Rodin/Solid/Integrators/MaterialTangent.h file

Material tangent stiffness integrator for Newton-Raphson linearization.

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

\[ a(\delta\mathbf{u}, \mathbf{v}) = \int_\Omega D\mathbf{P}[\nabla \delta\mathbf{u}] : \nabla \mathbf{v} \, dX \]

where $ D\mathbf{P}[\cdot] $ denotes the directional derivative of the first Piola-Kirchhoff stress.

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 Solution, class FES>
class Rodin::Solid::MaterialTangent
Local bilinear form integrator for the material tangent stiffness in hyperelastic problems.