diff --git a/src/beaminteraction/src/contact/beam_to_solid/4C_beaminteraction_contact_beam_to_solid_conditions.cpp b/src/beaminteraction/src/contact/beam_to_solid/4C_beaminteraction_contact_beam_to_solid_conditions.cpp
index 4548fb2f46e..064c330dab2 100644
--- a/src/beaminteraction/src/contact/beam_to_solid/4C_beaminteraction_contact_beam_to_solid_conditions.cpp
+++ b/src/beaminteraction/src/contact/beam_to_solid/4C_beaminteraction_contact_beam_to_solid_conditions.cpp
@@ -13,6 +13,7 @@
 #include "4C_beaminteraction_contact_beam_to_solid_input.hpp"
 #include "4C_beaminteraction_contact_beam_to_solid_mortar_manager.hpp"
 #include "4C_beaminteraction_contact_beam_to_solid_mortar_manager_contact.hpp"
+#include "4C_beaminteraction_contact_beam_to_solid_mortar_shape_functions_dual_hermite.hpp"
 #include "4C_beaminteraction_contact_beam_to_solid_surface_meshtying_pair_gauss_point.hpp"
 #include "4C_beaminteraction_contact_beam_to_solid_surface_meshtying_pair_gauss_point_FAD.hpp"
 #include "4C_beaminteraction_contact_beam_to_solid_surface_meshtying_pair_mortar.hpp"
@@ -163,6 +164,10 @@ BeamInteraction::BeamToSolidCondition::create_indirect_assembly_manager(
       mortar_manager_params.n_lambda_node_translational = n_lambda_node_pos;
       mortar_manager_params.n_lambda_element_translational = n_lambda_element_pos;
 
+      mortar_manager_params.check_diagonal_d_matrix =
+          beam_to_solid_params_->get_mortar_shape_function_type() ==
+          BeamToSolid::BeamToSolidMortarShapefunctions::dual_hermite;
+
       if (beam_to_solid_params_->is_rotational_coupling())
       {
         // Get the mortar shape functions for rotational coupling
@@ -360,6 +365,19 @@ BeamInteraction::create_beam_to_solid_volume_pair_mortar(const Core::FE::CellTyp
     case BeamToSolid::BeamToSolidMortarShapefunctions::line4:
       return create_beam_to_solid_volume_pair_mortar<BtsClass, BtsMortarTemplateArguments...,
           GeometryPair::t_line4>(shape, other_mortar_shape_function...);
+    case BeamToSolid::BeamToSolidMortarShapefunctions::dual_hermite:
+    {
+      if constexpr (!BeamInteraction::is_rotation_pair_v<BtsClass>)
+      {
+        return create_beam_to_solid_volume_pair_mortar<BtsClass, BtsMortarTemplateArguments...,
+            BeamInteraction::HermiteDual>(shape, other_mortar_shape_function...);
+      }
+
+      FOUR_C_THROW(
+          "Dual Hermite mortar shape functions are currently not implemented for rotational "
+          "beam-to-solid volume meshtying.");
+      return nullptr;
+    }
     default:
       FOUR_C_THROW("Wrong mortar shape function.");
       return nullptr;
@@ -410,7 +428,7 @@ BeamInteraction::BeamToSolidConditionVolumeMeshtying::create_contact_pair_intern
     }
     else
     {
-      // Create the rotational mortart pairs.
+      // Create the rotational mortar pairs.
       return create_beam_to_solid_volume_pair_mortar<BeamToSolidVolumeMeshtyingPairMortarRotation>(
           shape, mortar_shape_function, mortar_shape_function_rotation);
     }
diff --git a/src/beaminteraction/src/contact/beam_to_solid/4C_beaminteraction_contact_beam_to_solid_input.hpp b/src/beaminteraction/src/contact/beam_to_solid/4C_beaminteraction_contact_beam_to_solid_input.hpp
index 7ec009dd727..f89f43ebafd 100644
--- a/src/beaminteraction/src/contact/beam_to_solid/4C_beaminteraction_contact_beam_to_solid_input.hpp
+++ b/src/beaminteraction/src/contact/beam_to_solid/4C_beaminteraction_contact_beam_to_solid_input.hpp
@@ -153,7 +153,9 @@ namespace BeamToSolid
     //! Quadratic.
     line3,
     //! Cubic.
-    line4
+    line4,
+    //! Dual shape functions for cubic Hermite interpolation
+    dual_hermite,
   };
 
   /**
diff --git a/src/beaminteraction/src/contact/beam_to_solid/4C_beaminteraction_contact_beam_to_solid_mortar_manager.cpp b/src/beaminteraction/src/contact/beam_to_solid/4C_beaminteraction_contact_beam_to_solid_mortar_manager.cpp
index 371330c53af..b50e5883dcd 100644
--- a/src/beaminteraction/src/contact/beam_to_solid/4C_beaminteraction_contact_beam_to_solid_mortar_manager.cpp
+++ b/src/beaminteraction/src/contact/beam_to_solid/4C_beaminteraction_contact_beam_to_solid_mortar_manager.cpp
@@ -548,6 +548,12 @@ void BeamInteraction::BeamToSolidMortarManager::evaluate_and_assemble_global_cou
   kappa_->complete();
   lambda_active_->complete();
   constraint_->complete();
+
+  if (parameters_.check_diagonal_d_matrix)
+  {
+    check_diagonal_like_structure(constraint_lin_beam_);
+    check_diagonal_like_structure(force_beam_lin_lambda_);
+  }
 }
 
