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CauchyBorn.h
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rLAMMPS lammps
CauchyBorn.h
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#ifndef CAUCHYBORN_H
#define CAUCHYBORN_H
#include "CbPotential.h"
#include "MatrixLibrary.h"
#include "ATC_TypeDefs.h"
// This file provides all routines necessary for computing the Cauchy-Born
// stresses.
namespace
ATC
{
// forward declaration of CbPotential
class
CbPotential
;
class
AtomCluster
;
/**
* @class StressAtIP
* @brief Class for passing the vector of stresses at quadrature points
* Done by storing the quadrature point and providing indexing
*/
class
StressAtIP
{
INDEX
q
;
//*> Quadrature point.
DENS_MAT_VEC
&
S
;
//*> Stress components at all quad points.
public:
//* Constructor - sets stress reference and current quadrature point.
StressAtIP
(
DENS_MAT_VEC
&
s
,
INDEX
_q
=
0
)
:
q
(
_q
),
S
(
s
)
{}
//* Indexing operator, gets stress components for the quadrature point.
double
&
operator
()(
INDEX
i
,
INDEX
j
)
const
{
return
S
[
i
](
q
,
j
);
}
//* Sets quadrature point to a new index.
void
set_quadrature_point
(
INDEX
qp
)
{
q
=
qp
;
}
//* Operator that outputs the stress
friend
std
::
ostream
&
operator
<<
(
std
::
ostream
&
o
,
const
StressAtIP
&
s
)
{
o
<<
"stress
\n
"
;
o
<<
s
(
0
,
0
)
<<
" "
<<
s
(
0
,
1
)
<<
" "
<<
s
(
0
,
2
)
<<
"
\n
"
;
o
<<
s
(
1
,
0
)
<<
" "
<<
s
(
1
,
1
)
<<
" "
<<
s
(
1
,
2
)
<<
"
\n
"
;
o
<<
s
(
2
,
0
)
<<
" "
<<
s
(
2
,
1
)
<<
" "
<<
s
(
2
,
2
)
<<
"
\n
"
;
return
o
;
}
};
/**
* @class StressArgs
* @brief Class for storing parameters needed for computing the Cauchy-Born stress
*/
class
StressArgs
{
public:
StressArgs
(
AtomCluster
&
v
,
CbPotential
*
p
,
double
kB
,
double
hbar
,
double
T
)
:
vac
(
v
),
potential
(
p
),
boltzmann_constant
(
kB
),
planck_constant
(
hbar
),
temperature
(
T
)
{}
AtomCluster
&
vac
;
CbPotential
*
potential
;
double
boltzmann_constant
;
double
planck_constant
;
double
temperature
;
};
/**
* @class PairParam
* @brief Class for storing parameters used in pairwise stress computations
*/
struct
PairParam
{
PairParam
(
const
DENS_VEC
&
_R
,
double
_d
)
:
R
(
_R
),
d
(
_d
),
di
(
1.0
/
_d
)
{}
const
DENS_VEC
&
R
;
//*> Reference bond vector.
DENS_VEC
r
;
//*> Current bond vector.
double
d
,
di
;
//*> Current bond length and its inverse.
double
phi_r
;
//*> First derivative of pairwise term.
double
phi_rr
;
//*> Second derivative of pairwise term.
double
phi_rrr
;
//*> Third derivative of pairwise term.
double
rho_r
;
double
rho_rr
;
double
rho_rrr
;
double
F_p
;
double
F_pp
;
double
F_ppp
;
};
//* for EAM, calculate electron density
double
cb_electron_density
(
const
StressArgs
&
args
);
//* Compute stress, from virtual atom cluster, potential
//* temperature (can be 0K), and StressAtIP object to write to.
void
cb_stress
(
const
StressArgs
&
args
,
StressAtIP
&
s
,
double
*
F
=
0
);
//* Computes the elastic energy (free or potential if T=0).
double
cb_energy
(
const
StressArgs
&
args
);
//* Computes the entropic energy
double
cb_entropic_energy
(
const
StressArgs
&
args
);
//* Auxiliary functions for cb_stress
//@{
//* Computes the stress contribution given the pairwise parameters.
void
pairwise_stress
(
const
PairParam
&
p
,
StressAtIP
&
s
);
//* Computes the stress contribution given the embedding parameters.
void
embedding_stress
(
const
PairParam
&
p
,
StressAtIP
&
s
);
//* Computes the pairwise thermal components for the stress and free energy.
void
pairwise_thermal
(
const
PairParam
&
p
,
DENS_MAT
&
D
,
DENS_MAT_VEC
*
dDdF
=
0
);
//* Computes the embedding thermal components for the stress and free energy.
void
embedding_thermal
(
const
PairParam
&
p
,
DENS_MAT
&
D
,
DENS_MAT
&
L0
,
DENS_MAT_VEC
*
dDdF
=
0
);
//* Last stage of the pairwise finite-T Cauchy-Born stress computation.
void
thermal_end
(
const
DENS_MAT_VEC
&
DF
,
const
DENS_MAT
&
D
,
const
DENS_MAT
&
F
,
const
double
&
T
,
const
double
&
kb
,
StressAtIP
&
s
,
double
*
F_w
=
0
);
//* Returns the stretch tensor and its derivative with respect to C (R C-G).
void
stretch_tensor_derivative
(
const
DENS_VEC
&
C
,
DENS_VEC
&
U
,
DENS_MAT
&
dU
);
//@}
//* Testing functions (to be removed when all CB code is completed)
//@{
//* Computes the dynamical matrix (TESTING FUNCTION)
DENS_MAT
compute_dynamical_matrix
(
const
StressArgs
&
args
);
//* Computes the determinant of the dynamical matrix (TESTING FUNCTION)
double
compute_detD
(
const
StressArgs
&
args
);
//* Computes the derivative of the dynamical matrix (TESTING FUNCTION)
DENS_MAT_VEC
compute_dynamical_derivative
(
StressArgs
&
args
);
//@}
}
#endif
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