Module elastic_hyperviscous

Elastic-hyperviscous constitutive models.

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Elastic-hyperviscous constitutive models are defined by an elastic stress tensor function and a viscous dissipation function.

\mathbf{P}:\dot{\mathbf{F}} - \mathbf{P}^e(\mathbf{F}):\dot{\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} = \mathbf{P}^e + \frac{\partial\phi}{\partial\dot{\mathbf{F}}}

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

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

Structs

AlmansiHamel

The Almansi-Hamel viscoelastic constitutive model.

Traits

ElasticHyperviscous

Required methods for elastic-hyperviscous constitutive models.

FirstOrderMinimize

First-order optimization methods for elastic-hyperviscous constitutive models.

SecondOrderMinimize

Second-order optimization methods for elastic-hyperviscous constitutive models.