 /**
diff --git a/src/beaminteraction/src/contact/beam_to_solid/4C_beaminteraction_contact_beam_to_solid_mortar_manager.hpp b/src/beaminteraction/src/contact/beam_to_solid/4C_beaminteraction_contact_beam_to_solid_mortar_manager.hpp
index 32d39f5c59a..c3078644662 100644
--- a/src/beaminteraction/src/contact/beam_to_solid/4C_beaminteraction_contact_beam_to_solid_mortar_manager.hpp
+++ b/src/beaminteraction/src/contact/beam_to_solid/4C_beaminteraction_contact_beam_to_solid_mortar_manager.hpp
@@ -77,6 +77,9 @@ namespace BeamInteraction
     BeamToSolid::BeamToSolidLagrangeFormulation lagrange_formulation =
         BeamToSolid::BeamToSolidLagrangeFormulation::none;
 
+    //! Flag to check whether the relevant D matrix has diagonal-like structure.
+    bool check_diagonal_d_matrix = false;
+
     //! Penalty parameter for positional coupling.
     double penalty_parameter_translational = 0.0;
 
@@ -284,6 +287,12 @@ namespace BeamInteraction
      */
     double get_energy() const;
 
+    /**
+     * \brief Check if there is only one nonzero entry per row of a matrix.
+     */
+    void check_diagonal_like_structure(
+        const std::shared_ptr<Core::LinAlg::SparseMatrix>& D_matrix) const;
+
     /**
      * \brief  Assembles the LM constraint into the global RHS vector
      */
diff --git a/src/beaminteraction/src/contact/beam_to_solid/4C_beaminteraction_contact_beam_to_solid_mortar_shape_functions_dual_hermite.hpp b/src/beaminteraction/src/contact/beam_to_solid/4C_beaminteraction_contact_beam_to_solid_mortar_shape_functions_dual_hermite.hpp
new file mode 100644
index 00000000000..807e58eacff
--- /dev/null
+++ b/src/beaminteraction/src/contact/beam_to_solid/4C_beaminteraction_contact_beam_to_solid_mortar_shape_functions_dual_hermite.hpp
@@ -0,0 +1,93 @@
+// This file is part of 4C multiphysics licensed under the
+// GNU Lesser General Public License v3.0 or later.
+//
+// See the LICENSE.md file in the top-level for license information.
+//
+// SPDX-License-Identifier: LGPL-3.0-or-later
+
+#ifndef FOUR_C_BEAMINTERACTION_CONTACT_BEAM_TO_SOLID_MORTAR_SHAPE_FUNCTIONS_DUAL_HERMITE_HPP
+#define FOUR_C_BEAMINTERACTION_CONTACT_BEAM_TO_SOLID_MORTAR_SHAPE_FUNCTIONS_DUAL_HERMITE_HPP
+
+#include "4C_config.hpp"
+
+#include "4C_beam3_base.hpp"
+#include "4C_fem_general_utils_fem_shapefunctions.hpp"
+#include "4C_geometry_pair_element.hpp"
+#include "4C_geometry_pair_element_shape_functions.hpp"
+
+FOUR_C_NAMESPACE_OPEN
+
+namespace BeamInteraction
+{
+  struct HermiteDual : public GeometryPair::ElementDiscretizationBase<Core::FE::CellType::line2, 2>
+  {
+  };
+}  // namespace BeamInteraction
+
+namespace GeometryPair
+{
+  template <>
+  struct ShapeFunctionData<BeamInteraction::HermiteDual>
+  {
+    double ref_length_;
+  };
+
+  template <>
+  struct SetShapeFunctionData<BeamInteraction::HermiteDual>
+  {
+    static void set(ShapeFunctionData<BeamInteraction::HermiteDual>& shape_function_data,
+        const Core::Elements::Element* element)
+    {
+      const auto* beam_element = dynamic_cast<const Discret::Elements::Beam3Base*>(element);
+      if (beam_element == nullptr)
+        FOUR_C_THROW(
+            "The element pointer has to point to a valid beam element when evaluating the shape "
+            "function data of a dual Hermite mortar shape function, as we need to get "
+            "RefLength()!");
+
+      shape_function_data.ref_length_ = beam_element->ref_length();
+    }
+  };
+
+
+  template <>
+  struct EvaluateShapeFunction<BeamInteraction::HermiteDual>
+  {
+    template <typename V, typename T>
+    static void evaluate(V& N, const T& xi,
+        const ShapeFunctionData<BeamInteraction::HermiteDual>& shape_function_data)
+    {
+      const T xi2 = xi * xi;
+      const T xi3 = xi2 * xi;
+
+      N(0) = -35.0 / 4.0 * xi3 + 15.0 / 4.0 * xi2 + 15.0 / 4.0 * xi - 3.0 / 4.0;
+
+      N(1) = (105.0 * xi3 - 45.0 / 2.0 * xi2 - 60.0 * xi + 15.0 / 2.0) /
+             shape_function_data.ref_length_;
+
+      N(2) = 35.0 / 4.0 * xi3 + 15.0 / 4.0 * xi2 - 15.0 / 4.0 * xi - 3.0 / 4.0;
+
+      N(3) = (105.0 * xi3 + 45.0 / 2.0 * xi2 - 60.0 * xi - 15.0 / 2.0) /
+             shape_function_data.ref_length_;
+    }
+  };
+
+  template <>
+  struct PrintElementData<BeamInteraction::HermiteDual>
+  {
+    template <typename ScalarType>
+    static void print(const ElementData<BeamInteraction::HermiteDual, ScalarType>& element_data,
+        std::ostream& out)
+    {
+      constexpr auto max_precision{std::numeric_limits<double>::digits10 + 1};
+      out << std::setprecision(max_precision);
+      out << "\nElement reference length: " << element_data.shape_function_data_.ref_length_;
+      out << "\nElement state vector: ";
+      element_data.element_position_.print(out);
+    }
+  };
+}  // namespace GeometryPair
+
+FOUR_C_NAMESPACE_CLOSE
+
+#endif
\ No newline at end of file
diff --git a/src/beaminteraction/src/contact/beam_to_solid/4C_beaminteraction_contact_beam_to_solid_utils.cpp b/src/beaminteraction/src/contact/beam_to_solid/4C_beaminteraction_contact_beam_to_solid_utils.cpp
index dd286be8deb..04de95e5ff2 100644
--- a/src/beaminteraction/src/contact/beam_to_solid/4C_beaminteraction_contact_beam_to_solid_utils.cpp
+++ b/src/beaminteraction/src/contact/beam_to_solid/4C_beaminteraction_contact_beam_to_solid_utils.cpp
@@ -12,6 +12,7 @@
 #include "4C_beaminteraction_calc_utils.hpp"
 #include "4C_beaminteraction_contact_beam_to_solid_input.hpp"
 #include "4C_beaminteraction_contact_beam_to_solid_mortar_manager.hpp"
+#include "4C_beaminteraction_contact_beam_to_solid_mortar_shape_functions_dual_hermite.hpp"
 #include "4C_beaminteraction_contact_beam_to_solid_surface_params.hpp"
 #include "4C_beaminteraction_contact_beam_to_solid_volume_meshtying_params.hpp"
 #include "4C_beaminteraction_contact_pair.hpp"
@@ -130,6 +131,10 @@ BeamInteraction::mortar_shape_functions_to_number_of_lagrange_values(
       const int n_fourier_modes = beam_to_volume_parameters->get_number_of_fourier_modes();
       return (n_fourier_modes * 2 + 1);
     }
+    else if (shape_function == BeamToSolid::BeamToSolidMortarShapefunctions::dual_hermite)
+    {
+      return 2;
+    }
     else
     {
       return 1;
@@ -164,6 +169,12 @@ BeamInteraction::mortar_shape_functions_to_number_of_lagrange_values(
       const unsigned int n_lambda_element = 2 * n_dim * number_of_values_per_entry;
       return {n_lambda_node, n_lambda_element};
     }
+    case BeamToSolid::BeamToSolidMortarShapefunctions::dual_hermite:
+    {
+      const unsigned int n_lambda_node = n_dim * number_of_values_per_entry;
+      const unsigned int n_lambda_element = 0;
+      return {n_lambda_node, n_lambda_element};
+    }
     default:
       FOUR_C_THROW("Mortar shape function not implemented!");
   }
@@ -819,6 +830,51 @@ void BeamInteraction::assemble_local_mortar_contributions(
       Mortar::n_dof_, lambda_gid_pos.data(), local_kappa_active.data());
 }
 
