Struct Yeoh 

pub struct Yeoh {
    pub bulk_modulus: Quantity<Stress>,
    pub shear_moduli: Vec<Quantity<Modulus>>,
}

The Yeoh hyperelastic solid constitutive model.¹

Parameters

• The bulk modulus $\kappa$.
• The shear moduli $\mu_n$ for $n=1\ldots N$.

External variables

• The deformation gradient $\mathbf{F}$.

Internal variables

• None.

Notes

• The shear modulus is given by $\mu=\mu_1$.
• The Yeoh model reduces to the Neo-Hookean model when $N=1$.

---

1. O.H. Yeoh, Rubber Chem. Technol. 66, 754 (1993). ↩

Fields

bulk_modulus: Quantity<Stress>

The bulk modulus $\kappa$.

shear_moduli: Vec<Quantity<Modulus>>

The shear moduli $\mu_n$.

Trait Implementations

impl Clone for Yeoh

fn clone(&self) -> Yeoh

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Yeoh

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

Formats the value using the given formatter.

impl Elastic for Yeoh

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

\boldsymbol{\sigma}(\mathbf{F}) = \sum_{n=1}^N \frac{n\mu_n}{J}\left[\mathrm{tr}(\mathbf{B}^* ) - 3\right]^{n-1}\,{\mathbf{B}^*}' + \frac{\kappa}{2}\left(J - \frac{1}{J}\right)\mathbf{1}

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

\begin{aligned}
\mathcal{T}_{ijkL}(\mathbf{F}) =
\,& \sum_{n=1}^N \frac{n\mu_n}{J^{5/3}}\left[\mathrm{tr}(\mathbf{B}^* ) - 3\right]^{n-1}\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)
\\
&+ \sum_{n=2}^N \frac{2n(n-1)\mu_n}{J^{7/3}}\left[\mathrm{tr}(\mathbf{B}^* ) - 3\right]^{n-2}B_{ij}'B_{km}'F_{mL}^{-T} + \frac{\kappa}{2} \left(J + \frac{1}{J}\right)\delta_{ij}F_{kL}^{-T}
\end{aligned}

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

Calculates and returns the first Piola-Kirchhoff stress.

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

Calculates and returns the second Piola-Kirchhoff stress.

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

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

impl Hyperelastic for Yeoh

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

a(\mathbf{F}) = \sum_{n=1}^N \frac{\mu_n}{2}\big[\mathrm{tr}(\mathbf{B}^* ) - 3\big]^n + \frac{\kappa}{2}\left[\frac{1}{2}\left(J^2 - 1\right) - \ln J\right]

impl Solid for Yeoh

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.