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py_comparison_test_material_hyper_elasto_plastic1.py
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rMUSPECTRE µSpectre
py_comparison_test_material_hyper_elasto_plastic1.py
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#!/usr/bin/env python3
# -*- coding:utf-8 -*-
"""
@file py_comparison_test_material_hyper_elasto_plastic1.py
@author Till Junge <till.junge@epfl.ch>
@date 14 Nov 2018
@brief compares MaterialHyperElastoPlastic1 to de Geus's python
implementation
@section LICENSE
Copyright © 2018 Till Junge
µSpectre is free software; you can redistribute it and/or
modify it under the terms of the GNU 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 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.
"""
from
material_hyper_elasto_plastic1
import
*
import
itertools
import
numpy
as
np
import
unittest
#####################
dyad22
=
lambda
A2
,
B2
:
np
.
einsum
(
'ij ,kl ->ijkl'
,
A2
,
B2
)
dyad11
=
lambda
A1
,
B1
:
np
.
einsum
(
'i ,j ->ij '
,
A1
,
B1
)
dot22
=
lambda
A2
,
B2
:
np
.
einsum
(
'ij ,jk ->ik '
,
A2
,
B2
)
dot24
=
lambda
A2
,
B4
:
np
.
einsum
(
'ij ,jkmn->ikmn'
,
A2
,
B4
)
dot42
=
lambda
A4
,
B2
:
np
.
einsum
(
'ijkl,lm ->ijkm'
,
A4
,
B2
)
inv2
=
np
.
linalg
.
inv
ddot22
=
lambda
A2
,
B2
:
np
.
einsum
(
'ij ,ji -> '
,
A2
,
B2
)
ddot42
=
lambda
A4
,
B2
:
np
.
einsum
(
'ijkl,lk ->ij '
,
A4
,
B2
)
ddot44
=
lambda
A4
,
B4
:
np
.
einsum
(
'ijkl,lkmn->ijmn'
,
A4
,
B4
)
class
MatTest
(
unittest
.
TestCase
):
def
constitutive
(
self
,
F
,
F_t
,
be_t
,
ep_t
,
dim
):
I
=
np
.
eye
(
dim
)
II
=
dyad22
(
I
,
I
)
I4
=
np
.
einsum
(
'il,jk'
,
I
,
I
)
I4rt
=
np
.
einsum
(
'ik,jl'
,
I
,
I
)
I4s
=
(
I4
+
I4rt
)
/
2.
def
ln2
(
A2
):
vals
,
vecs
=
np
.
linalg
.
eig
(
A2
)
return
sum
(
[
np
.
log
(
vals
[
i
])
*
dyad11
(
vecs
[:,
i
],
vecs
[:,
i
])
for
i
in
range
(
dim
)])
def
exp2
(
A2
):
vals
,
vecs
=
np
.
linalg
.
eig
(
A2
)
return
sum
(
[
np
.
exp
(
vals
[
i
])
*
dyad11
(
vecs
[:,
i
],
vecs
[:,
i
])
for
i
in
range
(
dim
)])
# function to compute linearization of the logarithmic Finger tensor
def
dln2_d2
(
A2
):
vals
,
vecs
=
np
.
linalg
.
eig
(
A2
)
K4
=
np
.
zeros
([
dim
,
dim
,
dim
,
dim
])
for
m
,
n
in
itertools
.
product
(
range
(
dim
),
repeat
=
2
):
if
vals
[
n
]
==
vals
[
m
]:
gc
=
(
1.0
/
vals
[
m
])
else
:
gc
=
(
np
.
log
(
vals
[
n
])
-
np
.
log
(
vals
[
m
]))
/
(
vals
[
n
]
-
vals
[
m
])
K4
+=
gc
*
dyad22
(
dyad11
(
vecs
[:,
m
],
vecs
[:,
n
]),
dyad11
(
vecs
[:,
m
],
vecs
[:,
n
]))
return
K4
# elastic stiffness tensor
C4e
=
self
.
K
*
II
+
2.
*
self
.
mu
*
(
I4s
-
1.
/
3.
*
II
)
# trial state
Fdelta
=
dot22
(
F
,
inv2
(
F_t
))
be_s
=
dot22
(
Fdelta
,
dot22
(
be_t
,
Fdelta
.