+/**
+ *
+ */
+void BeamInteraction::BeamToSolidMortarManager::check_diagonal_like_structure(
+    const std::shared_ptr<Core::LinAlg::SparseMatrix>& D_matrix) const
+{
+  const double atol = 1.0e-14;
+  const double rtol = 1.0e-12;
+
+
+  for (int lid = 0; lid < D_matrix->row_map().num_my_elements(); ++lid)
+  {
+    const int row_gid = D_matrix->row_map().gid(lid);
+
+    int num_extracted = 0;
+    double* values = nullptr;
+    int* col_lids = nullptr;
+
+    D_matrix->extract_my_row_view(lid, num_extracted, values, col_lids);
+
+    if (num_extracted == 0 || num_extracted == 1)
+    {
+      continue;
+    }
+
+    int nnz_in_row = 0;
+    double row_scale = 0.0;
+
+    for (int k = 0; k < num_extracted; ++k)
+    {
+      row_scale = std::max(row_scale, std::abs(values[k]));
+      const double tol = atol + rtol * row_scale;
+      if (std::abs(values[k]) > tol)
+      {
+        ++nnz_in_row;
+      }
+    }
+
+    if (nnz_in_row != 1)
+    {
+      FOUR_C_THROW("Row {} has {} nonzero entries, but expected exactly one.", row_gid, nnz_in_row);
+    }
+  }
+}
+
 
 /**
  * Explicit template initialization of template functions.
@@ -920,50 +976,62 @@ namespace BeamInteraction
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_hex8, t_line2);
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_hex8, t_line3);
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_hex8, t_line4);
+  initialize_template_assemble_local_mortar_contributions(t_hermite, t_hex8, HermiteDual);
 
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_hex20, t_line2);
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_hex20, t_line3);
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_hex20, t_line4);
+  initialize_template_assemble_local_mortar_contributions(t_hermite, t_hex20, HermiteDual);
 
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_hex27, t_line2);
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_hex27, t_line3);
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_hex27, t_line4);
+  initialize_template_assemble_local_mortar_contributions(t_hermite, t_hex27, HermiteDual);
 
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_tet4, t_line2);
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_tet4, t_line3);
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_tet4, t_line4);
+  initialize_template_assemble_local_mortar_contributions(t_hermite, t_tet4, HermiteDual);
 
