FESADev/include/fesa/elements/nonlinear_mitc4_shell.h

#ifndef FESA_ELEMENTS_NONLINEAR_MITC4_SHELL_H_
#define FESA_ELEMENTS_NONLINEAR_MITC4_SHELL_H_

#include <array>
#include <cstddef>
#include <string>

#include "fesa/core/status.h"
#include "fesa/elements/mitc4_shell.h"
#include "fesa/math/matrix.h"
#include "fesa/math/vector.h"
#include "fesa/math/vector3.h"
#include "fesa/model/model_types.h"
#include "fesa/results/result_records.h"

namespace fesa {

/// @brief Stores one four-node nonlinear shell trial in global coordinates.
struct NonlinearMitc4TrialDofs {
  std::array<Vector3, 4> displacement;
  std::array<Vector3, 4> rotation_vector;
};

/// @brief Stores physical shell recovery at one midsurface Gauss location.
struct NonlinearMitc4RecoveryPoint {
  ShellMidsurfaceLocation location;
  std::array<double, 2> natural_coordinates;
  Mitc4LocalFrame local_frame;
  std::array<double, 8> generalized_strain;
  std::array<double, 8> section_resultant;
  std::array<ShellSectionStressRow, 3> stress;
};

/// @brief Stores the fixed four-row nonlinear physical recovery inventory.
struct NonlinearMitc4Recovery {
  std::array<NonlinearMitc4RecoveryPoint, 4> gauss_points;
  double physical_strain_energy;
};

/// @brief Stores complete internal equilibrium data for one nonlinear trial.
struct NonlinearMitc4InternalEquilibrium {
  Vector internal_residual;
  Matrix internal_tangent;
  Vector internal_force;
  NonlinearMitc4Recovery recovery;
  double physical_strain_energy;
  Vector physical_force{0U};
  Vector drilling_force{0U};
  Matrix drilling_tangent{0U, 0U};
  Matrix drilling_metric{0U, 0U};
  double drilling_energy = 0.0;
  Vector force_directional_second{0U};
  Vector drilling_constraint{0U};
  Matrix drilling_constraint_gradient{0U, 0U};
  std::array<Matrix, 4> drilling_constraint_hessian{
      Matrix{0U, 0U}, Matrix{0U, 0U}, Matrix{0U, 0U}, Matrix{0U, 0U}};
  std::array<Vector, 4> drilling_constraint_third_directional_gradient{
      Vector{0U}, Vector{0U}, Vector{0U}, Vector{0U}};
};

/// @brief Stores one nodal external drilling-null scalar and its variations.
/// @note The scalar is `-n(phi)^T F`, where `n` is the normalized physical
/// drill-null direction. Directional fields use `W=(phi_dot, 1)` and include
/// the supplied force time derivatives.
struct NonlinearMitc4ExternalDrillingConstraint {
  double value = 0.0;
  Vector gradient{0U};
  Matrix hessian{0U, 0U};
  double directional_first = 0.0;
  double directional_second = 0.0;
  Vector gradient_directional_first{0U};
  Vector gradient_directional_second{0U};
};

class NonlinearMitc4Shell;

/// @brief Evaluates the internal residual and tangent at one complete trial.
/// @param element Immutable nonlinear MITC4 reference evaluator.
/// @param trial Complete global translation and rotation trial coordinates.
/// @param coordinate_direction Optional 24-vector for D2(f_int)[v,v].
/// @return Internal force, consistent tangent and physical recovery, or
/// failure.
/// @note External load vectors and their tangents are intentionally excluded.
Result<NonlinearMitc4InternalEquilibrium> EvaluateInternalResidualAndTangent(
    const NonlinearMitc4Shell& element, const NonlinearMitc4TrialDofs& trial,
    const Vector* coordinate_direction = nullptr);

/// @brief Evaluates fixed-reference Total Lagrangian MITC4 kinematics.
/// @note This class owns no mutable trial or accepted analysis state.
class NonlinearMitc4Shell {
 public:
  /// @brief Creates one checked nonlinear MITC4 element kinematics object.
  /// @param nodes Four non-owning source nodes in natural source order.
  /// @param initial_frames Matching fixed initial node frames in source order.
  /// @param section Centered positive-thickness shell section.
  /// @param material Homogeneous isotropic material with shell-valid constants.
  /// @return A checked evaluator or a structured model failure.
  static Result<NonlinearMitc4Shell> Create(
      std::array<const Node*, 4> nodes,
      std::array<ShellNodeInitialFrame, 4> initial_frames,
      const ShellSection& section, const LinearElasticMaterial& material);

  /// @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.
  [[nodiscard]] Result<NonlinearMitc4Recovery> EvaluateKinematics(
      const NonlinearMitc4TrialDofs& trial) const;

  /// @brief Recovers the same physical quantities for one complete trial.
  /// @param trial Global nodal translation and fixed-global rotation vectors.
  /// @return Four ordered Gauss rows without nodal stress projection.
  [[nodiscard]] Result<NonlinearMitc4Recovery> RecoverState(
      const NonlinearMitc4TrialDofs& trial) const;

  /// @brief Evaluates the external nodal drill-null scalar through W.
  /// @param node Source-local node index in `[0, 4)`.
  /// @param phi Fixed-global principal-chart rotation in radians.
  /// @param phi_dot Fixed-global chart rate in radians per time.
  /// @param force Nodal external generalized moment.
  /// @param force_rate First time derivative of force.
  /// @param force_acceleration Second time derivative of force.
  /// @return The scalar `-n(phi)^T force` and exact coordinate/time
  /// derivatives, or a fail-closed diagnostic.
  [[nodiscard]] Result<NonlinearMitc4ExternalDrillingConstraint>
  EvaluateExternalDrillingConstraint(std::size_t node, const Vector3& phi,
                                     const Vector3& phi_dot,
                                     const Vector3& force,
                                     const Vector3& force_rate,
                                     const Vector3& force_acceleration) const;

 private:
  /// @brief Retains validated fixed-reference data without analysis ownership.
  NonlinearMitc4Shell(std::array<Vector3, 4> coordinates,
                      std::array<Matrix, 4> initial_frames,
                      std::array<Vector3, 4> initial_directors,
                      double thickness, double youngs_modulus,
                      double poisson_ratio, double drilling_stiffness,
                      SourceLocation source_location, std::string identity);

  friend Result<NonlinearMitc4InternalEquilibrium>
  EvaluateInternalResidualAndTangent(const NonlinearMitc4Shell& element,
                                     const NonlinearMitc4TrialDofs& trial,
                                     const Vector* coordinate_direction);

  std::array<Vector3, 4> coordinates_;
  std::array<Matrix, 4> initial_frames_;
  std::array<Vector3, 4> initial_directors_;
  double thickness_;
  double youngs_modulus_;
  double poisson_ratio_;
  double drilling_stiffness_;
  SourceLocation source_location_;
  std::string identity_;
};

}  // namespace fesa

#endif  // FESA_ELEMENTS_NONLINEAR_MITC4_SHELL_H_