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| 1 | // -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- | ||
| 2 | // vi: set et ts=4 sw=4 sts=4: | ||
| 3 | // | ||
| 4 | // SPDX-FileCopyrightText: Copyright © DuMux Project contributors, see AUTHORS.md in root folder | ||
| 5 | // SPDX-License-Identifier: GPL-3.0-or-later | ||
| 6 | // | ||
| 7 | #ifndef DUMUX_DYNAMIC_HYPERELASTICITY_TEST_PROBLEM_HH | ||
| 8 | #define DUMUX_DYNAMIC_HYPERELASTICITY_TEST_PROBLEM_HH | ||
| 9 | |||
| 10 | #include <dumux/common/boundarytypes.hh> | ||
| 11 | #include <dumux/common/fvproblemwithspatialparams.hh> | ||
| 12 | #include <dumux/common/numeqvector.hh> | ||
| 13 | #include <dumux/common/parameters.hh> | ||
| 14 | #include <dumux/common/properties.hh> | ||
| 15 | #include <dumux/common/math.hh> | ||
| 16 | |||
| 17 | #include <dumux/experimental/timestepping/newmarkbeta.hh> | ||
| 18 | |||
| 19 | namespace Dumux { | ||
| 20 | |||
| 21 | // This test case corresponds to the CSM benchmark problem | ||
| 22 | // of a hyperelastic solid material under gravity given in | ||
| 23 | // Turek, S., Hron, J. (2006). "Proposal for Numerical Benchmarking of Fluid-Structure Interaction | ||
| 24 | // between an Elastic Object and Laminar Incompressible Flow." | ||
| 25 | // https://doi.org/10.1007/3-540-34596-5_15 | ||
| 26 | template<class TypeTag> | ||
| 27 | class DynamicHyperelasticityProblem : public FVProblemWithSpatialParams<TypeTag> | ||
| 28 | { | ||
| 29 | using ParentType = FVProblemWithSpatialParams<TypeTag>; | ||
| 30 | using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>; | ||
| 31 | using SubControlVolume = typename GridGeometry::SubControlVolume; | ||
| 32 | using GridView = typename GridGeometry::GridView; | ||
| 33 | using Element = typename GridView::template Codim<0>::Entity; | ||
| 34 | using Scalar = GetPropType<TypeTag, Properties::Scalar>; | ||
| 35 | using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>; | ||
| 36 | using NumEqVector = Dumux::NumEqVector<PrimaryVariables>; | ||
| 37 | using BoundaryTypes = Dumux::BoundaryTypes<GetPropType<TypeTag, Properties::ModelTraits>::numEq()>; | ||
| 38 | static constexpr int dim = GridView::dimension; | ||
| 39 | using GlobalPosition = typename Element::Geometry::GlobalCoordinate; | ||
| 40 | using Tensor = Dune::FieldMatrix<Scalar, dim, dim>; | ||
| 41 | |||
| 42 | using SolutionVector = GetPropType<TypeTag, Properties::SolutionVector>; | ||
| 43 | |||
| 44 | public: | ||
| 45 | 1 | DynamicHyperelasticityProblem(std::shared_ptr<const GridGeometry> gridGeometry) | |
| 46 | : ParentType(gridGeometry) | ||
| 47 |
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3 | , gravity_(getParam<Scalar>("Problem.Gravity")) |
| 48 | 1 | {} | |
| 49 | |||
| 50 | /*! | ||
| 51 | * \brief Specifies which kind of boundary condition should be | ||
| 52 | * used for which equation on a given boundary control volume. | ||
| 53 | * | ||
| 54 | * \param globalPos The position of the center of the finite volume | ||
| 55 | */ | ||
| 56 | 212432 | BoundaryTypes boundaryTypesAtPos(const GlobalPosition &globalPos) const | |
| 57 | { | ||
| 58 |
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212432 | BoundaryTypes values; |
| 59 | 212432 | const auto r = std::hypot(globalPos[0]-0.2, globalPos[1]-0.2); | |
| 60 |
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212432 | if (r < 0.05 + eps_) |