T
))
lnbe_s
=
ln2
(
be_s
)
tau_s
=
ddot42
(
C4e
,
lnbe_s
)
/
2.
taum_s
=
ddot22
(
tau_s
,
I
)
/
3.
taud_s
=
tau_s
-
taum_s
*
I
taueq_s
=
np
.
sqrt
(
3.
/
2.
*
ddot22
(
taud_s
,
taud_s
))
div
=
np
.
where
(
taueq_s
<
1e-12
,
np
.
ones_like
(
taueq_s
),
taueq_s
)
N_s
=
3.
/
2.
*
taud_s
/
div
phi_s
=
taueq_s
-
(
self
.
tauy0
+
self
.
H
*
ep_t
)
phi_s
=
1.
/
2.
*
(
phi_s
+
np
.
abs
(
phi_s
))
# return map
dgamma
=
phi_s
/
(
self
.
H
+
3.
*
self
.
mu
)
ep
=
ep_t
+
dgamma
tau
=
tau_s
-
2.
*
dgamma
*
N_s
*
self
.
mu
lnbe
=
lnbe_s
-
2.
*
dgamma
*
N_s
be
=
exp2
(
lnbe
)
P
=
dot22
(
tau
,
inv2
(
F
)
.
T
)
# consistent tangent operator
a0
=
dgamma
*
self
.
mu
/
taueq_s
a1
=
self
.
mu
/
(
self
.
H
+
3.
*
self
.
mu
)
C4ep
=
(((
self
.
K
-
2.
/
3.
*
self
.
mu
)
/
2.
+
a0
*
self
.
mu
)
*
II
+
(
1.
-
3.
*
a0
)
*
self
.
mu
*
I4s
+
2.
*
self
.
mu
*
(
a0
-
a1
)
*
dyad22
(
N_s
,
N_s
))
dlnbe4_s
=
dln2_d2
(
be_s
)
dbe4_s
=
2.
*
dot42
(
I4s
,
be_s
)
#K4a = ((C4e/2.)*(phi_s<=0.).astype(np.float)+
# C4ep*(phi_s>0.).astype(np.float))
K4a
=
np
.
where
(
phi_s
<=
0
,
C4e
/
2.
,
C4ep
)
K4b
=
ddot44
(
K4a
,
ddot44
(
dlnbe4_s
,
dbe4_s
))
K4c
=
dot42
(
-
I4rt
,
tau
)
+
K4b
K4
=
dot42
(
dot24
(
inv2
(
F
),
K4c
),
inv2
(
F
)
.
T
)
return
P
,
tau
,
K4
,
be
,
ep
,
dlnbe4_s
,
dbe4_s
,
K4a
,
K4b
,
K4c
def
setUp
(
self
):
pass
def
prep
(
self
,
dimension
):
self
.
dim
=
dimension
self
.
K
=
2.
+
np
.
random
.
rand
()
self
.
mu
=
2.
+
np
.
random
.
rand
()
self
.
H
=.
1
+
np
.
random
.
rand
()
/
100
self
.
tauy0
=
4.
+
np
.
random
.
rand
()
/
10
self
.
F_prev
=
np
.
eye
(
self
.
dim
)
+
(
np
.
random
.
random
((
self
.
dim
,
self
.
dim
))
-.
5
)
/
10
self
.
F
=
self
.
F_prev
+
(
np
.
random
.
random
((
self
.
dim
,
self
.
dim
))
-.
5
)
/
10
self
.
be_prev
=.
5
*
(
self
.
F_prev
+
self
.
F_prev
.
T
)
self
.
eps_prev
=.
5
+
np
.
random
.
rand
()
/
10
self
.
tol
=
1e-13
self
.
verbose
=
True
def
test_equivalence_
τ
_C
(
self
):
for
dim
in
(
2
,
3
):
self
.
runner_equivalence_
τ
_C
(
dim
)
def
runner_equivalence_
τ
_C
(
self
,
dimension
):
self
.
prep
(
dimension
)
fun
=
kirchhoff_fun_2d
if
self
.
dim
==
2
else
kirchhoff_fun_3d
τ
_
µ
,
C_
µ
_s
=
fun
(
self
.
K
,
self
.
mu
,
self
.
H
,
self
.
tauy0
,
self
.
F_prev
,
self
.
