Module hyperviscoelastic

Hyperviscoelastic constitutive models.

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Hyperviscoelastic constitutive models are defined by a Helmholtz free energy density function and a viscous dissipation function.

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

Satisfying the second law of thermodynamics though a minimum viscous dissipation principal yields a relation for the stress.

\mathbf{P} = \frac{\partial a}{\partial\mathbf{F}} + \frac{\partial\phi}{\partial\dot{\mathbf{F}}}

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

\mathcal{U}_{iJkL} = \mathcal{U}_{kLiJ}

Structs

• SaintVenantKirchhoff
  The Saint Venant-Kirchhoff hyperviscoelastic constitutive model.

Traits

• Hyperviscoelastic
  Required methods for hyperviscoelastic constitutive models.