| 61 | { | ||
| 62 | 6532 | values.setDirichlet(0); | |
| 63 | 6532 | values.setDirichlet(1); | |
| 64 | } | ||
| 65 | else | ||
| 66 | 212432 | values.setAllNeumann(); | |
| 67 | 212432 | return values; | |
| 68 | } | ||
| 69 | |||
| 70 | 6532 | PrimaryVariables dirichletAtPos(const GlobalPosition& globalPos) const | |
| 71 | 13064 | { return PrimaryVariables(0.0); } | |
| 72 | |||
| 73 | 11468772 | NumEqVector sourceAtPos(const GlobalPosition& globalPos) const | |
| 74 | { | ||
| 75 | // gravity forcing | ||
| 76 | 11468772 | return {0.0, -this->spatialParams().solidDensity()*gravity_}; | |
| 77 | } | ||
| 78 | |||
| 79 | // Saint-Venant Kirchhoff material | ||
| 80 | 11468772 | Tensor firstPiolaKirchhoffStressTensor(const Tensor& F) const | |
| 81 | { | ||
| 82 | // material parameters | ||
| 83 | 11468772 | const auto mu = this->spatialParams().shearModulus(); | |
| 84 | 11468772 | const auto lambda = this->spatialParams().firstLameParameter(); | |
| 85 | |||
| 86 | // Lagrangian Green strain E = 1/2*(F^T F - I) | ||
| 87 | 11468772 | auto E = multiplyMatrices(transpose(F), F); | |
| 88 | 11468772 | E *= 0.5; | |
| 89 | Scalar trace = 0.0; | ||
| 90 |
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34406316 | for (int i = 0; i < dim; ++i) |
| 91 | { | ||
| 92 | 22937544 | E[i][i] -= 0.5; | |
| 93 | 22937544 | trace += E[i][i]; | |
| 94 | } | ||
| 95 | |||
| 96 | // 2nd Piola Kirchhoff stress tensor S = λtr(E)I + 2µE | ||
| 97 | 11468772 | auto& S = E; | |
| 98 | 11468772 | S *= 2*mu; | |
| 99 |
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34406316 | for (int i = 0; i < dim; ++i) |
| 100 | 22937544 | S[i][i] += lambda*trace; | |
| 101 | |||
| 102 | // 1st Piola Kirchhoff stress tensor P = FS | ||
| 103 | 11468772 | return multiplyMatrices(F, S); | |
| 104 | } | ||
| 105 | |||
| 106 | // the following methods are needed to solve structural dynamics | ||
| 107 | // with the Newmark-beta time integration scheme | ||
| 108 | |||
| 109 | // we use the Newmark scheme for time integration | ||
| 110 | 1 | void setNewmarkScheme(std::shared_ptr<const Experimental::NewmarkBeta<Scalar, SolutionVector>> newmark) | |
| 111 |
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1 | { newmark_ = std::move(newmark); } |
| 112 | |||
| 113 | // the effective density of the solid material | ||
| 114 | 11468772 | Scalar solidDensity(const Element&, const SubControlVolume&) const | |
| 115 | 11468772 | { return this->spatialParams().solidDensity(); } | |
| 116 | |||
| 117 | // the Newmark scheme is used for time integration and this | ||
| 118 | // computes the acceleration at the current time step for us | ||
| 119 | 11468772 | auto acceleration(const Element& element, | |
| 120 | const SubControlVolume& scv, | ||
| 121 | const Scalar dt, | ||
| 122 | const PrimaryVariables& d) const | ||
| 123 | { | ||
| 124 | 11468772 | const auto dofIndex = scv.dofIndex(); | |
| 125 | 11468772 | return newmark_->acceleration(dofIndex, dt, d); | |
| 126 | } | ||
| 127 | |||
| 128 | private: | ||
| 129 | static constexpr Scalar eps_ = 1e-7; | ||
| 130 | Scalar gravity_; | ||
| 131 | |||
| 132 | std::shared_ptr<const Experimental::NewmarkBeta<Scalar, SolutionVector>> newmark_; | ||
| 133 | }; | ||
| 134 | |||
| 135 | } // end namespace Dumux | ||
| 136 | |||
| 137 | #endif | ||
| 138 |