Add immutable MITC4 drilling selection and direct director springs

include/fesa/elements/nonlinear_mitc4_shell.h

@@ -54,6 +54,8 @@ struct NonlinearMitc4InternalEquilibrium {
   Matrix drilling_metric{0U, 0U};
   double drilling_energy = 0.0;
   Vector force_directional_second{0U};
+  /// @brief Stores D2(f_drill)[v,v] separately; direct springs give exact zero.
+  Vector drilling_force_directional_second{0U};
   Vector drilling_constraint{0U};
   Matrix drilling_constraint_gradient{0U, 0U};
   std::array<Matrix, 4> drilling_constraint_hessian{
@@ -104,6 +106,11 @@ class NonlinearMitc4Shell {
       std::array<ShellNodeInitialFrame, 4> initial_frames,
       const ShellSection& section, const LinearElasticMaterial& material);
 
+  /// @brief Returns this immutable kernel's numerical drilling formulation.
+  [[nodiscard]] Mitc4DrillingMode DrillingMode() const noexcept {
+    return drilling_mode_;
+  }
+
   /// @brief Evaluates trial physical kinematics and fixed recovery rows.
   /// @param trial Global nodal translation and fixed-global rotation vectors.
   /// @return Physical recovery or a fail-closed trial diagnostic.
@@ -134,6 +141,7 @@ class NonlinearMitc4Shell {
 
  private:
   friend struct nonlinear_mitc4_internal::ConfigurationSnapshot;
+  friend struct mitc4_drilling_internal::TestAccess;
 
   /// @brief Retains validated fixed-reference data without analysis ownership.
   NonlinearMitc4Shell(std::array<Vector3, 4> coordinates,
@@ -155,6 +163,7 @@ class NonlinearMitc4Shell {
   double youngs_modulus_;
   double poisson_ratio_;
   double drilling_stiffness_;
+  Mitc4DrillingMode drilling_mode_;
   SourceLocation source_location_;
   std::string identity_;
 };