diff --git a/test/geomechanics/CMakeLists.txt b/test/geomechanics/CMakeLists.txt
index 1e0c436339b782025138f8380331aff077b53207..efbfd0df8b55b01ac2decdb7736a107667dd8b9a 100644
--- a/test/geomechanics/CMakeLists.txt
+++ b/test/geomechanics/CMakeLists.txt
@@ -3,4 +3,5 @@
add_subdirectory(elastic)
add_subdirectory(hyperelastic)
+add_subdirectory(hyperelastic_dynamic)
add_subdirectory(poroelastic)
diff --git a/test/geomechanics/hyperelastic_dynamic/CMakeLists.txt b/test/geomechanics/hyperelastic_dynamic/CMakeLists.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b1a45bfe0d136ae9b8535a21926488f48541d53c
--- /dev/null
+++ b/test/geomechanics/hyperelastic_dynamic/CMakeLists.txt
@@ -0,0 +1,15 @@
+# SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+# SPDX-License-Identifier: GPL-3.0-or-later
+
+dune_symlink_to_source_files(FILES params.input solid.msh)
+dumux_add_test(
+ NAME test_saint_venant_kirchhoff_dynamic
+ LABELS geomechanics elastic
+ SOURCES main.cc
+ CMAKE_GUARD "( HAVE_UMFPACK AND dune-alugrid_FOUND )"
+ COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+ CMD_ARGS --script fuzzy
+ --files ${CMAKE_SOURCE_DIR}/test/references/test_saint_venant_kirchhoff_dynamic-reference.vtu
+ ${CMAKE_CURRENT_BINARY_DIR}/test_saint_venant_kirchhoff_dynamic-00002.vtu
+ --command "${CMAKE_CURRENT_BINARY_DIR}/test_saint_venant_kirchhoff_dynamic params.input -TimeLoop.TEnd 1 -VTKOutput.Every 50"
+)
diff --git a/test/geomechanics/hyperelastic_dynamic/main.cc b/test/geomechanics/hyperelastic_dynamic/main.cc
new file mode 100644
index 0000000000000000000000000000000000000000..57895b0a5ecb21c01c52239c70ba88e033e6f705
--- /dev/null
+++ b/test/geomechanics/hyperelastic_dynamic/main.cc
@@ -0,0 +1,130 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+#include <config.h>
+#include <iostream>
+
+#include <dumux/common/initialize.hh>
+#include <dumux/common/properties.hh>
+#include <dumux/common/parameters.hh>
+
+#include <dumux/nonlinear/newtonsolver.hh>
+#include <dumux/linear/linearsolvertraits.hh>
+#include <dumux/linear/linearalgebratraits.hh>
+#include <dumux/linear/istlsolvers.hh>
+
+#include <dumux/assembly/fvassembler.hh>
+
+#include <dumux/experimental/timestepping/newmarkbeta.hh>
+
+#include <dumux/io/vtkoutputmodule.hh>
+#include <dumux/io/grid/gridmanager_alu.hh>
+
+#include "properties.hh"
+
+int main(int argc, char** argv)
+{
+ using namespace Dumux;
+
+ // define the type tag for this problem
+ using TypeTag = Properties::TTag::DynamicHyperelasticityTest;
+
+ // maybe initialize MPI and/or multithreading backend
+ Dumux::initialize(argc, argv);
+
+ // initialize parameter tree
+ Parameters::init(argc, argv);
+
+ using Grid = GetPropType<TypeTag, Properties::Grid>;
+ GridManager<Grid> gridManager;
+ gridManager.init();
+
+ // we compute on the leaf grid view
+ const auto& leafGridView = gridManager.grid().leafGridView();
+
+ // create the finite volume grid geometry
+ using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
+ auto gridGeometry = std::make_shared<GridGeometry>(leafGridView);
+
+ // the problem (initial and boundary conditions)
+ using Problem = GetPropType<TypeTag, Properties::Problem>;
+ auto problem = std::make_shared<Problem>(gridGeometry);
+
+ // the solution vector
+ using SolutionVector = GetPropType<TypeTag, Properties::SolutionVector>;
+ SolutionVector x(gridGeometry->numDofs());
+ x = 0.0;
+
+ // the grid variables
+ using GridVariables = GetPropType<TypeTag, Properties::GridVariables>;
+ auto gridVariables = std::make_shared<GridVariables>(problem, gridGeometry);
+ gridVariables->init(x);
+
+ // initialize the vtk output module
+ VtkOutputModule<GridVariables, SolutionVector> vtkWriter(*gridVariables, x, problem->name());
