Rodin/Solid/Constitutive/SaintVenantKirchhoff.h file

Saint-Venant-Kirchhoff hyperelastic constitutive law.

Implements the stored energy density:

\[ W(\mathbf{E}) = \frac{\lambda}{2}(\operatorname{tr}\mathbf{E})^2 + \mu \, \mathbf{E} : \mathbf{E} \]

where $ \mathbf{E} = \tfrac{1}{2}(\mathbf{F}^T\mathbf{F} - \mathbf{I}) $ is the Green-Lagrange strain tensor.

The second Piola-Kirchhoff stress is:

\[ \mathbf{S} = \lambda (\operatorname{tr}\mathbf{E})\mathbf{I} + 2\mu\mathbf{E} \]

The first Piola-Kirchhoff stress is:

\[ \mathbf{P} = \mathbf{F}\mathbf{S} \]

Namespaces

namespace Rodin
The Rodin library for finite element methods and shape optimization.
namespace Rodin::Solid
Constitutive laws, kinematics, and solid-mechanics integration.

Classes

class Rodin::Solid::SaintVenantKirchhoff
Saint-Venant-Kirchhoff hyperelastic law.