Rodin/Solid/Kinematics/Invariants.h file

Strain invariants for isotropic and anisotropic hyperelasticity.

Provides isotropic invariants $ I_1, I_2, I_3 $ of the right Cauchy-Green tensor $ \mathbf{C} $ :

\[ I_1 = \operatorname{tr}(\mathbf{C}), \quad I_2 = \tfrac{1}{2}[\operatorname{tr}(\mathbf{C})^2 - \operatorname{tr}(\mathbf{C}^2)], \quad I_3 = \det(\mathbf{C}) = J^2 \]

and fiber invariants $ I_4, I_5 $ for structural tensors:

\[ I_4 = \mathbf{a}_0 \cdot \mathbf{C} \, \mathbf{a}_0, \quad I_5 = \mathbf{a}_0 \cdot \mathbf{C}^2 \, \mathbf{a}_0 \]

Namespaces

namespace Rodin
The Rodin library for finite element methods and shape optimization.
namespace Rodin::Solid
Hyperelastic solid mechanics module for large-deformation problems.

Classes

class Rodin::Solid::IsotropicInvariants
Isotropic invariants of the right Cauchy-Green tensor.
class Rodin::Solid::FiberInvariants
Fiber invariants for anisotropic hyperelasticity.