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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-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder | ||
| 5 | // SPDX-License-Identifier: GPL-3.0-or-later | ||
| 6 | // | ||
| 7 | #ifndef DUMUX_HYPERELASTICITY_TEST_PROBLEM_HH | ||
| 8 | #define DUMUX_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 | namespace Dumux { | ||
| 18 | |||
| 19 | // This test case is adapted from | ||
| 20 | // https://fenicsproject.org/olddocs/dolfin/1.6.0/python/demo/documented/hyperelasticity/python/documentation.html | ||
| 21 | // using a slightly different material law and finite volumes | ||
| 22 | template<class TypeTag> | ||
| 23 | 1 | class HyperelasticityProblem : public FVProblemWithSpatialParams<TypeTag> | |
| 24 | { | ||
| 25 | using ParentType = FVProblemWithSpatialParams<TypeTag>; | ||
| 26 | using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>; | ||
| 27 | using FVElementGeometry = typename GridGeometry::LocalView; | ||
| 28 | using SubControlVolume = typename GridGeometry::SubControlVolume; | ||
| 29 | using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace; | ||
| 30 | using GridView = typename GridGeometry::GridView; | ||
| 31 | using Element = typename GridView::template Codim<0>::Entity; | ||
| 32 | using Scalar = GetPropType<TypeTag, Properties::Scalar>; | ||
| 33 | using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>; | ||
| 34 | using NumEqVector = Dumux::NumEqVector<PrimaryVariables>; | ||
| 35 | using BoundaryTypes = Dumux::BoundaryTypes<GetPropType<TypeTag, Properties::ModelTraits>::numEq()>; | ||
| 36 | static constexpr int dimWorld = GridView::dimensionworld; | ||
| 37 | static constexpr int dim = GridView::dimension; | ||
| 38 | using GlobalPosition = typename Element::Geometry::GlobalCoordinate; | ||
| 39 | using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices; | ||
| 40 | using Tensor = Dune::FieldMatrix<Scalar, dim, dim>; | ||
| 41 | |||
| 42 | public: | ||
| 43 | 1 | HyperelasticityProblem(std::shared_ptr<const GridGeometry> gridGeometry) | |
| 44 |
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3 | : ParentType(gridGeometry) |
| 45 | 1 | {} | |
| 46 | |||
| 47 | 62016 | BoundaryTypes boundaryTypesAtPos(const GlobalPosition &globalPos) const | |
| 48 | { | ||
| 49 | 62016 | BoundaryTypes values; | |
| 50 |
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310080 | if (globalPos[0] < this->gridGeometry().bBoxMin()[0] + eps_ || globalPos[0] > this->gridGeometry().bBoxMax()[0] - eps_) |
| 51 | values.setAllDirichlet(); | ||
| 52 | 62016 | return values; | |
| 53 | } | ||
| 54 | |||
| 55 | template<class ElementVolumeVariables, class ElementFluxVariablesCache> | ||
| 56 | ✗ | NumEqVector neumann(const Element& element, | |
| 57 | const FVElementGeometry& fvGeometry, | ||
| 58 | const ElementVolumeVariables& elemVolVars, | ||
| 59 | const ElementFluxVariablesCache& elemFluxVarsCache, | ||
| 60 | const SubControlVolumeFace& scvf) const | ||
| 61 | { | ||
| 62 | ✗ | return {0.1, 0.0, 0.0}; | |
| 63 | } | ||
| 64 | |||
| 65 | 16384 | PrimaryVariables dirichletAtPos(const GlobalPosition& globalPos) const | |
| 66 | { | ||
| 67 |
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81920 | if (globalPos[0] > this->gridGeometry().bBoxMax()[0] - eps_) |
| 68 | 8192 | return {0.0, 0.0, 0.0}; | |
| 69 | |||
| 70 | 8192 | PrimaryVariables values(0.0); | |
| 71 | 8192 | const auto y = globalPos[1]; | |
| 72 | 8192 | const auto z = globalPos[2]; | |
| 73 | 8192 | values[0] = 0.0; | |
| 74 | 8192 | values[1] = 0.5*(0.5 + (y-0.5)*std::cos(M_PI/3.0) - (z-0.5)*std::sin(M_PI/3.0) - y); | |
| 75 | 8192 | values[2] = 0.5*(0.5 + (y-0.5)*std::sin(M_PI/3.0) + (z-0.5)*std::cos(M_PI/3.0) - z); | |
| 76 | 8192 | return values; | |
| 77 | } | ||
| 78 | |||
| 79 | ✗ | NumEqVector sourceAtPos(const GlobalPosition& globalPos) const | |
| 80 | 9830400 | { return {0.0, -0.5, 0.0}; } | |
| 81 | |||
| 82 | // Some Neo-Hookean material | ||
| 83 | // from Simo and Armero, 1992 (https://doi.org/10.1002/nme.1620330705) Eq. 77/78 | ||
| 84 | // ψ = K(0.5(J*J - 1) - ln J) + 0.5µ (J^(-2/3) tr(C) - 3) | ||
| 85 | // P = 2F∂ψ/∂C = µ J^(-2/3) (F - 1/3*tr(C)*F^-T) + K*(J*J - 1)F^-T | ||
| 86 | 14745600 | Tensor firstPiolaKirchhoffStressTensor(Tensor F) const | |
| 87 | { | ||
| 88 | // invariants | ||
| 89 | 14745600 | const auto J = F.determinant(); | |
| 90 | 14745600 | const auto Jm23 = std::pow(J, -2.0/3.0); | |
| 91 | 14745600 | auto trC = 0.0; | |
| 92 |
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58982400 | for (int i = 0; i < dimWorld; ++i) |
| 93 |
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176947200 | for (int j = 0; j < dimWorld; ++j) |
| 94 | 663552000 | trC += F[i][j]*F[i][j]; | |
| 95 | |||
| 96 | // inverse transpose of deformation gradient | ||
| 97 | 14745600 | const auto invFT = [&](){ | |
| 98 | 14745600 | auto invFT = F; | |
| 99 |
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14745600 | if (J != 0.0) |
| 100 | 14745600 | invFT.invert(); | |
| 101 | 14745600 | return transpose(invFT); | |
| 102 | 14745600 | }(); | |
| 103 | |||
| 104 | // material parameters | ||
| 105 | 14745600 | const auto mu = this->spatialParams().shearModulus(); | |
| 106 | 14745600 | const auto K = this->spatialParams().bulkModulus(); | |
| 107 | |||
| 108 | // assemble 1st Piola Kirchhoff stress tensor | ||
| 109 | 14745600 | Tensor P(0.0); | |
| 110 | 14745600 | P.axpy(K*(J*J - 1), invFT); | |
| 111 | 14745600 | auto& FTerm = F; | |
| 112 | 14745600 | FTerm.axpy(-1.0/3.0*trC, invFT); | |
| 113 | 14745600 | P.axpy(mu*Jm23, FTerm); | |
| 114 | 14745600 | return P; | |
| 115 | } | ||
| 116 | |||
| 117 | private: | ||
| 118 | static constexpr Scalar eps_ = 1e-7; | ||
| 119 | }; | ||
| 120 | |||
| 121 | } // end namespace Dumux | ||
| 122 | |||
| 123 | #endif | ||
| 124 |