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_tet10, t_line2);
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_tet10, t_line3);
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_tet10, t_line4);
+  initialize_template_assemble_local_mortar_contributions(t_hermite, t_tet10, HermiteDual);
 
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_nurbs27, t_line2);
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_nurbs27, t_line3);
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_nurbs27, t_line4);
+  initialize_template_assemble_local_mortar_contributions(t_hermite, t_nurbs27, HermiteDual);
 
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_quad4, t_line2);
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_quad4, t_line3);
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_quad4, t_line4);
+  initialize_template_assemble_local_mortar_contributions(t_hermite, t_quad4, HermiteDual);
 
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_quad8, t_line2);
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_quad8, t_line3);
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_quad8, t_line4);
+  initialize_template_assemble_local_mortar_contributions(t_hermite, t_quad8, HermiteDual);
 
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_quad9, t_line2);
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_quad9, t_line3);
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_quad9, t_line4);
+  initialize_template_assemble_local_mortar_contributions(t_hermite, t_quad9, HermiteDual);
 
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_tri3, t_line2);
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_tri3, t_line3);
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_tri3, t_line4);
+  initialize_template_assemble_local_mortar_contributions(t_hermite, t_tri3, HermiteDual);
 
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_tri6, t_line2);
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_tri6, t_line3);
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_tri6, t_line4);
+  initialize_template_assemble_local_mortar_contributions(t_hermite, t_tri6, HermiteDual);
 
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_nurbs9, t_line2);
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_nurbs9, t_line3);
   initialize_template_assemble_local_mortar_contributions(t_hermite, t_nurbs9, t_line4);
+  initialize_template_assemble_local_mortar_contributions(t_hermite, t_nurbs9, HermiteDual);
 }  // namespace BeamInteraction
 
 FOUR_C_NAMESPACE_CLOSE
diff --git a/src/beaminteraction/src/contact/beam_to_solid/volume/4C_beaminteraction_contact_beam_to_solid_volume_meshtying_pair_mortar.cpp b/src/beaminteraction/src/contact/beam_to_solid/volume/4C_beaminteraction_contact_beam_to_solid_volume_meshtying_pair_mortar.cpp
index 15206675b22..b8f6d4b6426 100644
--- a/src/beaminteraction/src/contact/beam_to_solid/volume/4C_beaminteraction_contact_beam_to_solid_volume_meshtying_pair_mortar.cpp
+++ b/src/beaminteraction/src/contact/beam_to_solid/volume/4C_beaminteraction_contact_beam_to_solid_volume_meshtying_pair_mortar.cpp
@@ -8,6 +8,7 @@
 #include "4C_beaminteraction_contact_beam_to_solid_volume_meshtying_pair_mortar.hpp"
 
 #include "4C_beaminteraction_contact_beam_to_solid_mortar_manager.hpp"
+#include "4C_beaminteraction_contact_beam_to_solid_mortar_shape_functions_dual_hermite.hpp"
 #include "4C_beaminteraction_contact_beam_to_solid_utils.hpp"
 #include "4C_beaminteraction_contact_beam_to_solid_visualization_output_writer_base.hpp"
 #include "4C_beaminteraction_contact_beam_to_solid_visualization_output_writer_visualization.hpp"
@@ -112,7 +113,8 @@ void BeamInteraction::BeamToSolidVolumeMeshtyingPairMortar<Beam, Solid,
   if (visualization_discret != nullptr || visualization_continuous != nullptr)
   {
     // Setup variables.
-    GeometryPair::ElementData<Mortar, double> element_data_lambda;
+    auto element_data_lambda =
+        GeometryPair::InitializeElementData<Mortar, double>::initialize(this->element1());
     Core::LinAlg::Matrix<3, 1, scalar_type> X;
     Core::LinAlg::Matrix<3, 1, scalar_type> r;
     Core::LinAlg::Matrix<3, 1, scalar_type> u;
@@ -330,8 +332,10 @@ void BeamInteraction::BeamToSolidVolumeMeshtyingPairMortar<Beam, Solid, Mortar>:
       N_mortar.clear();
       N_beam.clear();
       N_solid.clear();
+      GeometryPair::ShapeFunctionData<Mortar> shape_function_data;
+      GeometryPair::SetShapeFunctionData<Mortar>::set(shape_function_data, this->element1());
       GeometryPair::EvaluateShapeFunction<Mortar>::evaluate(
-          N_mortar, projected_gauss_point.get_eta());
+          N_mortar, projected_gauss_point.get_eta(), shape_function_data);
       GeometryPair::EvaluateShapeFunction<Beam>::evaluate(
           N_beam, projected_gauss_point.get_eta(), this->ele1pos_.shape_function_data_);
       GeometryPair::EvaluateShapeFunction<Solid>::evaluate(
@@ -425,6 +429,13 @@ namespace BeamInteraction
   template class BeamToSolidVolumeMeshtyingPairMortar<t_hermite, t_tet4, t_line4>;
   template class BeamToSolidVolumeMeshtyingPairMortar<t_hermite, t_tet10, t_line4>;
   template class BeamToSolidVolumeMeshtyingPairMortar<t_hermite, t_nurbs27, t_line4>;
+
+  template class BeamToSolidVolumeMeshtyingPairMortar<t_hermite, t_hex8, HermiteDual>;
+  template class BeamToSolidVolumeMeshtyingPairMortar<t_hermite, t_hex20, HermiteDual>;
+  template class BeamToSolidVolumeMeshtyingPairMortar<t_hermite, t_hex27, HermiteDual>;
+  template class BeamToSolidVolumeMeshtyingPairMortar<t_hermite, t_tet4, HermiteDual>;
+  template class BeamToSolidVolumeMeshtyingPairMortar<t_hermite, t_tet10, HermiteDual>;
+  template class BeamToSolidVolumeMeshtyingPairMortar<t_hermite, t_nurbs27, HermiteDual>;
 }  // namespace BeamInteraction
 
