Struct BlatzKo 

pub struct BlatzKo {
    pub bulk_modulus: Quantity<Stress>,
    pub shear_modulus: Quantity<Stress>,
    pub mixing_parameter: Scalar,
}

The Blatz-Ko hyperelastic solid constitutive model.¹

Parameters

• The bulk modulus $\kappa$.
• The shear modulus $\mu$.
• The mixing parameter $f$.

External variables

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

Internal variables

• None.

Notes

• The parameter $n = \kappa/2\mu - 1/3$ is determined by the bulk and shear moduli.
• This model reduces to the rubber case when $f\to 1$ and to the foam case when $f\to 0$.
• In the tangent stiffness, $K = (1-f)J^{2n} - fJ^{-2n}$ and $K' = 2n\left[(1-f)J^{2n} + fJ^{-2n}\right]$.

---

1. P.J. Blatz and W.L. Ko, Trans. Soc. Rheol. 6, 223 (1962). ↩

Fields

bulk_modulus: Quantity<Stress>

The bulk modulus $\kappa$.

shear_modulus: Quantity<Stress>

The shear modulus $\mu$.

mixing_parameter: Scalar

The mixing parameter $f$.

Implementations

impl BlatzKo

pub fn mixing_parameter(&self) -> Scalar

Returns the mixing parameter.

Trait Implementations

impl Clone for BlatzKo

fn clone(&self) -> BlatzKo

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for BlatzKo

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

Formats the value using the given formatter.

impl Elastic for BlatzKo

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

\boldsymbol{\sigma}(\mathbf{F}) = \frac{\mu}{J}\Big\{f\mathbf{B} - (1 - f)\mathbf{B}^{-1} + \left[(1-f)J^{2n} - fJ^{-2n}\right]\mathbf{1}\Big\}

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

\begin{aligned}
\mathcal{T}_{ijkL}(\mathbf{F}) =
\,& \frac{\mu f}{J}\Big[\delta_{ik}F_{jL} + \delta_{jk}F_{iL} - B_{ij}F_{kL}^{-T}\Big]
\\
&+ \frac{\mu(1-f)}{J}\Big[B_{ik}^{-1}F_{jL}^{-T} + F_{iL}^{-T}B_{jk}^{-1} + B_{ij}^{-1}F_{kL}^{-T}\Big]
\\
&+ \frac{\mu}{J}\left(K' - K\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 BlatzKo

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

a(\mathbf{F}) = \frac{\mu}{2}\left\{f\left[I_1 - 3 + \frac{1}{n}\left(I_3^{-n} - 1\right)\right] + (1-f)\left[\frac{I_2}{I_3} - 3 + \frac{1}{n}\left(I_3^n - 1\right)\right]\right\}

impl Solid for BlatzKo

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.