Rodin/Solid/Integrators/InternalVirtualWorkTangent.h file

Tangent integrator for the internal virtual work in hyperelastic formulations.

Evaluates the bilinear form arising from the linearization of the internal virtual work:

\[ D(\delta W^{\text{int}})[\Delta\mathbf{u}, \mathbf{v}] = \int_{\Omega_0} D\mathbf{P}[\nabla_0 \Delta\mathbf{u}] : \nabla_0 \mathbf{v} \, dX \]

where $ D\mathbf{P}[\cdot] = \mathbf{A} : (\cdot) $ denotes the action of the material tangent $ \mathbf{A} = \partial\mathbf{P}/\partial\mathbf{F} $ .

The integrator is generic: it obtains the finite element basis from the FE space (not hardcoded to P1), supports arbitrary quadrature rules, and builds a ConstitutivePoint (composed over Geometry::Point) at each quadrature point for constitutive evaluation.

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

template<class LawDerived, class TrialFunctionType, class TestFunctionType, class DisplacementType>
class Rodin::Solid::InternalVirtualWorkTangent
Local bilinear form integrator for the internal virtual work tangent in hyperelastic problems.