Line data Source code
1 0 : // Distributed under the MIT License.
2 : // See LICENSE.txt for details.
3 :
4 : #pragma once
5 :
6 : #include <cstddef>
7 : #include <limits>
8 : #include <memory>
9 : #include <pup.h>
10 :
11 : #include "DataStructures/Tensor/TypeAliases.hpp"
12 : #include "Options/String.hpp"
13 : #include "PointwiseFunctions/Elasticity/ConstitutiveRelations/ConstitutiveRelation.hpp"
14 : #include "Utilities/Serialization/CharmPupable.hpp"
15 : #include "Utilities/TMPL.hpp"
16 :
17 : /// \cond
18 : class DataVector;
19 : /// \endcond
20 :
21 : namespace Elasticity::ConstitutiveRelations {
22 :
23 : /*!
24 : * \brief A cubic crystalline material
25 : *
26 : * \details For a cubic crystalline material the Elasticity tensor in the linear
27 : * constitutive relation \f$T^{ij}=-Y^{ijkl}S_{kl}\f$ reduces to
28 : *
29 : * \f[
30 : * Y^{ijkl} =
31 : * \begin{cases}
32 : * c_{11} & \mathrm{for}\; i=j=k=l \\
33 : * c_{12} & \mathrm{for}\; i=j,k=l,i \neq k \\
34 : * c_{44} & \mathrm{for}\; i=k,j=l,i \neq j \;\mathrm{or}\; i=l,j=k,i\neq j \\
35 : * \end{cases}
36 : * \f]
37 : *
38 : * with the three independent parameters: the \f$\mathrm{Lam\acute{e}}\f$
39 : * parameter \f$\lambda\f$, the Shear modulus \f$\mu\f$ and the %Poisson
40 : * ratio \f$\nu\f$. In the parametrization chosen in this implementation we use
41 : * the experimental group parameters \f$c_{11}\f$, \f$c_{12}\f$ and
42 : * \f$c_{44}\f$, related by;
43 : *
44 : * \f[
45 : * c_{11} = \frac{1 - \nu}{\nu} \lambda = \frac{(1 - \nu)E}{(1 + \nu)(1 -
46 : * 2\nu)}, \quad
47 : * c_{12} = \lambda = \frac{E\nu}{(1 + \nu)(1 - 2\nu)}, \quad
48 : * c_{44} = \mu
49 : * \f]
50 : *
51 : * and inversely;
52 : *
53 : * \f[
54 : * E = \frac{(c_{11} + 2c_{12})(c_{11} - c_{12})}{c_{11} + c_{12}}, \quad
55 : * \nu = \left(1 + \frac{c_{11}}{c_{12}}\right)^{-1}, \quad
56 : * \mu = c_{44}
57 : * \f]
58 : *
59 : * The stress-strain relation then reduces to
60 : *
61 : * \f[
62 : * T^{ij} =
63 : * \begin{cases}
64 : * -(c_{11} - c_{12}) S^{ij} - c_{12} \mathrm{Tr}(S) & \mathrm{for}\; i=j \\
65 : * -2 c_{44} S^{ij} & \mathrm{for}\; i \neq j \\
66 : * \end{cases}
67 : * \f]
68 : *
69 : * In the case where the shear modulus satisfies \f$c_{44} =
70 : * \frac{c_{11}-c_{12}}{2}\f$ the constitutive relation is that of an isotropic
71 : * material (see `Elasticity::ConstitutiveRelations::IsotropicHomogeneous`).
72 : */
73 :
74 1 : class CubicCrystal : public ConstitutiveRelation<3> {
75 : public:
76 0 : static constexpr size_t volume_dim = 3;
77 :
78 0 : struct C_11 {
79 0 : using type = double;
80 0 : static constexpr Options::String help = {
81 : "c_11 parameter for a cubic crystal"};
82 0 : static type lower_bound() { return 0.0; }
83 : };
84 :
85 0 : struct C_12 {
86 0 : using type = double;
87 0 : static constexpr Options::String help = {
88 : "c_12 parameter for a cubic crystal"};
89 0 : static type lower_bound() { return 0.0; }
90 : };
91 :
92 0 : struct C_44 {
93 0 : using type = double;
94 0 : static constexpr Options::String help = {
95 : "c_44 parameter for a cubic crystal"};
96 0 : static type lower_bound() { return 0.0; }
97 : };
98 :
99 0 : using options = tmpl::list<C_11, C_12, C_44>;
100 :
101 0 : static constexpr Options::String help = {
102 : "A constitutive relation that describes a cubic, crystalline material in "
103 : "terms of the three independent group paremeters. The parameters "
104 : "are measured in units of stress, typically Pascals."};
105 :
106 0 : CubicCrystal() = default;
107 0 : CubicCrystal(const CubicCrystal&) = default;
108 0 : CubicCrystal& operator=(const CubicCrystal&) = default;
109 0 : CubicCrystal(CubicCrystal&&) = default;
110 0 : CubicCrystal& operator=(CubicCrystal&&) = default;
111 0 : ~CubicCrystal() override = default;
112 :
113 0 : CubicCrystal(double c_11, double c_12, double c_44);
114 :
115 1 : std::unique_ptr<ConstitutiveRelation<3>> get_clone() const override;
116 :
117 : /// The constitutive relation that characterizes the elastic properties of a
118 : /// material
119 1 : void stress(gsl::not_null<tnsr::II<DataVector, 3>*> stress,
120 : const tnsr::ii<DataVector, 3>& strain,
121 : const tnsr::I<DataVector, 3>& x) const override;
122 :
123 : /// The 1st group parameter \f$c_{11} = \frac{1 - \nu}{\nu} \lambda\f$
124 1 : double c_11() const;
125 : /// The 2nd group parameter; the \f$\mathrm{Lam\acute{e}}\f$ parameter
126 : /// \f$c_{12} = \lambda\f$
127 1 : double c_12() const;
128 : /// The 3rd group parameter; the shear modulus (rigidity) \f$c_{44} = \mu\f$
129 1 : double c_44() const;
130 : /// The Young's modulus \f$E\f$
131 1 : double youngs_modulus() const;
132 : /// The %Poisson ratio \f$\nu\f$
133 1 : double poisson_ratio() const;
134 :
135 : // clang-tidy: no runtime references
136 0 : void pup(PUP::er& /*p*/) override; // NOLINT
137 :
138 0 : explicit CubicCrystal(CkMigrateMessage* /*unused*/) {}
139 :
140 0 : WRAPPED_PUPable_decl_base_template( // NOLINT
141 : SINGLE_ARG(ConstitutiveRelation<3>), CubicCrystal);
142 :
143 : private:
144 0 : double c_11_ = std::numeric_limits<double>::signaling_NaN();
145 0 : double c_12_ = std::numeric_limits<double>::signaling_NaN();
146 0 : double c_44_ = std::numeric_limits<double>::signaling_NaN();
147 : }; // namespace ConstitutiveRelations
148 :
149 0 : bool operator==(const CubicCrystal& lhs, const CubicCrystal& rhs);
150 0 : bool operator!=(const CubicCrystal& lhs, const CubicCrystal& rhs);
151 :
152 : } // namespace Elasticity::ConstitutiveRelations
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