGradient, CauchyStress), 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}

fn solve( &self, applied_load: AppliedLoad, ) -> Result<(DeformationGradient, CauchyStress), ConstitutiveError>

Solve for the unknown components of the Cauchy stress and deformation gradient under an applied load.

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementors

impl<'a> Elastic<'a> for ArrudaBoyce<'a>

impl<'a> Elastic<'a> for Fung<'a>

impl<'a> Elastic<'a> for Gent<'a>

impl<'a> Elastic<'a> for MooneyRivlin<'a>

impl<'a> Elastic<'a> for NeoHookean<'a>

impl<'a> Elastic<'a> for SaintVenantKirchhoff<'a>

impl<'a> Elastic<'a> for Yeoh<'a>

impl<'a> Elastic<'a> for AlmansiHamel<'a>

impl<'a, C1: Elastic<'a>, C2: Elastic<'a>> Elastic<'a> for Additive<C1, C2>

impl<'a, C1: Elastic<'a>, C2: Elastic<'a>> Elastic<'a> for Multiplicative<C1, C2>