def _convert_properties(dim, elastic_modulus, poissons_ratio):
"""Convert from elastic modulus and Poisson's ratio to the Lame
parameter and shear modulus
Args:
dim: whether 2D or 3D
elastic_modulus: the elastic modulus in each phase
poissons_ration: the poissons ratio for each phase
Returns:
array of shape (n_phases, 2) where for example [1, 0], gives the
Lame parameter in the second phase
"""
return pipe(
zip(elastic_modulus, poissons_ratio),
map_(
lambda x: pipe(
ElasticConstants(young=x[0], poisson=x[1]),
lambda y: (y.lam, dim / 3.0 * y.mu),
)
),
list,
np.array,
)
def test_elastic_constants(self):
import numpy as nm
from sfepy.mechanics.matcoefs import ElasticConstants
ok = True
names = ['bulk', 'lam', 'mu', 'young', 'poisson', 'p_wave']
ec = ElasticConstants(lam=1.0, mu=1.5)
vals = ec.get(names)
self.report('using values:', vals)
for i1 in range(len(names)):
for i2 in range(i1+1, len(names)):
kwargs = {names[i1] : vals[i1], names[i2] : vals[i2]}
try:
ec.init(**kwargs)
except:
_ok = False
else:
_ok = True
ec_vals = ec.get(names)
_ok = _ok and nm.allclose(ec_vals, vals)
self.report(names[i1], names[i2], '->', _ok)
if not _ok:
self.report('correct:', vals)
self.report(' got:', ec_vals)
ok = ok and _ok
return ok
def test_elastic_constants(self):
import numpy as nm
from sfepy.mechanics.matcoefs import ElasticConstants
ok = True
names = ['bulk', 'lam', 'mu', 'young', 'poisson', 'p_wave']
ec = ElasticConstants(lam=1.0, mu=1.5)
vals = ec.get(names)
self.report('using values:', vals)
for i1 in range(len(names)):
for i2 in range(i1+1, len(names)):
kwargs = {names[i1] : vals[i1], names[i2] : vals[i2]}
try:
ec.init(**kwargs)
except:
_ok = False
else:
_ok = True
ec_vals = ec.get(names)
_ok = _ok and nm.allclose(ec_vals, vals)
self.report(names[i1], names[i2], '->', _ok)
if not _ok:
self.report('correct:', vals)
self.report(' got:', ec_vals)
ok = ok and _ok
return ok
def _convert_properties(dim, elastic_modulus, poissons_ratio):
"""Convert from elastic modulus and Poisson's ratio to the Lame
parameter and shear modulus
Args:
dim: whether 2D or 3D
elastic_modulus: the elastic modulus in each phase
poissons_ration: the poissons ratio for each phase
Returns:
array of shape (n_phases, 2) where for example [1, 0], gives the
Lame parameter in the second phase
>>> assert(np.allclose(
... _convert_properties(
... dim=2, elastic_modulus=(1., 2.), poissons_ratio=(1., 1.)
... ),
... np.array([[-0.5, 1. / 6.], [-1., 1. / 3.]])
... ))
Test case with 3 phases.
>>> X2D = np.array([[[0, 1, 2, 1],
... [2, 1, 0, 0],
... [1, 0, 2, 2]]])
>>> X2D_property = _convert_properties(
... dim=2, elastic_modulus=(1., 2., 3.), poissons_ratio=(1., 1., 1.)
... )[X2D]
>>> lame = lame0, lame1, lame2 = -0.5, -1., -1.5
>>> mu = mu0, mu1, mu2 = 1. / 6, 1. / 3, 1. / 2
>>> lm = list(zip(lame, mu))
>>> assert(np.allclose(X2D_property,
... [[lm[0], lm[1], lm[2], lm[1]],
... [lm[2], lm[1], lm[0], lm[0]],
... [lm[1], lm[0], lm[2], lm[2]]]))
Test case with 2 phases.
>>> X3D = np.array([[[0, 1],
... [0, 0]],
... [[1, 1],
... [0, 1]]])
>>> X3D_property = _convert_properties(
... dim=2, elastic_modulus=(1., 2.), poissons_ratio=(1., 1.)
... )[X3D]
>>> assert(np.allclose(
... X3D_property,
... [[[lm[0], lm[1]],
... [lm[0], lm[0]]],
... [[lm[1], lm[1]],
... [lm[0], lm[1]]]]
... ))
"""
return pipe(
zip(elastic_modulus, poissons_ratio),
map_(lambda x: pipe(
ElasticConstants(young=x[0], poisson=x[1]),
lambda y: (y.lam, dim / 3.0 * y.mu),
)),
list,
np.array,
)
.. math::
D_{ijkl} = \mu (\delta_{ik} \delta_{jl}+\delta_{il} \delta_{jk}) +
\lambda \ \delta_{ij} \delta_{kl}
\;.
"""
from sfepy.mechanics.matcoefs import lame_from_youngpoisson
from sfepy.discrete.fem.utils import refine_mesh
from sfepy import data_dir
filename_mesh = data_dir + '/meshes/2d/simple_square.mesh'
young = 2000.0 # Young's modulus [MPa]
poisson = 0.4 # Poisson's ratio
from sfepy.mechanics.matcoefs import ElasticConstants, ElasticTensor
elas = ElasticConstants(young=2000., poisson=.4)
bulk, mu = elas.get(['bulk', 'mu'])
elasTensor = ElasticTensor(bulk=bulk, mu=mu, plane='strain')
materials = {
'Asphalt' : ({
'lam' : lame_from_youngpoisson(young, poisson)[0],
'mu' : lame_from_youngpoisson(young, poisson)[1],
'Voight' : elasTensor.voight,
'Mandel' : elasTensor.mandel,
},),
'Load' : ({'.val' : [0.0, -1000.0]},),
}
regions = {
'Omega' : 'all',
def _convert(E, nu):
ec = ElasticConstants(young=E, poisson=nu)
mu = dim / 3. * ec.mu # pylint: disable=no-member
lame = ec.lam # pylint: disable=no-member
return lame, mu
def _convert(E, nu):
ec = ElasticConstants(young=E, poisson=nu)
mu = dim / 3. * ec.mu
lame = ec.lam
return lame, mu