 FOUR_C_NAMESPACE_CLOSE
diff --git a/src/beaminteraction/src/contact/beam_to_solid/volume/4C_beaminteraction_contact_beam_to_solid_volume_meshtying_pair_mortar_rotation.hpp b/src/beaminteraction/src/contact/beam_to_solid/volume/4C_beaminteraction_contact_beam_to_solid_volume_meshtying_pair_mortar_rotation.hpp
index 94e820ad425..872d4e9bee1 100644
--- a/src/beaminteraction/src/contact/beam_to_solid/volume/4C_beaminteraction_contact_beam_to_solid_volume_meshtying_pair_mortar_rotation.hpp
+++ b/src/beaminteraction/src/contact/beam_to_solid/volume/4C_beaminteraction_contact_beam_to_solid_volume_meshtying_pair_mortar_rotation.hpp
@@ -127,6 +127,17 @@ namespace BeamInteraction
         Core::LinAlg::Matrix<Solid::n_dof_, n_dof_rot_, double>& local_stiff_SB,
         Core::LinAlg::Matrix<Solid::n_dof_, Solid::n_dof_, double>& local_stiff_SS) const;
   };
+
+  /**
+   * \brief Compile time flag to check whether a beam-to-solid volume mortar pair includes
+   * rotational coupling
+   */
+  template <template <typename...> class T>
+  inline constexpr bool is_rotation_pair_v = false;
+  template <>
+  inline constexpr bool
+      is_rotation_pair_v<BeamInteraction::BeamToSolidVolumeMeshtyingPairMortarRotation> = true;
+
 }  // namespace BeamInteraction
 
