Elastic solid constitutive models are not defined by a Helmholtz free energy density and depend on only the deformation gradient.
These constitutive models are therefore defined by a relation for some stress measure as a function of the deformation gradient.
Consequently, the tangent stiffness associated with the first Piola-Kirchhoff stress is not symmetric for these constitutive models.
```math
\mathcal{C}_{iJkL} \neq \mathcal{C}_{kLiJ}
```