Struct ElasticMultiplicative 

pub struct ElasticMultiplicative<C1, C2>
where
    C1: Elastic,
    C2: Elastic,
{ /* private fields */ }

A hybrid elastic constitutive model based on the multiplicative decomposition.

Trait Implementations

impl<C1, C2> Clone for ElasticMultiplicative<C1, C2>

where C1: Elastic + Clone, C2: Elastic + Clone,

fn clone(&self) -> ElasticMultiplicative<C1, C2>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<C1, C2> Debug for ElasticMultiplicative<C1, C2>

where C1: Elastic + Debug, C2: Elastic + Debug,

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

Formats the value using the given formatter.

impl<C1, C2> Deref for ElasticMultiplicative<C1, C2>

where C1: Elastic, C2: Elastic,

type Target = Multiplicative<C1, C2>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<C1, C2> ElasticIV<TensorRank2<3, Intermediate, Reference>> for ElasticMultiplicative<C1, C2>

where C1: Elastic, C2: Elastic,

fn cauchy_stress( &self, deformation_gradient: &DeformationGradient, deformation_gradient_2: &DeformationGradient2, ) -> Result<CauchyStress, ConstitutiveError>

Calculates and returns the Cauchy stress.

\boldsymbol{\sigma} = \frac{1}{J_2}\,\boldsymbol{\sigma}_1

fn cauchy_tangent_stiffness( &self, deformation_gradient: &DeformationGradient, deformation_gradient_2: &DeformationGradient2, ) -> Result<CauchyTangentStiffness, ConstitutiveError>

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

\boldsymbol{\mathcal{T}} = \frac{1}{J_2}\,\boldsymbol{\mathcal{T}}_1\cdot\mathbf{F}_2^{-T}

fn first_piola_kirchhoff_stress( &self, deformation_gradient: &DeformationGradient, deformation_gradient_2: &DeformationGradient2, ) -> Result<FirstPiolaKirchhoffStress, ConstitutiveError>

Calculates and returns the first Piola-Kirchhoff stress.

\mathbf{P} = \mathbf{P}_1\cdot\mathbf{F}_2^{-T}

fn second_piola_kirchhoff_stress( &self, deformation_gradient: &DeformationGradient, deformation_gradient_2: &DeformationGradient2, ) -> Result<SecondPiolaKirchhoffStress, ConstitutiveError>

Calculates and returns the second Piola-Kirchhoff stress.

\mathbf{S} = \mathbf{F}_2^{-1}\cdot\mathbf{S}_1\cdot\mathbf{F}_2^{-T}

fn internal_variables_residual( &self, deformation_gradient: &DeformationGradient, deformation_gradient_2: &DeformationGradient2, ) -> Result<FirstPiolaKirchhoffStress2, ConstitutiveError>

Calculates and returns the residual associated with the second deformation gradient.

\mathbf{R} = \mathbf{P}_2 - \mathbf{M}_1\cdot\mathbf{F}_2^{-T}

fn tangents( &self, deformation_gradient: &DeformationGradient, deformation_gradient_2: &DeformationGradient2, ) -> Result<(FirstPiolaKirchhoffTangentStiffness, TensorRank4<3, Intermediate, Reference, Current, Reference, Stress>, TensorRank4<3, Current, Reference, Intermediate, Reference, Stress>, FirstPiolaKirchhoffTangentStiffness2), ConstitutiveError>

Calculates and returns the tangents of the coupled system.

\mathcal{C}_{iJkL} = \frac{\partial P_{iJ}}{\partial F_{kL}}

\frac{\partial R_{IJ}}{\partial F_{kL}} = -F_{IL}^{2-T}P_{kJ} - F_{mI}^1\mathcal{C}_{mJkL}

\frac{\partial P_{iJ}}{\partial F_{KL}^2} = -P_{iL}F_{KJ}^{2-T} - \mathcal{C}_{iJmL}F_{mK}^1

\frac{\partial R_{IJ}}{\partial F_{KL}^2} = \mathcal{C}_{IJKL}^2 + F_{IM}^1P_{ML}{F_{KJ}^{2-T}} - \frac{\partial R_{IJ}}{\partial F_{mL}}\,F_{mK}^1

fn internal_variables_fixed(&self) -> &[usize]

The second deformation gradient is lower triangular to fix rotational freedom.

type Residual = TensorRank2<3, Intermediate, Reference, Stress>

The residual associated with the internal variables. the internal variables are in equilibrium over, typically a stress.

type TangentVu = TensorRank4<3, Intermediate, Reference, Current, Reference, Stress>

The tangent of the internal variables residual with the deformation gradient.

type TangentUv = TensorRank4<3, Current, Reference, Intermediate, Reference, Stress>

The tangent of the deformation gradient residual with the internal variables.

type TangentVv = TensorRank4<3, Intermediate, Reference, Intermediate, Reference, Stress>

The tangent of the internal variables residual with the internal variables.

fn internal_variables_initial(&self) -> DeformationGradient2

Returns the initial value for the internal variables.

fn first_piola_kirchhoff_tangent_stiffness( &self, deformation_gradient: &DeformationGradient, internal_variables: &V, ) -> Result<FirstPiolaKirchhoffTangentStiffness, ConstitutiveError>

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

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

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

impl<C1, C2> From<(C1, C2)> for ElasticMultiplicative<C1, C2>

where C1: Elastic, C2: Elastic,

fn from((constitutive_model_1, constitutive_model_2): (C1, C2)) -> Self

Converts to this type from the input type.

impl<C1, C2> HyperelasticIV<TensorRank2<3, Intermediate, Reference>> for ElasticMultiplicative<C1, C2>

where C1: Hyperelastic, C2: Hyperelastic,

fn helmholtz_free_energy_density( &self, deformation_gradient: &DeformationGradient, deformation_gradient_2: &DeformationGradient2, ) -> Result<Quantity<EnergyDensity>, ConstitutiveError>

Calculates and returns the Helmholtz free energy density.

a(\mathbf{F}) = a_1(\mathbf{F}_1) + a_2(\mathbf{F}_2)

impl<C1, C2> Solid for ElasticMultiplicative<C1, C2>

where C1: Elastic, C2: Elastic,

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.