InternalVirtualWork.h file

Façade for the internal virtual work nonlinear form in hyperelastic formulations.

Provides the unified API for constructing the internal virtual work contributions to a nonlinear solid mechanics problem:

auto ivw = Solid::InternalVirtualWork(law, displacement);

// Residual contribution (linear form):
LinearForm F(fes);
F += ivw.Residual(v);

// Tangent contribution (bilinear form):
BilinearForm K(trialFES, testFES);
K += ivw.Tangent(u, v);

// Both at once for problem definition:
Problem newton(u, v);
newton = ivw(u, v) - Integral(f, v) + DirichletBC(u, g).on(bc);

Sign convention with Problem and NewtonSolver

Residual(v) returns the internal virtual work with its physical sign,

Tangent(du, v) returns its positive Gateaux derivative . When a Problem assembles a ProblemBody into a linear system, linear form contributions are moved to the right-hand side with a minus sign. Therefore

Problem newton(du, v);
newton = ivw(du, v) + DirichletBC(du, zero);

assembles the Newton system

and NewtonSolver then applies . Do not write Tangent(du, v) - Residual(v) for this Newton form: the Problem assembly will negate the already-negated residual and produce .

All three forms share the same constitutive law, displacement state, quadrature order, and input hook — ensuring consistency of the Newton linearization.

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 Law, class State> class Rodin::Solid::InternalVirtualWork: Façade for the internal virtual work nonlinear form.