+ vtkWriter.addVolumeVariable([](const auto& v){
+ return Dune::FieldVector<double, 2>{v.displacement(0), v.displacement(1)};
+ }, "d");
+ vtkWriter.write(0.0);
+
+ // solution at previous time
+ auto xOld = x;
+
+ // get some time loop parameters
+ using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+ const auto tEnd = getParam<Scalar>("TimeLoop.TEnd");
+ const auto dt = getParam<Scalar>("TimeLoop.DtInitial");
+ auto timeLoop = std::make_shared<CheckPointTimeLoop<Scalar>>(0.0, dt, tEnd);
+
+ // the time stepping scheme
+ auto newmarkBeta = std::make_shared<Experimental::NewmarkBeta<Scalar, SolutionVector>>();
+ newmarkBeta->initialize(x);
+ problem->setNewmarkScheme(newmarkBeta);
+
+ // the assembler with time loop for a transient problem
+ using Assembler = FVAssembler<TypeTag, DiffMethod::numeric>;
+ auto assembler = std::make_shared<Assembler>(problem, gridGeometry, gridVariables, timeLoop, xOld);
+
+ // the linear solver
+ using LAT = LinearAlgebraTraitsFromAssembler<Assembler>;
+ using LinearSolver = UMFPackIstlSolver<SeqLinearSolverTraits, LAT>;
+ auto linearSolver = std::make_shared<LinearSolver>();
+
+ // the non-linear solver
+ using NewtonSolver = Dumux::NewtonSolver<Assembler, LinearSolver>;
+ auto nonLinearSolver = std::make_shared<NewtonSolver>(assembler, linearSolver);
+
+ const int vtkInterval = getParam<int>("VTKOutput.Every", 5);
+
+ // time loop
+ timeLoop->start(); do
+ {
+ // linearize & solve
+ nonLinearSolver->solve(x);
+
+ // update the solution in the time stepping scheme
+ newmarkBeta->update(dt, x);
+
+ // make the new solution the old solution
+ xOld = x;
+ gridVariables->advanceTimeStep();
+
+ // advance to the time loop to the next step
+ timeLoop->advanceTimeStep();
+
+ // write VTK output
+ if (timeLoop->timeStepIndex() % vtkInterval == 0 || timeLoop->finished())
+ vtkWriter.write(timeLoop->time());
+
+ // report statistics of this time step
+ timeLoop->reportTimeStep();
+
+ } while (!timeLoop->finished());
+
+ timeLoop->finalize(leafGridView.comm());
+
+ return 0;
+}
diff --git a/test/geomechanics/hyperelastic_dynamic/params.input b/test/geomechanics/hyperelastic_dynamic/params.input
new file mode 100644
index 0000000000000000000000000000000000000000..6abda455fc8b2f95493fc229dacb4de295dc6bdb
--- /dev/null
+++ b/test/geomechanics/hyperelastic_dynamic/params.input
@@ -0,0 +1,24 @@
+[TimeLoop]
+TEnd = 10
+DtInitial = 0.01
+
+[Grid]
+File = solid.msh
+
+[Problem]
+Name = test_saint_venant_kirchhoff_dynamic
+Gravity = 2.0
+
+[SpatialParams]
+YoungsModulus = 1.4e6
+PoissonRatio = 0.4
+SolidDensity = 1000
+
+[Vtk]
+Precision = Float64
+CoordPrecision = Float64
+AddProcessRank = false
+
+[Newton]
+EnableDynamicOutput = false
+MaxRelativeShift = 1e-6
diff --git a/test/geomechanics/hyperelastic_dynamic/problem.hh b/test/geomechanics/hyperelastic_dynamic/problem.hh
new file mode 100644
index 0000000000000000000000000000000000000000..a0e86a28a9d32fa7d5bc5223f04aea70c3c99c61
--- /dev/null
+++ b/test/geomechanics/hyperelastic_dynamic/problem.hh
@@ -0,0 +1,135 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+#ifndef DUMUX_DYNAMIC_HYPERELASTICITY_TEST_PROBLEM_HH
+#define DUMUX_DYNAMIC_HYPERELASTICITY_TEST_PROBLEM_HH
+
+#include <dumux/common/boundarytypes.hh>
+#include <dumux/common/fvproblemwithspatialparams.hh>
+#include <dumux/common/numeqvector.hh>
+#include <dumux/common/parameters.hh>
+#include <dumux/common/properties.hh>
+#include <dumux/common/math.hh>
+
+namespace Dumux {
+
+// This test case corresponds to the CSM benchmark problem
+// of a hyperelastic solid material under gravity given in
+// Turek, S., Hron, J. (2006). "Proposal for Numerical Benchmarking of Fluid-Structure Interaction
+// between an Elastic Object and Laminar Incompressible Flow."
