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stimulation_volterra.cc
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/**
* @file stimulation_dislo.cc
*
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
* @author Till Junge <till.junge@epfl.ch>
* @author Jaehyun Cho <jaehyun.cho@epfl.ch>
*
* @date Wed Jul 09 21:59:47 2014
*
* @brief This stmulation command imposes the Volterra displacement fields of
* strainght screw edge or mixed dislocations
*
* @section LICENSE
*
* Copyright (©) 2010-2011 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* LibMultiScale 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 of the License, or (at your option) any
* later version.
*
* LibMultiScale 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 Lesser General Public License for more
* details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with LibMultiScale. If not, see <http://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "stimulation_volterra.hh"
#include "lib_continuum.hh"
#include "lib_dd.hh"
#include "lib_md.hh"
#include "lm_common.hh"
#include "ref_point_data.hh"
/* -------------------------------------------------------------------------- */
__BEGIN_LIBMULTISCALE__
StimulationVolterra::StimulationVolterra(const std::string &name)
: LMObject(name){};
/* -------------------------------------------------------------------------- */
StimulationVolterra::~StimulationVolterra() {}
/* -------------------------------------------------------------------------- */
void StimulationVolterra::init() {
burgers_direction.normalize();
slip_plane_normal.normalize();
line_direction.normalize();
}
/* -------------------------------------------------------------------------- */
/*
Volterra tools:
everything is computed for
- the line direction to be X
- the pack plane direction to be Y
- the edge direction to be Z
*/
/* -------------------------------------------------------------------------- */
Real computeVolterraZDisplacement(Vector<3> &X, Vector<3> &burgers, Real pois) {
auto b_edge = burgers[2];
auto x = -X[2];
auto y = X[1];
auto r2 = x * x + y * y;
auto epsilon = 1e-15;
auto res = b_edge / (2. * M_PI) *
(std::atan2(y, x) + x * y / (2. * (1 - pois) * (r2 + epsilon)));
return res;
}
/* -------------------------------------------------------------------------- */
Real computeVolterraYDisplacement(Vector<3> &X, Vector<3> &burgers, Real pois) {
auto x = -X[2];
auto y = X[1];
auto x_2 = x * x;
auto y_2 = y * y;
auto b_edge = burgers[2];
auto b_edge2 = b_edge * b_edge;
auto r2 = x_2 + y_2;
Real epsilon = 1e-15;
auto c1 = (1 - 2. * pois);
auto c2 = 4. * (1. - pois);
auto res =
-b_edge / (2. * M_PI) * (c1 / c2 * std::log((r2 + epsilon) / b_edge2) +
(x_2 - y_2) / c2 / (r2 + epsilon));
return res;
}
/* ------------------------------------------------------------------------ */
Real computeVolterraXDisplacement(Vector<3> &X, Vector<3> &burgers) {
auto x = X[2];
auto y = X[1];
auto b_screw = burgers[0];
auto res = b_screw / (2. * M_PI) * (std::atan2(y, x));
return res;
}
/* ------------------------------------------------------------------------ */
inline Vector<3>
StimulationVolterra::computeVolterraDisplacement(Vector<3> &burgers,
Vector<3> &X) {
Vector<3> res;
res[0] = computeVolterraXDisplacement(X, burgers);
res[1] = computeVolterraYDisplacement(X, burgers, this->poisson);
res[2] = computeVolterraZDisplacement(X, burgers, this->poisson);
return res;
}
/* ------------------------------------------------------------------------ */
template <typename Cont>
std::enable_if_t<Cont::Dim != 3> StimulationVolterra::stimulate(Cont &cont) {
LM_FATAL("This stimulator cannot work with a spatial dimension lower than 3");
}
/* ------------------------------------------------------------------------ */
template <typename Cont>
std::enable_if_t<Cont::Dim == 3> StimulationVolterra::stimulate(Cont &cont) {
Vector<3> slip_direction = line_direction.cross(slip_plane_normal);
Matrix<3> rotation_matrix;
rotation_matrix.col(0) = line_direction;
rotation_matrix.col(1) = slip_plane_normal;
rotation_matrix.col(2) = slip_direction;
for (auto &&at : cont) {
auto X0 = at.position0(); // position in physical space
auto X = at.position(); // position in physical space
X = X0;
X -= pos.template cast<Real>();
// apply rotation point to the dislocation coordinate system
Vector<3> x = rotation_matrix * X;
Vector<3> rotated_burgers = rotation_matrix * (burgers * burgers_direction);
// compute isotropy volterra displacement
auto disp = computeVolterraDisplacement(rotated_burgers, x);
// rotate back
Vector<3> Disp = rotation_matrix.transpose() * disp;
at.position() += Disp;
}
}
/* --------------------------------------------------------------------------
*/
/* LMDESC DISLO
This stimulation command imposes the Volterra displacement
field of straight screw, edge, or combination of these two last\\\\
Displacement field of Screw dislocation:
\begin{equation}
u_{z}(x, y) = \frac{b}{2\pi} \cdot atan2(y,x)
\end{equation}
Displacement fields of Edge dislocation:
\begin{equation}
u_{x}(x, y) = \frac{b}{2\pi} \cdot
\left(
atan2(y,x) + \frac{xy}{2 (1-\nu) (x^2 + y^2)} \right)
\end{equation}
\begin{equation}
u_{y}(x, y) = -\frac{b}{2\pi} \cdot
\left(
\frac{1-2\nu}{4(1 - \nu)}\ln(x^2 + y^2)
+ \frac{x^2 - y^2}{4(1-\nu)(x^2 + y^2)}
\right)
\end{equation}
are introduced.
*/
/* LMEXAMPLE STIMULATION myVolterra DISLO INPUT md STAGE PRE_DUMP BURGERS
* burgers
* POS 0 0 0 REPLICA 10 0 POISSON 0.3468 THETA 180 ONESHOT 0 */
/* LMHERITANCE action_interface */
void StimulationVolterra::declareParams() {
StimulationInterface::declareParams();
/* LMKEYWORD BURGERS
Specify the magnitude of Burger's vector
*/
this->parseKeyword("BURGERS", this->burgers);
/* LMKEYWORD BURGERS
Specify the direction of the Burger's vector
*/
this->parseKeyword("BURGERS_DIR", this->burgers_direction);
/* LMKEYWORD POS
Specify the coordinates of a point on the dislocation line
*/
this->parseKeyword("POS", this->pos);
/* LMKEYWORD SLIP_PLANE
Specifies the normal vector to the slip plane
*/
this->parseKeyword("SLIP_PLANE", this->slip_plane_normal);
/* LMKEYWORD LINE_DIR
Specifies the normal vector to the slip plane
*/
this->parseKeyword("LINE_DIR", this->line_direction);
/* LMKEYWORD POISSON
Specify Poisson's ratio of the material
*/
this->parseKeyword("POISSON", this->poisson);
/* LMKEYWORD RESOLUTION
Specify the number of increments in the spread of dislocation density in
Z direction
*/
// this->parseKeyword("RESOLUTION", this->resolution);
/* LMKEYWORD WIDTH
Specify the width of the core dislocation in Z direction
*/
// this->parseKeyword("WIDTH", this->width);
}
/* --------------------------------------------------------------------------
*/
DECLARE_STIMULATION_MAKE_CALL(StimulationVolterra);
__END_LIBMULTISCALE__

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