 FOUR_C_NAMESPACE_CLOSE
diff --git a/src/beaminteraction/tests/4C_beaminteraction_contact_beam_to_solid_mortar_shape_functions_dual_hermite_test.cpp b/src/beaminteraction/tests/4C_beaminteraction_contact_beam_to_solid_mortar_shape_functions_dual_hermite_test.cpp
new file mode 100644
index 00000000000..9803864a0d3
--- /dev/null
+++ b/src/beaminteraction/tests/4C_beaminteraction_contact_beam_to_solid_mortar_shape_functions_dual_hermite_test.cpp
@@ -0,0 +1,35 @@
+// This file is part of 4C multiphysics licensed under the
+// GNU Lesser General Public License v3.0 or later.
+//
+// See the LICENSE.md file in the top-level for license information.
+//
+// SPDX-License-Identifier: LGPL-3.0-or-later
+
+#include <gtest/gtest.h>
+
+#include "4C_beaminteraction_contact_beam_to_solid_mortar_shape_functions_dual_hermite.hpp"
+
+namespace
+{
+  using namespace FourC;
+
+  TEST(BeamInteractionMortarShapeFunctionsTest, TestDualHermiteLine2Length03)
+  {
+    const double xi = 0.123456789;
+    const double ref_length = 0.3;
+
+    Core::LinAlg::Matrix<4, 1> phi(Core::LinAlg::Initialization::zero);
+
+    GeometryPair::ShapeFunctionData<BeamInteraction::HermiteDual> shape_function_data;
+    shape_function_data.ref_length_ = ref_length;
+
+    GeometryPair::EvaluateShapeFunction<BeamInteraction::HermiteDual>::evaluate(
+        phi, xi, shape_function_data);
+
+    const std::vector<double> phi_ref = {
+        -0.24634578918994066, -0.17588947613808397, -1.1393423701836305, -47.889652663609505};
+
+    for (std::size_t i = 0; i < phi_ref.size(); ++i) EXPECT_NEAR(phi(i), phi_ref[i], 1.0e-10);
+  }
+
+}  // namespace
diff --git a/tests/input_files/beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_regularized_line3.4C.yaml b/tests/input_files/beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_regularized_line3.4C.yaml
index 38c08a6cc9a..4d91d8097d9 100644
--- a/tests/input_files/beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_regularized_line3.4C.yaml
+++ b/tests/input_files/beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_regularized_line3.4C.yaml
@@ -1,5 +1,5 @@
 TITLE:
-  - "Description: Simulate a beam coupled to a solid via penalty mortar coupling."
+  - "Description: Simulate a beam coupled to a solid via lagrange regularized variant of mortar coupling."
   - "The shape functions for the Lagrange multplicators are line3."
 PROBLEM TYPE:
   PROBLEMTYPE: "Structure"
diff --git a/tests/input_files/beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_saddlepoint_dual_hermite.4C.yaml b/tests/input_files/beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_saddlepoint_dual_hermite.4C.yaml
new file mode 100644
index 00000000000..f4cddbc35da
--- /dev/null
+++ b/tests/input_files/beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_saddlepoint_dual_hermite.4C.yaml
@@ -0,0 +1,580 @@
+TITLE:
+  - "Description: Simulate a beam coupled to a solid using mortar coupling and lagrange multipliers with
+    the saddlepoint variant"
+  - "Dual hermite shape functions are used to interpolate the Lagrange Multipliers."
+PROBLEM TYPE:
+  PROBLEMTYPE: "Structure"
+IO:
+  OUTPUT_BIN: false
+  STRUCT_DISP: false
+  VERBOSITY: "Standard"
+IO/RUNTIME VTK OUTPUT:
+  INTERVAL_STEPS: 1
+  EVERY_ITERATION: false
+  OUTPUT_DATA_FORMAT: ascii
+IO/RUNTIME VTK OUTPUT/BEAMS:
+  OUTPUT_BEAMS: true
+  DISPLACEMENT: true
+  TRIAD_VISUALIZATIONPOINT: true
+  STRAINS_GAUSSPOINT: true
+STRUCTURAL DYNAMIC:
+  DYNAMICTYPE: "Statics"
+  TIMESTEP: 0.5
+  NUMSTEP: 2
+  MAXTIME: 1
+  LINEAR_SOLVER: 1
+SOLVER 1:
+  SOLVER: "Superlu"
+  NAME: "Structure_Solver"
+IO/RUNTIME VTK OUTPUT/STRUCTURE:
+  OUTPUT_STRUCTURE: true
+  DISPLACEMENT: true
+  ELEMENT_OWNER: true
+BEAM INTERACTION:
+  REPARTITIONSTRATEGY: "Everydt"
+BEAM INTERACTION/BEAM TO SOLID VOLUME MESHTYING:
+  CONTACT_DISCRETIZATION: mortar
+  CONSTRAINT_STRATEGY: lagrange
+  LAGRANGE_FORMULATION: saddlepoint
+  MORTAR_SHAPE_FUNCTION: dual_hermite
+  GEOMETRY_PAIR_SEGMENTATION_SEARCH_POINTS: 2
+BEAM INTERACTION/BEAM TO SOLID VOLUME MESHTYING/RUNTIME VTK OUTPUT:
+  WRITE_OUTPUT: true
+  NODAL_FORCES: true
+  MORTAR_LAMBDA_DISCRET: true
+  MORTAR_LAMBDA_CONTINUOUS: true
+  SEGMENTATION: true
+  INTEGRATION_POINTS: true
+  UNIQUE_IDS: true
+RESULT DESCRIPTION:
+  - STRUCTURE:
+      DIS: "structure"
+      NODE: 175
+      QUANTITY: "dispx"
+      VALUE: -4.57012978871066344e-01
+      TOLERANCE: 1e-10
+  - STRUCTURE:
+      DIS: "structure"
+      NODE: 175
+      QUANTITY: "dispy"
+      VALUE: -5.09106643401164433e-02
+      TOLERANCE: 1e-10
+  - STRUCTURE:
+      DIS: "structure"
+      NODE: 175
+      QUANTITY: "dispz"
+      VALUE: 2.32089865733741574e+00
+      TOLERANCE: 1e-10
+  - STRUCTURE:
+      DIS: "structure"
+      NODE: 204
+      QUANTITY: "dispx"
+      VALUE: -2.44649917710540177e-01
+      TOLERANCE: 1e-10
+  - STRUCTURE:
+      DIS: "structure"
+      NODE: 204
+      QUANTITY: "dispy"