+// https://doi.org/10.1007/3-540-34596-5_15
+template<class TypeTag>
+class DynamicHyperelasticityProblem : public FVProblemWithSpatialParams<TypeTag>
+{
+ using ParentType = FVProblemWithSpatialParams<TypeTag>;
+ using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
+ using SubControlVolume = typename GridGeometry::SubControlVolume;
+ using GridView = typename GridGeometry::GridView;
+ using Element = typename GridView::template Codim<0>::Entity;
+ using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+ using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>;
+ using NumEqVector = Dumux::NumEqVector<PrimaryVariables>;
+ using BoundaryTypes = Dumux::BoundaryTypes<GetPropType<TypeTag, Properties::ModelTraits>::numEq()>;
+ static constexpr int dim = GridView::dimension;
+ using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+ using Tensor = Dune::FieldMatrix<Scalar, dim, dim>;
+
+ using SolutionVector = GetPropType<TypeTag, Properties::SolutionVector>;
+
+public:
+ DynamicHyperelasticityProblem(std::shared_ptr<const GridGeometry> gridGeometry)
+ : ParentType(gridGeometry)
+ , gravity_(getParam<Scalar>("Problem.Gravity"))
+ {}
+
+ /*!
+ * \brief Specifies which kind of boundary condition should be
+ * used for which equation on a given boundary control volume.
+ *
+ * \param globalPos The position of the center of the finite volume
+ */
+ BoundaryTypes boundaryTypesAtPos(const GlobalPosition &globalPos) const
+ {
+ BoundaryTypes values;
+ const auto r = std::hypot(globalPos[0]-0.2, globalPos[1]-0.2);
+ if (r < 0.05 + eps_)
+ {
+ values.setDirichlet(0);
+ values.setDirichlet(1);
+ }
+ else
+ values.setAllNeumann();
+ return values;
+ }
+
+ PrimaryVariables dirichletAtPos(const GlobalPosition& globalPos) const
+ { return PrimaryVariables(0.0); }
+
+ NumEqVector sourceAtPos(const GlobalPosition& globalPos) const
+ {
+ // gravity forcing
+ return {0.0, -this->spatialParams().solidDensity()*gravity_};
+ }
+
+ // Saint-Venant Kirchhoff material
+ Tensor firstPiolaKirchhoffStressTensor(const Tensor& F) const
+ {
+ // material parameters
+ const auto mu = this->spatialParams().shearModulus();
+ const auto lambda = this->spatialParams().firstLameParameter();
+
+ // Lagrangian Green strain E = 1/2*(F^T F - I)
+ auto E = multiplyMatrices(transpose(F), F);
+ E *= 0.5;
+ Scalar trace = 0.0;
+ for (int i = 0; i < dim; ++i)
+ {
+ E[i][i] -= 0.5;
+ trace += E[i][i];
+ }
+
+ // 2nd Piola Kirchhoff stress tensor S = λtr(E)I + 2µE
+ auto& S = E;
+ S *= 2*mu;
+ for (int i = 0; i < dim; ++i)
+ S[i][i] += lambda*trace;
+
+ // 1st Piola Kirchhoff stress tensor P = FS
+ return multiplyMatrices(F, S);
+ }
+
+ // the following methods are needed to solve structural dynamics
+ // with the Newmark-beta time integration scheme
+
+ // we use the Newmark scheme for time integration
+ void setNewmarkScheme(std::shared_ptr<const Experimental::NewmarkBeta<Scalar, SolutionVector>> newmark)
+ { newmark_ = std::move(newmark); }
+
+ // the effective density of the solid material
+ Scalar solidDensity(const Element&, const SubControlVolume&) const
+ { return this->spatialParams().solidDensity(); }
+
+ // the Newmark scheme is used for time integration and this
+ // computes the acceleration at the current time step for us
+ auto acceleration(const Element& element,
