Line data Source code
1 : //
2 : // This model implements an isotropic linear elastic material.
3 : // See `this link <https://en.wikipedia.org/wiki/Linear_elasticity#(An)isotropic_(in)homogeneous_media>`_
4 : // for more information about the theory.
5 : //
6 : // Free energy for a linear material is defined as
7 : //
8 : // .. math::
9 : //
10 : // W(\nabla\mathbf{u}) =
11 : // \frac{1}{2}\nabla\mathbf{u}\cdot\mathbb{C}\,\nabla\mathbf{u}
12 : //
13 : // For an isotropic material, stress and strain are related through
14 : //
15 : // .. math::
16 : //
17 : // \mathbb{C}_{ijkl} = \lambda \delta_{ij}\varepsilon_{kk} + 2\mu\varepsilon_{ij}
18 : //
19 : // where :math:`\lambda` and :math:`\mu` are the Lame constant and shear modulus, respectively.
20 : // Users can specify these either through (:code:`lame` and :code:`shear`)
21 : // OR (:code:`lambda` and :code:`mu`) OR (:code:`E` and :code:`nu`).
22 : //
23 : // Class methods:
24 : //
25 : // #. :code:`Isotropic()`:
26 : // Basic constructor. Does nothing, and leaves all values initiated as NAN.
27 : // #. :code:`Isotropic(Solid<Set::Sym::Isotropic> base)`
28 : // Basic constructor. Does nothing gut allows for inheritance.
29 : // #. :code:`Isotropic(Set::Scalar a_mu, Set::Scalar a_lambda)`
30 : // BAD old-fashioned constructor. Do not use!
31 : // #. :code:`~Isotropic()`
32 : // Simple destructor. Don't need to change it.
33 : // #. :code:`void Define(Set::Scalar a_mu, Set::Scalar a_lambda)`
34 : // BAD old-fashioned way of doing things. Use :code:`Parse` instead.
35 : // #. :code:`Set::Scalar W(const Set::Matrix & gradu) const override`
36 : // Returns elastic free energy density
37 : // #. :code:`Set::Matrix DW(const Set::Matrix & gradu) const override`
38 : // Returns first derivative of free energy, the stress tensor
39 : // #. :code:`Set::Matrix4<...> DDW(const Set::Matrix & ) const override`
40 : // Returns second derivative of free energy, the modulus tensor
41 : // #. :code:`virtual void Print(std::ostream &out) const override`
42 : // Prints the modulus tensor object to output stream (usually the terminal)
43 : // #. :code:`static Isotropic Random()`
44 : // Static method that generates a random yet acceptable model.
45 : // #. :code:`static Isotropic Zero()`
46 : // Static method that generates a "zero" element (so that there is no effect under addition)
47 : // #. :code:`static void Parse(Isotropic & value, IO::ParmParse & pp)`
48 : // Parser where all the IO occurs
49 : //
50 : //
51 :
52 : #ifndef MODEL_SOLID_LINEAR_ISOTROPIC_H_
53 : #define MODEL_SOLID_LINEAR_ISOTROPIC_H_
54 :
55 : #include "Model/Solid/Solid.H"
56 : #include "IO/ParmParse.H"
57 :
58 : namespace Model
59 : {
60 : namespace Solid
61 : {
62 : namespace Linear
63 : {
64 : class Isotropic : public Solid<Set::Sym::Isotropic>
65 : {
66 : public:
67 :
68 5911872 : Isotropic() {};
69 : Isotropic(Solid<Set::Sym::Isotropic> base) : Solid<Set::Sym::Isotropic>(base) {};
70 0 : Isotropic(Set::Scalar a_mu, Set::Scalar a_lambda)
71 0 : {
72 0 : Define(a_mu,a_lambda);
73 0 : };
74 5955272 : virtual ~Isotropic() {};
75 :
76 1828218 : void Define(Set::Scalar a_mu, Set::Scalar a_lambda)
77 : {
78 1828218 : ddw = Set::Matrix4<AMREX_SPACEDIM,Set::Sym::Isotropic>(a_lambda,a_mu);
79 1828218 : }
80 :
81 260 : Set::Scalar W(const Set::Matrix & gradu) const override
82 : {
83 520 : return ( 0.5 * gradu.transpose() * (ddw*gradu) ).trace();
84 : }
85 1919659 : Set::Matrix DW(const Set::Matrix & gradu) const override
86 : {
87 3839318 : return ddw*gradu;
88 : }
89 1849088 : Set::Matrix4<AMREX_SPACEDIM,Set::Sym::Isotropic> DDW(const Set::Matrix & /*gradu*/) const override
90 : {
91 1849088 : return ddw;
92 : }
93 10 : virtual void Print(std::ostream &out) const override
94 : {
95 10 : out << ddw;
96 10 : }
97 :
98 : public:
99 : Set::Matrix4<AMREX_SPACEDIM,Set::Sym::Isotropic> ddw;
100 : static const KinematicVariable kinvar = KinematicVariable::gradu;
101 :
102 : public:
103 44 : static Isotropic Random()
104 : {
105 44 : Isotropic ret;
106 44 : ret.Define(Util::Random(),Util::Random());
107 44 : return ret;
108 0 : }
109 1828164 : static Isotropic Zero()
110 : {
111 1828164 : Isotropic ret;
112 1828164 : ret.Define(0.,0.);
113 1828164 : return ret;
114 : }
115 10 : static void Parse(Isotropic & value, IO::ParmParse & pp)
116 : {
117 : Set::Scalar mu, lambda;
118 10 : bool planestress = false;
119 :
120 : // Whether or not to use the
121 : // `plane stress <https://en.wikipedia.org/wiki/Plane_stress>`_
122 : // approximation.
123 10 : pp_query("planestress",planestress);
124 30 : if (pp.contains("lame") && pp.contains("shear"))
125 : {
126 0 : pp_query("lame",lambda); // Lame parameter
127 0 : pp_query("shear",mu); // Shear modulus (redundant with "mu")
128 : }
129 34 : if (pp.contains("lambda") && pp.contains("mu"))
130 : {
131 0 : pp_query("lambda",lambda); // Lame parameter
132 0 : pp_query("mu",mu); // Shear modulus (redundant with "shear")
133 : }
134 50 : else if (pp.contains("E") && pp.contains("nu"))
135 : {
136 : Set::Scalar E, nu;
137 10 : pp_query("E",E); // Elastic modulus
138 10 : pp_query("nu",nu); // Poisson's ratio
139 10 : lambda = E * nu / (1.0 + nu) / (1.0 - 2.0*nu);
140 10 : mu = E / 2.0 / (1.0 + nu);
141 : }
142 0 : else Util::Abort(INFO,"Invalid elastic constants specified");
143 :
144 7 : if (AMREX_SPACEDIM==2 && planestress)
145 5 : value.Define(mu,lambda*(1.0 - lambda/(2.*mu + lambda)));
146 : else
147 5 : value.Define(mu,lambda);
148 30 : Util::Message(INFO,value);
149 10 : }
150 :
151 : #define OP_CLASS Isotropic
152 : #define OP_VARS X(ddw)
153 : #include "Model/Solid/InClassOperators.H"
154 : };
155 : #include "Model/Solid/ExtClassOperators.H"
156 :
157 :
158 :
159 : }
160 : }
161 : }
162 :
163 : #endif
|