+      VALUE: -2.80193731640499925e-02
+      TOLERANCE: 1e-10
+  - STRUCTURE:
+      DIS: "structure"
+      NODE: 204
+      QUANTITY: "dispz"
+      VALUE: 1.89862575223904129e+00
+      TOLERANCE: 1e-10
+STRUCT NOX/Status Test:
+  XML File: "beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange.xml"
+MATERIALS:
+  - MAT: 1
+    MAT_Struct_StVenantKirchhoff:
+      YOUNG: 1
+      NUE: 0
+      DENS: 0
+  - MAT: 2
+    MAT_BeamReissnerElastHyper:
+      YOUNG: 100
+      POISSONRATIO: 0
+      DENS: 0
+      CROSSAREA: 0.007853981633974483
+      SHEARCORR: 1
+      MOMINPOL: 9.817477042468105e-06
+      MOMIN2: 4.9087385212340526e-06
+      MOMIN3: 4.9087385212340526e-06
+FUNCT1:
+  - SYMBOLIC_FUNCTION_OF_SPACE_TIME: "t"
+DESIGN POINT DIRICH CONDITIONS:
+  - E: 1
+    NUMDOF: 9
+    ONOFF: [0, 0, 0, 0, 0, 1, 0, 0, 0]
+    VAL: [0, 0, 0, 0, 0, 0, 0, 0, 0]
+    FUNCT: [0, 0, 0, 0, 0, 0, 0, 0, 0]
+DESIGN SURF DIRICH CONDITIONS:
+  - E: 1
+    NUMDOF: 3
+    ONOFF: [1, 1, 1]
+    VAL: [0, 0, 0]
+    FUNCT: [0, 0, 0]
+DESIGN LINE NEUMANN CONDITIONS:
+  - E: 1
+    NUMDOF: 9
+    ONOFF: [1, 1, 1, 0, 0, 0, 0, 0, 0]
+    VAL: [0, 0, 0.00025, 0, 0, 0, 0, 0, 0]
+    FUNCT: [1, 1, 1, 0, 0, 0, 0, 0, 0]
+BEAM INTERACTION/BEAM TO SOLID VOLUME MESHTYING VOLUME:
+  - E: 1
+    COUPLING_ID: 1
+BEAM INTERACTION/BEAM TO SOLID VOLUME MESHTYING LINE:
+  - E: 1
+    COUPLING_ID: 1
+DNODE-NODE TOPOLOGY:
+  - "NODE 190 DNODE 1"
+DLINE-NODE TOPOLOGY:
+  - "NODE 190 DLINE 1"
+  - "NODE 191 DLINE 1"
+  - "NODE 192 DLINE 1"
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+  - "NODE 201 DLINE 1"
+  - "NODE 202 DLINE 1"
+  - "NODE 203 DLINE 1"
+  - "NODE 204 DLINE 1"
+DSURF-NODE TOPOLOGY:
+  - "NODE 1 DSURFACE 1"
+  - "NODE 2 DSURFACE 1"
+  - "NODE 3 DSURFACE 1"
+  - "NODE 4 DSURFACE 1"
+  - "NODE 9 DSURFACE 1"
+  - "NODE 10 DSURFACE 1"
+  - "NODE 11 DSURFACE 1"
+  - "NODE 12 DSURFACE 1"
+  - "NODE 22 DSURFACE 1"
+DVOL-NODE TOPOLOGY:
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+  - "NODE 3 DVOLUME 1"
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+    KINEM nonlinear"
+  - "3 SOLID HEX27 28 29 30 31 46 47 48 49 36 37 38 39 50 51 52 53 54 55 56 57 41 62 61 63 60 59 58 MAT
+    1 KINEM nonlinear"
+  - "4 SOLID HEX27 46 47 48 49 64 65 66 67 54 55 56 57 68 69 70 71 72 73 74 75 59 80 79 81 78 77 76 MAT
+    1 KINEM nonlinear"
+  - "5 SOLID HEX27 64 65 66 67 82 83 84 85 72 73 74 75 86 87 88 89 90 91 92 93 77 98 97 99 96 95 94 MAT
+    1 KINEM nonlinear"
+  - "6 SOLID HEX27 82 83 84 85 100 101 102 103 90 91 92 93 104 105 106 107 108 109 110 111 95 116 115
+    117 114 113 112 MAT 1 KINEM nonlinear"
+  - "7 SOLID HEX27 100 101 102 103 118 119 120 121 108 109 110 111 122 123 124 125 126 127 128 129 113
+    134 133 135 132 131 130 MAT 1 KINEM nonlinear"
+  - "8 SOLID HEX27 118 119 120 121 136 137 138 139 126 127 128 129 140 141 142 143 144 145 146 147 131
+    152 151 153 150 149 148 MAT 1 KINEM nonlinear"
+  - "9 SOLID HEX27 136 137 138 139 154 155 156 157 144 145 146 147 158 159 160 161 162 163 164 165 149
+    170 169 171 168 167 166 MAT 1 KINEM nonlinear"
+  - "10 SOLID HEX27 154 155 156 157 172 173 174 175 162 163 164 165 176 177 178 179 180 181 182 183 167
+    188 187 189 186 185 184 MAT 1 KINEM nonlinear"
+  - "11 BEAM3R LINE3 190 192 191 MAT 2 TRIADS 0 0 0 0 0 0 0 0 0 HERMITE_CENTERLINE true"
+  - "12 BEAM3R LINE3 192 194 193 MAT 2 TRIADS 0 0 0 0 0 0 0 0 0 HERMITE_CENTERLINE true"
+  - "13 BEAM3R LINE3 194 196 195 MAT 2 TRIADS 0 0 0 0 0 0 0 0 0 HERMITE_CENTERLINE true"
+  - "14 BEAM3R LINE3 196 198 197 MAT 2 TRIADS 0 0 0 0 0 0 0 0 0 HERMITE_CENTERLINE true"
+  - "15 BEAM3R LINE3 198 200 199 MAT 2 TRIADS 0 0 0 0 0 0 0 0 0 HERMITE_CENTERLINE true"
+  - "16 BEAM3R LINE3 200 202 201 MAT 2 TRIADS 0 0 0 0 0 0 0 0 0 HERMITE_CENTERLINE true"
+  - "17 BEAM3R LINE3 202 204 203 MAT 2 TRIADS 0 0 0 0 0 0 0 0 0 HERMITE_CENTERLINE true"
diff --git a/tests/input_files/beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_saddlepoint_line3.4C.yaml b/tests/input_files/beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_saddlepoint_line3.4C.yaml
index 841d016bcf2..3d55d74a521 100644
--- a/tests/input_files/beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_saddlepoint_line3.4C.yaml
+++ b/tests/input_files/beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_saddlepoint_line3.4C.yaml
@@ -1,5 +1,6 @@
 TITLE:
-  - "Description: Simulate a beam coupled to a solid via penalty mortar coupling."
+  - "Description: Simulate a beam coupled to a solid via mortar coupling using Lagrange multipler method
+    with the saddlepoint variant."
   - "The shape functions for the Lagrange multplicators are line3."
 PROBLEM TYPE:
   PROBLEMTYPE: "Structure"
diff --git a/tests/input_files/ref/beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_saddlepoint_dual_hermite-beam-to-solid-volume-mortar-continuous.pvd b/tests/input_files/ref/beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_saddlepoint_dual_hermite-beam-to-solid-volume-mortar-continuous.pvd