+ const SubControlVolume& scv,
+ const Scalar dt,
+ const PrimaryVariables& d) const
+ {
+ const auto dofIndex = scv.dofIndex();
+ return newmark_->acceleration(dofIndex, dt, d);
+ }
+
+private:
+ static constexpr Scalar eps_ = 1e-7;
+ Scalar gravity_;
+
+ std::shared_ptr<const Experimental::NewmarkBeta<Scalar, SolutionVector>> newmark_;
+};
+
+} // end namespace Dumux
+
+#endif
diff --git a/test/geomechanics/hyperelastic_dynamic/properties.hh b/test/geomechanics/hyperelastic_dynamic/properties.hh
new file mode 100644
index 0000000000000000000000000000000000000000..0c45c396de75a0a7e02727e8ab9552f3a428c24a
--- /dev/null
+++ b/test/geomechanics/hyperelastic_dynamic/properties.hh
@@ -0,0 +1,46 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+//
+// SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
+// SPDX-License-Identifier: GPL-3.0-or-later
+//
+#ifndef DUMUX_DYNAMIC_HYPERELASTICITY_TEST_PROPERTIES_HH
+#define DUMUX_DYNAMIC_HYPERELASTICITY_TEST_PROPERTIES_HH
+
+#include <type_traits>
+
+#include <dune/alugrid/grid.hh>
+#include <dumux/discretization/box.hh>
+#include <dumux/geomechanics/hyperelastic/model.hh>
+
+#include "problem.hh"
+
+namespace Dumux::Properties {
+
+namespace TTag {
+struct DynamicHyperelasticityTest
+{
+ using InheritsFrom = std::tuple<Hyperelastic, BoxModel>;
+ using Grid = Dune::ALUGrid<2, 2, Dune::simplex, Dune::conforming>;
+ using EnableGridVolumeVariablesCache = std::true_type;
+ using EnableGridFluxVariablesCache = std::true_type;
+ using EnableGridGeometryCache = std::true_type;
+};
+} // end namespace TTag
+
+template<class TypeTag>
+struct Problem<TypeTag, TTag::DynamicHyperelasticityTest>
+{ using type = DynamicHyperelasticityProblem<TypeTag>; };
+
+template<class TypeTag>
+struct SpatialParams<TypeTag, TTag::DynamicHyperelasticityTest>
+{
+ using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
+ using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+ using type = DefaultDynamicHyperelasticSpatialParams<GridGeometry, Scalar>;
+};
+
+
+} // end namespace Dumux::Properties
+
+#endif
diff --git a/test/geomechanics/hyperelastic_dynamic/solid.geo b/test/geomechanics/hyperelastic_dynamic/solid.geo
new file mode 100644
index 0000000000000000000000000000000000000000..b17abb704685d487cef4104872a96e115e8356e9
--- /dev/null
+++ b/test/geomechanics/hyperelastic_dynamic/solid.geo
@@ -0,0 +1,7 @@
+//+
+SetFactory("OpenCASCADE");
+Rectangle(1) = {0.2, 0.19, 0, 0.4, 0.02, 0};
+//+
+Disk(2) = {0.2, 0.2, 0, 0.05, 0.05};
+//+
+BooleanDifference{ Surface{1}; Delete; }{ Surface{2}; Delete; }
diff --git a/test/geomechanics/hyperelastic_dynamic/solid.msh b/test/geomechanics/hyperelastic_dynamic/solid.msh
new file mode 100644
index 0000000000000000000000000000000000000000..5c84585f46aaefc35c659e1e0c14d5a9802f0b1f
--- /dev/null
+++ b/test/geomechanics/hyperelastic_dynamic/solid.msh
@@ -0,0 +1,3273 @@
+$MeshFormat
+2.2 0 8
+$EndMeshFormat
+$Nodes
+1087
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diff --git a/test/references/test_saint_venant_kirchhoff_dynamic-reference.vtu b/test/references/test_saint_venant_kirchhoff_dynamic-reference.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..98c180da339e5c8141038823dd4fdd26be774451
--- /dev/null
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