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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 | /*! | ||
| 8 | * \file | ||
| 9 | * \ingroup BoxFlux | ||
| 10 | * \brief Specialization of Hooke's law for the box scheme. This computes | ||
| 11 | * the stress tensor and surface forces resulting from mechanical deformation. | ||
| 12 | */ | ||
| 13 | #ifndef DUMUX_DISCRETIZATION_BOX_HOOKES_LAW_HH | ||
| 14 | #define DUMUX_DISCRETIZATION_BOX_HOOKES_LAW_HH | ||
| 15 | |||
| 16 | #include <dune/common/fmatrix.hh> | ||
| 17 | |||
| 18 | #include <dumux/flux/hookeslaw.hh> | ||
| 19 | #include <dumux/discretization/method.hh> | ||
| 20 | #include <dumux/discretization/extrusion.hh> | ||
| 21 | |||
| 22 | namespace Dumux { | ||
| 23 | |||
| 24 | /*! | ||
| 25 | * \ingroup BoxFlux | ||
| 26 | * \brief Hooke's law for box scheme | ||
| 27 | * \tparam ScalarType the scalar type for scalar physical quantities | ||
| 28 | * \tparam GridGeometry the grid geometry | ||
| 29 | */ | ||
| 30 | template<class ScalarType, class GridGeometry> | ||
| 31 | class HookesLaw<ScalarType, GridGeometry, typename GridGeometry::DiscretizationMethod> | ||
| 32 | { | ||
| 33 | using FVElementGeometry = typename GridGeometry::LocalView; | ||
| 34 | using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace; | ||
| 35 | using Extrusion = Extrusion_t<GridGeometry>; | ||
| 36 | |||
| 37 | using GridView = typename GridGeometry::GridView; | ||
| 38 | using Element = typename GridView::template Codim<0>::Entity; | ||
| 39 | |||
| 40 | static constexpr int dim = GridView::dimension; | ||
| 41 | static constexpr int dimWorld = GridView::dimensionworld; | ||
| 42 | static_assert(dim == dimWorld, "Hookes Law not implemented for network/surface grids"); | ||
| 43 | |||
| 44 | public: | ||
| 45 | //! export the type used for scalar values | ||
| 46 | using Scalar = ScalarType; | ||
| 47 | //! export the type used for the stress tensor | ||
| 48 | using StressTensor = Dune::FieldMatrix<Scalar, dim, dimWorld>; | ||
| 49 | //! export the type used for force vectors | ||
| 50 | using ForceVector = typename StressTensor::row_type; | ||
| 51 | //! state the discretization method this implementation belongs to | ||
| 52 | |||
| 53 | using DiscretizationMethod = DiscretizationMethods::Box; | ||
| 54 | // state the discretization method this implementation belongs to | ||
| 55 | static constexpr DiscretizationMethod discMethod{}; | ||
| 56 | |||
| 57 | /*! | ||
| 58 | * \brief Returns the force (in Newton) acting on a sub-control volume face. | ||
| 59 | */ | ||
| 60 | template<class Problem, class ElementVolumeVariables, class ElementFluxVarsCache> | ||
| 61 | 7200 | static ForceVector force(const Problem& problem, | |
| 62 | const Element& element, | ||
| 63 | const FVElementGeometry& fvGeometry, | ||
| 64 | const ElementVolumeVariables& elemVolVars, | ||
| 65 | const SubControlVolumeFace& scvf, | ||
| 66 | const ElementFluxVarsCache& elemFluxVarCache) | ||
| 67 | { | ||
| 68 | 14400 | const auto sigma = stressTensor(problem, element, fvGeometry, elemVolVars, elemFluxVarCache[scvf]); | |
| 69 | |||
| 70 | 7200 | ForceVector scvfForce(0.0); | |
| 71 | 7200 | sigma.mv(scvf.unitOuterNormal(), scvfForce); | |
| 72 | 14400 | scvfForce *= Extrusion::area(fvGeometry, scvf); | |
| 73 | |||
| 74 | 7200 | return scvfForce; | |
| 75 | } | ||
| 76 | |||
| 77 | //! assembles the stress tensor at a given integration point | ||
| 78 | template<class Problem, class ElementVolumeVariables, class FluxVarsCache> | ||
| 79 | 1204576 | static StressTensor stressTensor(const Problem& problem, | |
| 80 | const Element& element, | ||
| 81 | const FVElementGeometry& fvGeometry, | ||
| 82 | const ElementVolumeVariables& elemVolVars, | ||
| 83 | const FluxVarsCache& fluxVarCache) | ||
| 84 | { | ||
| 85 | 2409152 | const auto& lameParams = problem.spatialParams().lameParams(element, fvGeometry, elemVolVars, fluxVarCache); | |
| 86 | |||
| 87 | // evaluate displacement gradient | ||
| 88 | 1204576 | StressTensor gradU(0.0); | |
| 89 |
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4790304 | for (int dir = 0; dir < dim; ++dir) |
| 90 |
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64095104 | for (const auto& scv : scvs(fvGeometry)) |
| 91 | 170770944 | gradU[dir].axpy(elemVolVars[scv.indexInElement()].displacement(dir), fluxVarCache.gradN(scv.indexInElement())); | |
| 92 | |||
| 93 | // evaluate strain tensor | ||
| 94 | 1204576 | StressTensor epsilon; | |
| 95 |
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4790304 | for (int i = 0; i < dim; ++i) |
| 96 |
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14286912 | for (int j = 0; j < dimWorld; ++j) |
| 97 | 74908288 | epsilon[i][j] = 0.5*(gradU[i][j] + gradU[j][i]); | |
| 98 | |||
| 99 | // calculate sigma | ||
| 100 | 1204576 | StressTensor sigma(0.0); | |
| 101 | const auto traceEpsilon = trace(epsilon); | ||
| 102 |
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| 103 | { | ||
| 104 | 7171456 | sigma[i][i] = lameParams.lambda()*traceEpsilon; | |
| 105 |
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14286912 | for (int j = 0; j < dimWorld; ++j) |
| 106 | 53505920 | sigma[i][j] += 2.0*lameParams.mu()*epsilon[i][j]; | |
| 107 | } | ||
| 108 | |||
| 109 | 1204576 | return sigma; | |
| 110 | } | ||
| 111 | }; | ||
| 112 | |||
| 113 | } // end namespace Dumux | ||
| 114 | |||
| 115 | #endif | ||
| 116 |