F_prev
,
self
.
be_prev
,
self
.
eps_prev
)
shape
=
(
self
.
dim
,
self
.
dim
,
self
.
dim
,
self
.
dim
)
C_
µ
=
C_
µ
_s
.
reshape
(
shape
)
.
transpose
((
1
,
0
,
3
,
2
))
response_p
=
self
.
constitutive
(
self
.
F_prev
,
self
.
F_prev
,
self
.
be_prev
,
self
.
eps_prev
,
self
.
dim
)
τ
_p
,
C_p
=
response_p
[
1
],
response_p
[
8
]
τ
_error
=
np
.
linalg
.
norm
(
τ
_
µ
-
τ
_p
)
/
np
.
linalg
.
norm
(
τ
_
µ
)
if
not
τ
_error
<
self
.
tol
:
print
(
"Error(τ) = {}"
.
format
(
τ
_error
))
print
(
"τ_µ:
\n
{}"
.
format
(
τ
_
µ
))
print
(
"τ_p:
\n
{}"
.
format
(
τ
_p
))
self
.
assertLess
(
τ
_error
,
self
.
tol
)
C_error
=
np
.
linalg
.
norm
(
C_
µ
-
C_p
)
/
np
.
linalg
.
norm
(
C_
µ
)
if
not
C_error
<
self
.
tol
:
print
(
"Error(C) = {}"
.
format
(
C_error
))
flat_shape
=
(
self
.
dim
**
2
,
self
.
dim
**
2
)
print
(
"C_µ:
\n
{}"
.
format
(
C_
µ
.
reshape
(
flat_shape
)))
print
(
"C_p:
\n
{}"
.
format
(
C_p
.
reshape
(
flat_shape
)))
self
.
assertLess
(
C_error
,
self
.
tol
)
def
test_equivalence_P_K
(
self
):
for
dim
in
(
2
,
3
):
self
.
runner_equivalence_P_K
(
dim
)
def
runner_equivalence_P_K
(
self
,
dimension
):
self
.
prep
(
dimension
)
fun
=
PK1_fun_2d
if
self
.
dim
==
2
else
PK1_fun_3d
P_
µ
,
K_
µ
_s
=
fun
(
self
.
K
,
self
.
mu
,
self
.
H
,
self
.
tauy0
,
self
.
F_prev
,
self
.
F_prev
,
self
.
be_prev
,
self
.
eps_prev
)
shape
=
(
self
.
dim
,
self
.
dim
,
self
.
dim
,
self
.
dim
)
K_
µ
=
K_
µ
_s
.
reshape
(
shape
)
.
transpose
((
1
,
0
,
2
,
3
))
response_p
=
self
.
constitutive
(
self
.
F_prev
,
self
.
F_prev
,
self
.
be_prev
,
self
.
eps_prev
,
self
.
dim
)
P_p
,
K_p
=
response_p
[
0
],
response_p
[
2
]
P_error
=
np
.
linalg
.
norm
(
P_
µ
-
P_p
)
/
np
.
linalg
.
norm
(
P_
µ
)
if
not
P_error
<
self
.
tol
:
print
(
"Error(P) = {}"
.
format
(
P_error
))
print
(
"P_µ:
\n
{}"
.
format
(
P_
µ
))
print
(
"P_p:
\n
{}"
.
format
(
P_p
))
self
.
assertLess
(
P_error
,
self
.
tol
)
K_error
=
np
.
linalg
.
norm
(
K_
µ
-
K_p
)
/
np
.
linalg
.
norm
(
K_
µ
)
if
not
K_error
<
self
.
tol
:
print
(
"Error(K) = {}"
.
format
(
K_error
))
flat_shape
=
(
self
.
dim
**
2
,
self
.
dim
**
2
)
print
(
"K_µ:
\n
{}"
.
format
(
K_
µ
.
reshape
(
flat_shape
)))
print
(
"K_p:
\n
{}"
.
format
(
K_p
.
reshape
(
flat_shape
)))
print
(
"diff:
\n
{}"
.
format
(
K_p
.
reshape
(
flat_shape
)
-
K_
µ
.
reshape
(
flat_shape
)))
self
.
assertLess
(
K_error
,
self
.
tol
)
if
__name__
==
"__main__"
:
unittest
.
main
()
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