Struct Gent

pub struct Gent {
    pub bulk_modulus: Scalar,
    pub shear_modulus: Scalar,
    pub extensibility: Scalar,
}

The Gent hyperelastic constitutive model.¹

Parameters

• The bulk modulus $\kappa$.
• The shear modulus $\mu$.
• The extensibility $J_m$.

External variables

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

Internal variables

• None.

Notes

• The Gent model reduces to the Neo-Hookean model when $J_m\to\infty$.

---

1. A.N. Gent, Rubber Chem. Technol. 69, 59 (1996). ↩

Fields

bulk_modulus: Scalar

The bulk modulus $\kappa$.

shear_modulus: Scalar

The shear modulus $\mu$.

extensibility: Scalar

The extensibility $J_m$.

Implementations

impl Gent

pub fn extensibility(&self) -> &Scalar

Returns the extensibility.

Trait Implementations

impl Debug for Gent

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

Formats the value using the given formatter.

impl Elastic for Gent

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

\boldsymbol{\sigma}(\mathbf{F}) = \frac{J^{-1}\mu J_m {\mathbf{B}^* }'}{J_m - \mathrm{tr}(\mathbf{B}^* ) + 3} + \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}) =
\,& \frac{J^{-5/3}\mu J_m}{J_m - \mathrm{tr}(\mathbf{B}^* ) + 3}\Bigg[\delta_{ik}F_{jL} + \delta_{jk}F_{iL} - \frac{2}{3}\,\delta_{ij}F_{kL} + \frac{2{B_{ij}^* }' F_{kL}}{J_m - \mathrm{tr}(\mathbf{B}^* ) + 3}
\\
&- \left(\frac{5}{3} + \frac{2}{3}\frac{\mathrm{tr}(\mathbf{B}^* )}{J_m - \mathrm{tr}(\mathbf{B}^* ) + 3}\right) J^{2/3} {B_{ij}^* }' F_{kL}^{-T} \Bigg] + \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 Gent

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

a(\mathbf{F}) = -\frac{\mu J_m}{2}\,\ln\left[1 - \frac{\mathrm{tr}(\mathbf{B}^* ) - 3}{J_m}\right] + \frac{\kappa}{2}\left[\frac{1}{2}\left(J^2 - 1\right) - \ln J\right]

impl Solid for Gent

fn bulk_modulus(&self) -> &Scalar

Returns the bulk modulus.

fn shear_modulus(&self) -> &Scalar

Returns the shear modulus.