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/**
* @file common.hh
*
* @author Till Junge <till.junge@epfl.ch>
*
* @date 01 May 2017
*
* @brief Small definitions of commonly used types throughout µSpectre
*
* @section LICENSE
*
* Copyright © 2017 Till Junge
*
* µSpectre is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public License as
* published by the Free Software Foundation, either version 3, or (at
* your option) any later version.
*
* µSpectre is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with µSpectre; see the file COPYING. If not, write to the
* Free Software Foundation, Inc., 59 Temple Place - Suite 330,
* * Boston, MA 02111-1307, USA.
*
* Additional permission under GNU GPL version 3 section 7
*
* If you modify this Program, or any covered work, by linking or combining it
* with proprietary FFT implementations or numerical libraries, containing parts
* covered by the terms of those libraries' licenses, the licensors of this
* Program grant you additional permission to convey the resulting work.
*/
#include <array>
#include <cmath>
#include <complex>
#include <iostream>
#include <string>
#include <type_traits>
#ifndef SRC_COMMON_COMMON_HH_
#define SRC_COMMON_COMMON_HH_
namespace muSpectre {
/**
* Eigen uses signed integers for dimensions. For consistency,
µSpectre uses them througout the code. needs to represent -1 for
eigen
*/
using Dim_t = int;
constexpr Dim_t oneD{1}; //!< constant for a one-dimensional problem
constexpr Dim_t twoD{2}; //!< constant for a two-dimensional problem
constexpr Dim_t threeD{3}; //!< constant for a three-dimensional problem
constexpr Dim_t firstOrder{1}; //!< constant for vectors
constexpr Dim_t secondOrder{2}; //!< constant second-order tensors
constexpr Dim_t fourthOrder{4}; //!< constant fourth-order tensors
//@{
//! @anchor scalars
//! Scalar types used for mathematical calculations
using Uint = unsigned int;
using Int = int;
using Real = double;
using Complex = std::complex<Real>;
//@}
//! Ccoord_t are cell coordinates, i.e. integer coordinates
template <Dim_t dim>
using Ccoord_t = std::array<Dim_t, dim>;
//! Real space coordinates
template <Dim_t dim>
using Rcoord_t = std::array<Real, dim>;
/**
* Allows inserting `muSpectre::Ccoord_t` and `muSpectre::Rcoord_t`
* into `std::ostream`s
*/
template <typename T, size_t dim>
std::ostream & operator<<(std::ostream & os,
const std::array<T, dim> & index) {
os << "(";
for (size_t i = 0; i < dim - 1; ++i) {
os << index[i] << ", ";
}
os << index.back() << ")";
return os;
}
//! element-wise division
template <size_t dim>
Rcoord_t<dim> operator/(const Rcoord_t<dim> & a, const Rcoord_t<dim> & b) {
Rcoord_t<dim> retval{a};
for (size_t i = 0; i < dim; ++i) {
retval[i] /= b[i];
}
return retval;
}
//! element-wise division
template <size_t dim>
Rcoord_t<dim> operator/(const Rcoord_t<dim> & a, const Ccoord_t<dim> & b) {
Rcoord_t<dim> retval{a};
for (size_t i = 0; i < dim; ++i) {
retval[i] /= b[i];
}
return retval;
}
//! convenience definitions
constexpr Real pi{3.1415926535897932384626433};
//! compile-time potentiation required for field-size computations
template <typename R, typename I>
constexpr R ipow(R base, I exponent) {
static_assert(std::is_integral<I>::value, "Type must be integer");
R retval{1};
for (I i = 0; i < exponent; ++i) {
retval *= base;
}
return retval;
}
/**
* Copyright banner to be printed to the terminal by executables
* Arguments are the executable's name, year of writing and the name
* + address of the copyright holder
*/
void banner(std::string name, Uint year, std::string cpy_holder);
/**
* Planner flags for FFT (follows FFTW, hopefully this choice will
* be compatible with alternative FFT implementations)
* @enum muSpectre::FFT_PlanFlags
*/
enum class FFT_PlanFlags {
estimate, //!< cheapest plan for slowest execution
measure, //!< more expensive plan for fast execution
patient //!< very expensive plan for fastest execution
};
//! continuum mechanics flags
enum class Formulation {
finite_strain, //!< causes evaluation in PK1(F)
small_strain, //!< causes evaluation in σ(ε)
small_strain_sym //!< symmetric storage as vector ε
};
//! finite differences flags
enum class FiniteDiff {
forward, //!< ∂f/∂x ≈ (f(x+Δx) - f(x))/Δx
backward, //!< ∂f/∂x ≈ (f(x) - f(x-Δx))/Δx
centred //!< ∂f/∂x ≈ (f(x+Δx) - f(x-Δx))/2Δx
};
/**
* compile time computation of voigt vector
*/
template <bool sym = true>
constexpr Dim_t vsize(Dim_t dim) {
if (sym) {
return (dim * (dim - 1) / 2 + dim);
} else {
return dim * dim;
}
}
//! compute the number of degrees of freedom to store for the strain