new file mode 100644
index 00000000000..ca9e15161a1
--- /dev/null
+++ b/tests/input_files/ref/beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_saddlepoint_dual_hermite-beam-to-solid-volume-mortar-continuous.pvd
@@ -0,0 +1,10 @@
+<?xml version="1.0"?>
+<!--
+# vtk DataFile Version 3.0
+-->
+<VTKFile type="Collection" version="0.1" ByteOrder="LittleEndian">
+  <Collection>
+    <DataSet timestep="5.00000000000000e-01" group="" part="0" file="beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_saddlepoint_dual_hermite-vtk-files/beam-to-solid-volume-mortar-continuous-00001.pvtu"/>
+    <DataSet timestep="1.00000000000000e+00" group="" part="0" file="beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_saddlepoint_dual_hermite-vtk-files/beam-to-solid-volume-mortar-continuous-00002.pvtu"/>
+  </Collection>
+</VTKFile>
\ No newline at end of file
diff --git a/tests/input_files/ref/beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_saddlepoint_dual_hermite-vtk-files/beam-to-solid-volume-mortar-continuous-00002-0.vtu b/tests/input_files/ref/beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_saddlepoint_dual_hermite-vtk-files/beam-to-solid-volume-mortar-continuous-00002-0.vtu
new file mode 100644
index 00000000000..136320b19ae
--- /dev/null
+++ b/tests/input_files/ref/beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_saddlepoint_dual_hermite-vtk-files/beam-to-solid-volume-mortar-continuous-00002-0.vtu
@@ -0,0 +1,530 @@
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diff --git a/tests/input_files/ref/beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_saddlepoint_dual_hermite-vtk-files/beam-to-solid-volume-mortar-continuous-00002.pvtu b/tests/input_files/ref/beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_saddlepoint_dual_hermite-vtk-files/beam-to-solid-volume-mortar-continuous-00002.pvtu
new file mode 100644
index 00000000000..ebddfda2c20
--- /dev/null
+++ b/tests/input_files/ref/beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_saddlepoint_dual_hermite-vtk-files/beam-to-solid-volume-mortar-continuous-00002.pvtu
@@ -0,0 +1,22 @@
+<?xml version="1.0" ?> 
+<!-- 
+# vtk DataFile Version 3.0
+-->
+<VTKFile type="PUnstructuredGrid" version="0.1" byte_order="LittleEndian">
+  <PUnstructuredGrid GhostLevel="0">
+    <PPoints>
+      <PDataArray type="Float64" NumberOfComponents="3"/>
+    </PPoints>
+    <PPointData>
+      <PDataArray type="Float64" Name="displacement" NumberOfComponents="3" format="ascii"/>
+      <PDataArray type="Float64" Name="lambda" NumberOfComponents="3" format="ascii"/>
+      <PDataArray type="Int32" Name="uid_0_pair_beam_id" format="ascii"/>
+      <PDataArray type="Int32" Name="uid_1_pair_solid_id" format="ascii"/>
+    </PPointData>
+    <PCellData>
+      <PDataArray type="Int32" Name="uid_0_pair_beam_id" format="ascii"/>
+      <PDataArray type="Int32" Name="uid_1_pair_solid_id" format="ascii"/>
+    </PCellData>
+    <Piece Source="beam-to-solid-volume-mortar-continuous-00002-0.vtu"/>
+  </PUnstructuredGrid>
+</VTKFile>
diff --git a/tests/list_of_tests.cmake b/tests/list_of_tests.cmake
index 54bd016c798..2ae16616deb 100644
--- a/tests/list_of_tests.cmake
+++ b/tests/list_of_tests.cmake
@@ -2885,6 +2885,8 @@ __four_c_test_restart(BASED_ON ${current} SAME_FILE NP 3 RESTART_STEP 3 REQUIRED
 four_c_test(TEST_FILE beam3r_herm2line3_static_beam_to_solid_volume_meshtying_gp_restart_first.4C.yaml NP 2 RETURN_AS current REQUIRED_DEPENDENCIES ArborX)
 __four_c_test_restart(BASED_ON ${current} TEST_FILE beam3r_herm2line3_static_beam_to_solid_volume_meshtying_gp_restart_second.4C.yaml NP 3 RESTART_STEP 1 REQUIRED_DEPENDENCIES ArborX)
 four_c_test(TEST_FILE beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_regularized_line3.4C.yaml NP 3 REQUIRED_DEPENDENCIES ArborX)
+four_c_test(TEST_FILE beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_saddlepoint_dual_hermite.4C.yaml NP 3 REQUIRED_DEPENDENCIES ArborX RETURN_AS current)
+__four_c_test_vtk(BASED_ON ${current} PVD_RESULT xxx-beam-to-solid-volume-mortar-continuous.pvd PVD_REFERENCE ref/beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_saddlepoint_dual_hermite-beam-to-solid-volume-mortar-continuous.pvd TOLERANCE 1e-08 TIME_STEPS 1.0)
 four_c_test(TEST_FILE beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_saddlepoint_line3.4C.yaml NP 3 REQUIRED_DEPENDENCIES ArborX RETURN_AS current)
 __four_c_test_vtk(BASED_ON ${current} PVD_RESULT xxx-beam-to-solid-volume-mortar-continuous.pvd PVD_REFERENCE ref/beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_saddlepoint_line3-beam-to-solid-volume-mortar-continuous.pvd TOLERANCE 1e-08)
 four_c_test(TEST_FILE beam3r_herm2line3_static_beam_to_solid_volume_meshtying_mortar_lagrange_augmented_line3.4C.yaml NP 3 REQUIRED_DEPENDENCIES ArborX)