conspire/constitutive/solid/hyperelastic/neo_hookean/
mod.rs

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#[cfg(test)]
mod test;

use super::*;

#[doc = include_str!("model.md")]
#[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 bulk_modulus(&self) -> &Scalar {
        &self.parameters[0]
    }
    fn shear_modulus(&self) -> &Scalar {
        &self.parameters[1]
    }
}

impl<'a> Elastic<'a> for NeoHookean<'a> {
    #[doc = include_str!("cauchy_stress.md")]
    fn cauchy_stress(
        &self,
        deformation_gradient: &DeformationGradient,
    ) -> Result<CauchyStress, ConstitutiveError> {
        let jacobian = self.jacobian(deformation_gradient)?;
        Ok(
            deformation_gradient.left_cauchy_green().deviatoric() / jacobian.powf(FIVE_THIRDS)
                * self.shear_modulus()
                + IDENTITY * self.bulk_modulus() * 0.5 * (jacobian - 1.0 / jacobian),
        )
    }
    #[doc = include_str!("cauchy_tangent_stiffness.md")]
    fn cauchy_tangent_stiffness(
        &self,
        deformation_gradient: &DeformationGradient,
    ) -> Result<CauchyTangentStiffness, ConstitutiveError> {
        let jacobian = self.jacobian(deformation_gradient)?;
        let inverse_transpose_deformation_gradient = deformation_gradient.inverse_transpose();
        let scaled_shear_modulus = self.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.bulk_modulus() * (jacobian + 1.0 / jacobian))
                        - deformation_gradient.left_cauchy_green().deviatoric()
                            * (scaled_shear_modulus * FIVE_THIRDS)),
                    &inverse_transpose_deformation_gradient,
                ),
        )
    }
}

impl<'a> Hyperelastic<'a> for NeoHookean<'a> {
    #[doc = include_str!("helmholtz_free_energy_density.md")]
    fn helmholtz_free_energy_density(
        &self,
        deformation_gradient: &DeformationGradient,
    ) -> Result<Scalar, ConstitutiveError> {
        let jacobian = self.jacobian(deformation_gradient)?;
        Ok(0.5
            * (self.shear_modulus()
                * (deformation_gradient.left_cauchy_green().trace() / jacobian.powf(TWO_THIRDS)
                    - 3.0)
                + self.bulk_modulus() * (0.5 * (jacobian.powi(2) - 1.0) - jacobian.ln())))
    }
}