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custom-material.py
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Fri, Nov 1, 00:24
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text/x-python
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rAKA akantu
custom-material.py
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#!/usr/bin/env python3
import
numpy
as
np
import
akantu
as
aka
# ------------------------------------------------------------------------------
class
LocalElastic
(
aka
.
Material
):
def
__init__
(
self
,
model
,
_id
):
super
()
.
__init__
(
model
,
_id
)
super
()
.
registerParamReal
(
'E'
,
aka
.
_pat_readable
|
aka
.
_pat_parsable
,
'Youngs modulus'
)
super
()
.
registerParamReal
(
'nu'
,
aka
.
_pat_readable
|
aka
.
_pat_parsable
,
'Poisson ratio'
)
def
initMaterial
(
self
):
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
)
# register material to the MaterialFactory
def
allocator
(
_dim
,
unused
,
model
,
_id
):
return
LocalElastic
(
model
,
_id
)
mat_factory
=
aka
.
MaterialFactory
.
getInstance
()
mat_factory
.
registerAllocator
(
"local_elastic"
,
allocator
)
# ------------------------------------------------------------------------------
# main
# ------------------------------------------------------------------------------
spatial_dimension
=
2
aka
.
parseInput
(
'material.dat'
)
mesh_file
=
'bar.msh'
max_steps
=
250
time_step
=
1e-3
# ------------------------------------------------------------------------------
# Initialization
# ------------------------------------------------------------------------------
mesh
=
aka
.
Mesh
(
spatial_dimension
)
mesh
.
read
(
mesh_file
)
# parse input file
aka
.
parseInput
(
'material.dat'
)
model
=
aka
.
SolidMechanicsModel
(
mesh
)
model
.
initFull
(
_analysis_method
=
aka
.
_explicit_lumped_mass
)
model
.
setBaseName
(
"waves"
)
model
.
addDumpFieldVector
(
"displacement"
)
model
.
addDumpFieldVector
(
"acceleration"
)
model
.
addDumpFieldVector
(
"velocity"
)
model
.
addDumpFieldVector
(
"internal_force"
)
model
.
addDumpFieldVector
(
"external_force"
)
model
.
addDumpField
(
"strain"
)
model
.
addDumpField
(
"stress"
)
model
.
addDumpField
(
"blocked_dofs"
)
# ------------------------------------------------------------------------------
# boundary conditions
# ------------------------------------------------------------------------------
model
.
applyBC
(
aka
.
ixedValue
(
0
,
aka
.
_x
),
"XBlocked"
)
model
.
applyBC
(
aka
.
ixedValue
(
0
,
aka
.
_y
),
"YBlocked"
)
# ------------------------------------------------------------------------------
# initial conditions
# ------------------------------------------------------------------------------
displacement
=
model
.
getDisplacement
()
nb_nodes
=
mesh
.
getNbNodes
()
position
=
mesh
.
getNodes
()
pulse_width
=
1
A
=
0.01
for
i
in
range
(
0
,
nb_nodes
):
# Sinus * Gaussian
x
=
position
[
i
,
0
]
-
5.
L
=
pulse_width
k
=
0.1
*
2
*
np
.
pi
*
3
/
L
displacement
[
i
,
0
]
=
A
*
\
np
.
sin
(
k
*
x
)
*
np
.
exp
(
-
(
k
*
x
)
*
(
k
*
x
)
/
(
L
*
L
))
# ------------------------------------------------------------------------------
# timestep value computation
# ------------------------------------------------------------------------------
time_factor
=
0.8
stable_time_step
=
model
.
getStableTimeStep
()
*
time_factor
print
(
"Stable Time Step = {0}"
.
format
(
stable_time_step
))
print
(
"Required Time Step = {0}"
.
format
(
time_step
))
time_step
=
stable_time_step
*
time_factor
model
.
setTimeStep
(
time_step
)
# ------------------------------------------------------------------------------
# loop for evolution of motion dynamics
# ------------------------------------------------------------------------------
print
(
"step,step * time_step,epot,ekin,epot + ekin"
)
for
step
in
range
(
0
,
max_steps
+
1
):
model
.
solveStep
()
if
step
%
10
==
0
:
model
.
dump
()
epot
=
model
.
getEnergy
(
'potential'
)
ekin
=
model
.
getEnergy
(
'kinetic'
)
# output energy calculation to screen
print
(
"{0},{1},{2},{3},{4}"
.
format
(
step
,
step
*
time_step
,
epot
,
ekin
,
(
epot
+
ekin
)))
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