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Hyperelastic constitutive models.
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 0Satisfying 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 these constitutive models.
\mathcal{C}_{iJkL} = \mathcal{C}_{kLiJ}Structs§
- Arruda
Boyce - The Arruda-Boyce hyperelastic constitutive model.
- Fung
- The Fung hyperelastic constitutive model.
- Gent
- The Gent hyperelastic constitutive model.
- Mooney
Rivlin - The Mooney-Rivlin hyperelastic constitutive model.,
- NeoHookean
- The Neo-Hookean hyperelastic constitutive model.
- Saint
Venant Kirchhoff - The Saint Venant-Kirchhoff hyperelastic constitutive model.
- Yeoh
- The Yeoh hyperelastic constitutive model.
Traits§
- Hyperelastic
- Required methods for hyperelastic constitutive models.