conspire 0.6.0

The Rust interface to conspire.
Documentation 
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//! Hyperelastic solid constitutive models with internal variables.

use crate::{
    constitutive::{
        ConstitutiveError,
        solid::elastic::{
            AppliedLoad,
            internal_variables::{ElasticIV, bcs},
        },
    },
    math::{
        Scalar, Tensor, TensorArray, TensorTuple,
        optimize::{EqualityConstraint, FirstOrderOptimization, SecondOrderOptimization},
    },
    mechanics::{DeformationGradient, FirstPiolaKirchhoffTangentStiffness},
};

/// Required methods for hyperelastic solid constitutive models with internal variables.
pub trait HyperelasticIV<V, T1, T2, T3>
where
    Self: ElasticIV<V, T1, T2, T3>,
{
    /// Calculates and returns the Helmholtz free energy density.
    ///
    /// ```math
    /// a = a(\mathbf{F})
    /// ```
    fn helmholtz_free_energy_density(
        &self,
        deformation_gradient: &DeformationGradient,
        internal_variables: &V,
    ) -> Result<Scalar, ConstitutiveError>;
}

/// First-order minimization methods for hyperelastic solid constitutive models with internal variables.
pub trait FirstOrderMinimize<V, T1, T2, T3> {
    /// Type representing all variables.
    type Variables;
    /// Solve for the unknown components of the deformation gradient under an applied load.
    ///
    /// ```math
    /// \Pi(\mathbf{F},\boldsymbol{\lambda}) = a(\mathbf{F}) - \boldsymbol{\lambda}:(\mathbf{F} - \mathbf{F}_0) - \mathbf{P}_0:\mathbf{F}
    /// ```
    fn minimize(
        &self,
        applied_load: AppliedLoad,
        solver: impl FirstOrderOptimization<Scalar, Self::Variables>,
    ) -> Result<(DeformationGradient, V), ConstitutiveError>;
}

/// Second-order minimization methods for hyperelastic solid constitutive models with internal variables.
pub trait SecondOrderMinimize<V, T1, T2, T3>
where
    T1: Tensor,
    T2: Tensor,
    T3: Tensor,
    V: Tensor,
{
    /// Type representing all variables.
    type Variables;
    /// Solve for the unknown components of the deformation gradient under an applied load.
    ///
    /// ```math
    /// \Pi(\mathbf{F},\boldsymbol{\lambda}) = a(\mathbf{F}) - \boldsymbol{\lambda}:(\mathbf{F} - \mathbf{F}_0) - \mathbf{P}_0:\mathbf{F}
    /// ```
    fn minimize(
        &self,
        applied_load: AppliedLoad,
        solver: impl SecondOrderOptimization<
            Scalar,
            Self::Variables,
            TensorTuple<FirstPiolaKirchhoffTangentStiffness, TensorTuple<T1, TensorTuple<T2, T3>>>,
            Self::Variables,
        >,
    ) -> Result<(DeformationGradient, V), ConstitutiveError>;
}

impl<T, V, T1, T2, T3> FirstOrderMinimize<V, T1, T2, T3> for T
where
    T: HyperelasticIV<V, T1, T2, T3>,
    T1: Tensor,
    T2: Tensor,
    T3: Tensor,
    T: ElasticIV<V, T1, T2, T3>,
    V: Tensor,
{
    type Variables = TensorTuple<DeformationGradient, V>;
    fn minimize(
        &self,
        applied_load: AppliedLoad,
        solver: impl FirstOrderOptimization<Scalar, Self::Variables>,
    ) -> Result<(DeformationGradient, V), ConstitutiveError> {
        let (matrix, vector) = bcs(self, applied_load);
        match solver.minimize(
            |variables: &Self::Variables| {
                let (deformation_gradient, internal_variables) = variables.into();
                Ok(self.helmholtz_free_energy_density(deformation_gradient, internal_variables)?)
            },
            |variables: &Self::Variables| {
                let (deformation_gradient, internal_variables) = variables.into();
                Ok(TensorTuple::from((
                    self.first_piola_kirchhoff_stress(deformation_gradient, internal_variables)?,
                    self.internal_variables_residual(deformation_gradient, internal_variables)?,
                )))
            },
            Self::Variables::from((
                DeformationGradient::identity(),
                self.internal_variables_initial(),
            )),
            EqualityConstraint::Linear(matrix, vector),
        ) {
            Ok(solution) => Ok(solution.into()),
            Err(error) => Err(ConstitutiveError::Upstream(
                format!("{error}"),
                format!("{self:?}"),
            )),
        }
    }
}

impl<T, V, T1, T2, T3> SecondOrderMinimize<V, T1, T2, T3> for T
where
    T1: Tensor,
    T2: Tensor,
    T3: Tensor,
    T: HyperelasticIV<V, T1, T2, T3>,
    V: Tensor,
{
    type Variables = TensorTuple<DeformationGradient, V>;
    fn minimize(
        &self,
        applied_load: AppliedLoad,
        solver: impl SecondOrderOptimization<
            Scalar,
            Self::Variables,
            TensorTuple<FirstPiolaKirchhoffTangentStiffness, TensorTuple<T1, TensorTuple<T2, T3>>>,
            Self::Variables,
        >,
    ) -> Result<(DeformationGradient, V), ConstitutiveError> {
        let (matrix, vector) = bcs(self, applied_load);
        match solver.minimize(
            |variables: &Self::Variables| {
                let (deformation_gradient, internal_variables) = variables.into();
                Ok(self.helmholtz_free_energy_density(deformation_gradient, internal_variables)?)
            },
            |variables: &Self::Variables| {
                let (deformation_gradient, internal_variables) = variables.into();
                Ok(TensorTuple::from((
                    self.first_piola_kirchhoff_stress(deformation_gradient, internal_variables)?,
                    self.internal_variables_residual(deformation_gradient, internal_variables)?,
                )))
            },
            |variables: &Self::Variables| {
                let (deformation_gradient, internal_variables) = variables.into();
                let tangent_0 = self.first_piola_kirchhoff_tangent_stiffness(
                    deformation_gradient,
                    internal_variables,
                )?;
                let (tangent_1, tangent_2, tangent_3) =
                    self.internal_variables_tangents(deformation_gradient, internal_variables)?;
                Ok((tangent_0, (tangent_1, (tangent_2, tangent_3).into()).into()).into())
            },
            Self::Variables::from((
                DeformationGradient::identity(),
                self.internal_variables_initial(),
            )),
            EqualityConstraint::Linear(matrix, vector),
            None,
        ) {
            Ok(solution) => Ok(solution.into()),
            Err(error) => Err(ConstitutiveError::Upstream(
                format!("{error}"),
                format!("{self:?}"),
            )),
        }
    }
}