Hyperelastic constitutive models

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

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

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

• Arruda-Boyce model
• Fung model
• Gent model
• Mooney-Rivlin model
• Neo-Hookean model
• Saint Venant-Kirchhoff model
• Yeoh model