Module hyperelastic

Hyperelastic constitutive models.

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Hyperelastic constitutive models are completely defined by a Helmholtz free energy density function of the deformation gradient.

$\mathbf{P}:\dot{\mathbf{F}} - \dot{a}(\mathbf{F}) \geq 0$

Satisfying the second law of thermodynamics (here, equivalent to extremized or zero dissipation) yields a relation for the stress.

$\mathbf{P} = \frac{\partial a}{\partial\mathbf{F}}$

Consequently, the tangent stiffness associated with the first Piola-Kirchhoff stress is symmetric for hyperelastic constitutive models.

$\mathcal{C}_{iJkL} = \mathcal{C}_{kLiJ}$

Structs

ArrudaBoyce

The Arruda-Boyce hyperelastic constitutive model.

Fung

The Fung hyperelastic constitutive model.

Gent

The Gent hyperelastic constitutive model.

MooneyRivlin

The Mooney-Rivlin hyperelastic constitutive model.^,

NeoHookean

The Neo-Hookean hyperelastic constitutive model.

SaintVenantKirchhoff

The Saint Venant-Kirchhoff hyperelastic constitutive model.

Yeoh

The Yeoh hyperelastic constitutive model.

Traits

Hyperelastic

Required methods for hyperelastic constitutive models.