flavio 0.5.0

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#[cfg(test)]
mod test;

use super::*;

/// The Neo-Hookean hyperelastic constitutive model.[^cite]
///
/// [^cite]: R.S. Rivlin, [Philos. Trans. R. Soc. London, Ser. A **240**, 459 (1948)](https://doi.org/10.1098/rsta.1948.0002).
///
/// **Parameters**
/// - The bulk modulus $`\kappa`$.
/// - The shear modulus $`\mu`$.
///
/// **External variables**
/// - The deformation gradient $`\mathbf{F}`$.
///
/// **Internal variables**
/// - None.
#[derive(Debug)]
pub struct NeoHookean<'a> {
    parameters: Parameters<'a>,
}

impl<'a> Constitutive<'a> for NeoHookean<'a> {
    fn new(parameters: Parameters<'a>) -> Self {
        Self { parameters }
    }
}

impl<'a> Solid<'a> for NeoHookean<'a> {
    fn get_bulk_modulus(&self) -> &Scalar {
        &self.parameters[0]
    }
    fn get_shear_modulus(&self) -> &Scalar {
        &self.parameters[1]
    }
}

impl<'a> Elastic<'a> for NeoHookean<'a> {
    /// Calculates and returns the Cauchy stress.
    ///
    /// ```math
    /// \boldsymbol{\sigma}(\mathbf{F}) = \frac{\mu}{J}\,{\mathbf{B}^*}' + \frac{\kappa}{2}\left(J - \frac{1}{J}\right)\mathbf{1}
    /// ```
    fn calculate_cauchy_stress(
        &self,
        deformation_gradient: &DeformationGradient,
    ) -> Result<CauchyStress, ConstitutiveError> {
        let jacobian = deformation_gradient.determinant();
        if jacobian > 0.0 {
            Ok(self
                .calculate_left_cauchy_green_deformation(deformation_gradient)
                .deviatoric()
                / jacobian.powf(FIVE_THIRDS)
                * self.get_shear_modulus()
                + IDENTITY * self.get_bulk_modulus() * 0.5 * (jacobian - 1.0 / jacobian))
        } else {
            Err(ConstitutiveError::InvalidJacobian(
                jacobian,
                deformation_gradient.copy(),
                format!("{:?}", &self),
            ))
        }
    }
    /// Calculates and returns the tangent stiffness associated with the Cauchy stress.
    ///
    /// ```math
    /// \mathcal{T}_{ijkL}(\mathbf{F}) = \frac{\mu}{J^{5/3}}\left(\delta_{ik}F_{jL} + \delta_{jk}F_{iL} - \frac{2}{3}\,\delta_{ij}F_{kL} - \frac{5}{3} \, B_{ij}'F_{kL}^{-T} \right) + \frac{\kappa}{2} \left(J + \frac{1}{J}\right)\delta_{ij}F_{kL}^{-T}
    /// ```
    fn calculate_cauchy_tangent_stiffness(
        &self,
        deformation_gradient: &DeformationGradient,
    ) -> Result<CauchyTangentStiffness, ConstitutiveError> {
        let jacobian = deformation_gradient.determinant();
        if jacobian > 0.0 {
            let inverse_transpose_deformation_gradient = deformation_gradient.inverse_transpose();
            let scaled_shear_modulus = self.get_shear_modulus() / jacobian.powf(FIVE_THIRDS);
            Ok(
                (CauchyTangentStiffness::dyad_ik_jl(&IDENTITY, deformation_gradient)
                    + CauchyTangentStiffness::dyad_il_jk(deformation_gradient, &IDENTITY)
                    - CauchyTangentStiffness::dyad_ij_kl(&IDENTITY, deformation_gradient)
                        * (TWO_THIRDS))
                    * scaled_shear_modulus
                    + CauchyTangentStiffness::dyad_ij_kl(
                        &(IDENTITY * (0.5 * self.get_bulk_modulus() * (jacobian + 1.0 / jacobian))
                            - self
                                .calculate_left_cauchy_green_deformation(deformation_gradient)
                                .deviatoric()
                                * (scaled_shear_modulus * FIVE_THIRDS)),
                        &inverse_transpose_deformation_gradient,
                    ),
            )
        } else {
            Err(ConstitutiveError::InvalidJacobian(
                jacobian,
                deformation_gradient.copy(),
                format!("{:?}", &self),
            ))
        }
    }
}

impl<'a> Hyperelastic<'a> for NeoHookean<'a> {
    /// Calculates and returns the Helmholtz free energy density.
    ///
    /// ```math
    /// a(\mathbf{F}) = \frac{\mu}{2}\left[\mathrm{tr}(\mathbf{B}^*) - 3\right] + \frac{\kappa}{2}\left[\frac{1}{2}\left(J^2 - 1\right) - \ln J\right]
    /// ```
    fn calculate_helmholtz_free_energy_density(
        &self,
        deformation_gradient: &DeformationGradient,
    ) -> Result<Scalar, ConstitutiveError> {
        let jacobian = deformation_gradient.determinant();
        if jacobian > 0.0 {
            Ok(0.5
                * (self.get_shear_modulus()
                    * (self
                        .calculate_left_cauchy_green_deformation(deformation_gradient)
                        .trace()
                        / jacobian.powf(TWO_THIRDS)
                        - 3.0)
                    + self.get_bulk_modulus() * (0.5 * (jacobian.powi(2) - 1.0) - jacobian.ln())))
        } else {
            Err(ConstitutiveError::InvalidJacobian(
                jacobian,
                deformation_gradient.copy(),
                format!("{:?}", &self),
            ))
        }
    }
}