Struct Multiplicative 

pub struct Multiplicative<C1, C2>(/* private fields */);

A hybrid constitutive model based on the multiplicative decomposition.

Trait Implementations

impl<C1: Clone, C2: Clone> Clone for Multiplicative<C1, C2>

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

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

Formats the value using the given formatter.

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

where C1: Elastic, C2: Elastic,

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

Calculates and returns the Cauchy stress.

\boldsymbol{\sigma}(\mathbf{F}) = \frac{1}{J_2}\,\boldsymbol{\sigma}_1(\mathbf{F}_1)

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

Dummy method that will panic.

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

Calculates and returns the first Piola-Kirchhoff stress.

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

fn first_piola_kirchhoff_tangent_stiffness( &self, _: &DeformationGradient, ) -> Result<FirstPiolaKirchhoffTangentStiffness, ConstitutiveError>

Dummy method that will panic.

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

Calculates and returns the second Piola-Kirchhoff stress.

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

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

Dummy method that will panic.

impl<C1, C2> ElasticIV<TensorRank2<3, 2, 0>, TensorRank4<3, 2, 0, 1, 0>, TensorRank4<3, 1, 0, 2, 0>, TensorRank4<3, 2, 0, 2, 0>> for Multiplicative<C1, C2>

where C1: Elastic, C2: Elastic,

fn cauchy_stress_foo( &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_foo( &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_foo( &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_foo( &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<DeformationGradient2, 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 internal_variables_tangents( &self, deformation_gradient: &DeformationGradient, deformation_gradient_2: &DeformationGradient2, ) -> Result<(TensorRank4<3, 2, 0, 1, 0>, TensorRank4<3, 1, 0, 2, 0>, FirstPiolaKirchhoffTangentStiffness2), ConstitutiveError>

Calculates and returns the tangents associated with the internal variables.

\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}} = -F_{IL}^{2-T}P_{kJ} - F_{mI}^1\mathcal{C}_{mJkL}

\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_initial(&self) -> DeformationGradient2

Returns the initial value for the internal variables.

fn internal_variables_constraints(&self) -> (&[usize], usize)

Returns the constraint indices for the internal variables.

fn first_piola_kirchhoff_tangent_stiffness_foo( &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_foo( &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> ElasticViscoplastic for Multiplicative<C1, C2>

where C1: Elastic, C2: Viscoplastic,

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

Calculates and returns the Cauchy stress.

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

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

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

Calculates and returns the first Piola-Kirchhoff stress.

fn first_piola_kirchhoff_tangent_stiffness( &self, deformation_gradient: &DeformationGradient, deformation_gradient_p: &DeformationGradientPlastic, ) -> 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, deformation_gradient_p: &DeformationGradientPlastic, ) -> Result<SecondPiolaKirchhoffStress, ConstitutiveError>

Calculates and returns the second Piola-Kirchhoff stress.

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

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

fn state_variables_evolution( &self, deformation_gradient: &DeformationGradient, state_variables: &StateVariables, ) -> Result<StateVariables, ConstitutiveError>

Calculates and returns the evolution of the state variables.

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

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

Converts to this type from the input type.

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

where C1: Hyperelastic, C2: Hyperelastic,

fn helmholtz_free_energy_density( &self, deformation_gradient: &DeformationGradient, ) -> Result<Scalar, 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> HyperelasticViscoplastic for Multiplicative<C1, C2>

where C1: Hyperelastic, C2: Viscoplastic,

fn helmholtz_free_energy_density( &self, deformation_gradient: &DeformationGradient, deformation_gradient_p: &DeformationGradientPlastic, ) -> Result<Scalar, ConstitutiveError>

Calculates and returns the Helmholtz free energy density.

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

where C1: Elastic, C2: Elastic,

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

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

where C1: Elastic, C2: Viscoplastic,

fn initial_yield_stress(&self) -> Scalar

Returns the initial yield stress.

fn hardening_slope(&self) -> Scalar

Returns the isotropic hardening slope.

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

where C1: Solid, C2: Clone + Debug,

fn bulk_modulus(&self) -> Scalar

Returns the bulk modulus.

fn shear_modulus(&self) -> Scalar

Returns the shear modulus.

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

where C1: Elastic, C2: Viscoplastic,

fn rate_sensitivity(&self) -> Scalar

Returns the rate_sensitivity parameter.

fn reference_flow_rate(&self) -> Scalar

Returns the reference flow rate.

fn plastic_stretching_rate( &self, deviatoric_mandel_stress_e: MandelStressElastic, yield_stress: Scalar, ) -> Result<StretchingRatePlastic, ConstitutiveError>

Calculates and returns the rate of plastic stretching.

fn yield_stress_evolution( &self, plastic_stretching_rate: &StretchingRatePlastic, ) -> Result<Scalar, ConstitutiveError>

Calculates and returns the evolution of the yield stress.