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patch_test_linear_solid_mechanics_fixture.py
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Mon, Aug 26, 09:16
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text/x-python
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Wed, Aug 28, 09:16 (1 d, 23 h)
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rAKA akantu
patch_test_linear_solid_mechanics_fixture.py
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#!/usr/bin/env python3
# ------------------------------------------------------------------------------
__author__
=
"Guillaume Anciaux"
__copyright__
=
"Copyright (C) 2016-2018, EPFL (Ecole Polytechnique Fédérale"
\
" de Lausanne) Laboratory (LSMS - Laboratoire de Simulation"
\
" en Mécanique des Solides)"
__credits__
=
[
"Guillaume Anciaux"
]
__license__
=
"L-GPLv3"
__maintainer__
=
"Guillaume Anciaux"
__email__
=
"guillaume.anciaux@epfl.ch"
# ------------------------------------------------------------------------------
import
patch_test_linear_fixture
import
numpy
as
np
import
akantu
# custom material (this patch test also checks for custom material features)
class
LocalElastic
(
akantu
.
Material
):
def
__init__
(
self
,
model
,
_id
):
super
()
.
__init__
(
model
,
_id
)
super
()
.
registerParamReal
(
'E'
,
akantu
.
_pat_readable
|
akantu
.
_pat_parsable
,
'Youngs modulus'
)
super
()
.
registerParamReal
(
'nu'
,
akantu
.
_pat_readable
|
akantu
.
_pat_parsable
,
'Poisson ratio'
)
# declares all the internals
def
initMaterial
(
self
,
internals
,
params
):
nu
=
self
.
getReal
(
'nu'
)
E
=
self
.
getReal
(
'E'
)
self
.
mu
=
E
/
(
2
*
(
1
+
nu
))
self
.
lame_lambda
=
nu
*
E
/
(
(
1.
+
nu
)
*
(
1.
-
2.
*
nu
))
# Second Lame coefficient (shear modulus)
self
.
lame_mu
=
E
/
(
2.
*
(
1.
+
nu
))
super
()
.
initMaterial
()
# declares all the parameters that are needed
def
getPushWaveSpeed
(
self
,
element
):
rho
=
self
.
getReal
(
'rho'
)
return
np
.
sqrt
((
self
.
lame_lambda
+
2
*
self
.
lame_mu
)
/
rho
)
# compute small deformation tensor
@staticmethod
def
computeEpsilon
(
grad_u
):
return
0.5
*
(
grad_u
+
np
.
einsum
(
'aij->aji'
,
grad_u
))
# constitutive law
def
computeStress
(
self
,
el_type
,
ghost_type
):
grad_u
=
self
.
getGradU
(
el_type
,
ghost_type
)
sigma
=
self
.
getStress
(
el_type
,
ghost_type
)
n_quads
=
grad_u
.
shape
[
0
]
grad_u
=
grad_u
.
reshape
((
n_quads
,
2
,
2
))
epsilon
=
self
.
computeEpsilon
(
grad_u
)
sigma
=
sigma
.
reshape
((
n_quads
,
2
,
2
))
trace
=
np
.
einsum
(
'aii->a'
,
grad_u
)
sigma
[:,
:,
:]
=
(
np
.
einsum
(
'a,ij->aij'
,
trace
,
self
.
lame_lambda
*
np
.
eye
(
2
))
+
2.
*
self
.
lame_mu
*
epsilon
)
# constitutive law tangent modulii
def
computeTangentModuli
(
self
,
el_type
,
tangent_matrix
,
ghost_type
):
n_quads
=
tangent_matrix
.
shape
[
0
]
tangent
=
tangent_matrix
.
reshape
(
n_quads
,
3
,
3
)
Miiii
=
self
.
lame_lambda
+
2
*
self
.
lame_mu
Miijj
=
self
.
lame_lambda
Mijij
=
self
.
lame_mu
tangent
[:,
0
,
0
]
=
Miiii
tangent
[:,
1
,
1
]
=
Miiii
tangent
[:,
0
,
1
]
=
Miijj
tangent
[:,
1
,
0
]
=
Miijj
tangent
[:,
2
,
2
]
=
Mijij
# computes the energy density
def
computePotentialEnergy
(
self
,
el_type
):
sigma
=
self
.
getStress
(
el_type
)
grad_u
=
self
.
getGradU
(
el_type
)
nquads
=
sigma
.
shape
[
0
]
stress
=
sigma
.
reshape
(
nquads
,
2
,
2
)
grad_u
=
grad_u
.
reshape
((
nquads
,
2
,
2
))
epsilon
=
self
.
computeEpsilon
(
grad_u
)
energy_density
=
self
.
getPotentialEnergy
(
el_type
)
energy_density
[:,
0
]
=
0.5
*
np
.
einsum
(
'aij,aij->a'
,
stress
,
epsilon
)
class
TestPatchTestSMMLinear
(
patch_test_linear_fixture
.
TestPatchTestLinear
):
plane_strain
=
True
model_type
=
akantu
.
SolidMechanicsModel
def
__init__
(
self
,
*
args
,
**
kwargs
):
super
()
.
__init__
(
*
args
,
**
kwargs
)
def
initModel
(
self
,
method
,
material_file
):
# mat.__dict__['dim'] = self.dim
super
()
.
initModel
(
method
,
material_file
)
def
applyBC
(
self
):
super
()
.
applyBC
()
displacement
=
self
.
model
.
getDisplacement
()
self
.
applyBConDOFs
(
displacement
)
def
checkAll
(
self
):
displacement
=
self
.
model
.
getDisplacement
()
mat
=
self
.
model
.
getMaterial
(
0
)
self
.
checkDOFs
(
displacement
)
self
.
checkGradient
(
mat
.
getGradU
(
self
.
elem_type
),
displacement
)
def
foo
(
pstrain
):
nu
=
self
.
model
.
getMaterial
(
0
)
.
getReal
(
"nu"
)
E
=
self
.
model
.
getMaterial
(
0
)
.
getReal
(
"E"
)
strain
=
(
pstrain
+
pstrain
.
transpose
())
/
2.
trace
=
strain
.
trace
()
_lambda
=
nu
*
E
/
((
1
+
nu
)
*
(
1
-
2
*
nu
))
mu
=
E
/
(
2
*
(
1
+
nu
))
if
(
not
self
.
plane_strain
):
_lambda
=
nu
*
E
/
(
1
-
nu
*
nu
)
stress
=
np
.
zeros
((
self
.
dim
,
self
.
dim
))
if
self
.
dim
==
1
:
stress
[
0
,
0
]
=
E
*
strain
[
0
,
0
]
else
:
stress
[:,
:]
=
(
_lambda
*
trace
*
np
.
eye
(
self
.
dim
)
+
2
*
mu
*
strain
)
return
stress
self
.
checkResults
(
foo
,
mat
.
getStress
(
self
.
elem_type
),
displacement
)
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