Elastic constitutive models

Elastic constitutive models cannot be defined by a Helmholtz free energy density but still 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 elastic constitutive models.

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

• Almansi-Hamel model