//! tenor given dimension dim
constexpr Dim_t dof_for_formulation(const Formulation form, const Dim_t dim) {
switch (form) {
case Formulation::small_strain_sym: {
return vsize(dim);
break;
}
default:
return ipow(dim, 2);
break;
}
}
//! inserts `muSpectre::Formulation`s into `std::ostream`s
std::ostream & operator<<(std::ostream & os, Formulation f);
/* ---------------------------------------------------------------------- */
//! Material laws can declare which type of stress measure they provide,
//! and µSpectre will handle conversions
enum class StressMeasure {
Cauchy, //!< Cauchy stress σ
PK1, //!< First Piola-Kirchhoff stress
PK2, //!< Second Piola-Kirchhoff stress
Kirchhoff, //!< Kirchhoff stress τ
Biot, //!< Biot stress
Mandel, //!< Mandel stress
no_stress_ //!< only for triggering static_asserts
};
//! inserts `muSpectre::StressMeasure`s into `std::ostream`s
std::ostream & operator<<(std::ostream & os, StressMeasure s);
/* ---------------------------------------------------------------------- */
//! Material laws can declare which type of strain measure they require and
//! µSpectre will provide it
enum class StrainMeasure {
Gradient, //!< placement gradient (δy/δx)
Infinitesimal, //!< small strain tensor .5(∇u + ∇uᵀ)
GreenLagrange, //!< Green-Lagrange strain .5(Fᵀ·F - I)
Biot, //!< Biot strain
Log, //!< logarithmic strain
Almansi, //!< Almansi strain
RCauchyGreen, //!< Right Cauchy-Green tensor
LCauchyGreen, //!< Left Cauchy-Green tensor
no_strain_ //!< only for triggering static_assert
};
//! inserts `muSpectre::StrainMeasure`s into `std::ostream`s
std::ostream & operator<<(std::ostream & os, StrainMeasure s);
/* ---------------------------------------------------------------------- */
/**
* all isotropic elastic moduli to identify conversions, such as E
* = µ(3λ + 2µ)/(λ+µ). For the full description, see
* https://en.wikipedia.org/wiki/Lam%C3%A9_parameters
* Not all the conversions are implemented, so please add as needed
*/
enum class ElasticModulus {
Bulk, //!< Bulk modulus K
K = Bulk, //!< alias for ``ElasticModulus::Bulk``
Young, //!< Young's modulus E
E = Young, //!< alias for ``ElasticModulus::Young``
lambda, //!< Lamé's first parameter λ
Shear, //!< Shear modulus G or µ
G = Shear, //!< alias for ``ElasticModulus::Shear``
mu = Shear, //!< alias for ``ElasticModulus::Shear``
Poisson, //!< Poisson's ratio ν
nu = Poisson, //!< alias for ``ElasticModulus::Poisson``
Pwave, //!< P-wave modulus M
M = Pwave, //!< alias for ``ElasticModulus::Pwave``
no_modulus_
}; //!< only for triggering static_asserts
/**
* define comparison in order to exploit that moduli can be
* expressed in terms of any two other moduli in any order (e.g. K
* = K(E, ν) = K(ν, E)
*/
constexpr inline bool operator<(ElasticModulus A, ElasticModulus B) {
return static_cast<int>(A) < static_cast<int>(B);
}
/* ---------------------------------------------------------------------- */
/** Compile-time function to g strain measure stored by muSpectre
depending on the formulation
**/
constexpr StrainMeasure get_stored_strain_type(Formulation form) {
switch (form) {
case Formulation::finite_strain: {
return StrainMeasure::Gradient;
break;
}
case Formulation::small_strain: {
return StrainMeasure::Infinitesimal;
break;
}
default:
return StrainMeasure::no_strain_;
break;
}
}
/** Compile-time function to g stress measure stored by muSpectre
depending on the formulation
**/
constexpr StressMeasure get_stored_stress_type(Formulation form) {
switch (form) {
case Formulation::finite_strain: {
return StressMeasure::PK1;
break;
}
case Formulation::small_strain: {
return StressMeasure::Cauchy;
break;
}
default:
return StressMeasure::no_stress_;
break;
}
}
/* ---------------------------------------------------------------------- */
/** Compile-time functions to get the stress and strain measures
after they may have been modified by choosing a formulation.
For instance, a law that expecs a Green-Lagrange strain as input
will get the infinitesimal strain tensor instead in a small
strain computation
**/
constexpr StrainMeasure get_formulation_strain_type(Formulation form,
StrainMeasure expected) {
switch (form) {
case Formulation::finite_strain: {
return expected;
break;
}
case Formulation::small_strain: {
return get_stored_strain_type(form);
break;
}
default:
return StrainMeasure::no_strain_;
break;
}
}
} // namespace muSpectre
#ifndef EXPLICITLY_TURNED_ON_CXX17
#include "common/utilities.hh"
#endif
#endif // SRC_COMMON_COMMON_HH_
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