.. math::
D_{ijkl} = \mu (\delta_{ik} \delta_{jl}+\delta_{il} \delta_{jk}) +
\lambda \ \delta_{ij} \delta_{kl}
\;.
"""
from its2D_1 import *
from sfepy.mechanics.matcoefs import stiffness_tensor_youngpoisson
def stress_strain(out, pb, state, extend=False):
"""
Calculate and output strain and stress for given displacements.
"""
from sfepy.base.base import Struct
ev = pb.evaluate
strain = ev('de_cauchy_strain.2.Omega(u)', mode='el_avg')
stress = ev('de_cauchy_stress.2.Omega(Asphalt.D, u)', mode='el_avg')
out['cauchy_strain'] = Struct(name='output_data', mode='cell',
data=strain, dofs=None)
out['cauchy_stress'] = Struct(name='output_data', mode='cell',
data=stress, dofs=None)
return out
asphalt = materials['Asphalt'][0]
asphalt.update({'D' : stiffness_tensor_youngpoisson(2, young, poisson)})
options.update({'post_process_hook' : 'stress_strain',})
dim = 3
region_lbn = (0, 0, 0)
region_rtf = (1, 1, 1)
#! Regions
#! -------
#! Regions, edges, ...
regions = {
'Y' : ('all', {}),
'Ym' : ('elements of group 1', {}),
'Yc' : ('elements of group 2', {}),
}
regions.update( define_box_regions( dim, region_lbn, region_rtf ) )
#! Materials
#! ---------
materials = {
'matrix' : ({'D' : stiffness_tensor_youngpoisson( dim, 0.7e9, 0.4 ) },),
'reinf' : ({'D' : stiffness_tensor_youngpoisson( dim, 70.0e9, 0.2 ) },),
}
#! Fields
#! ------
#! Scalar field for corrector basis functions.
fields = {
'corrector' : ('real', dim, 'Y', 1),
}
#! Variables
#! ---------
#! Unknown and corresponding test variables. Parameter fields
#! used for evaluation of homogenized coefficients.
variables = {
'u' : ('unknown field', 'corrector', 0),
'v' : ('test field', 'corrector', 'u'),
plt.ylabel('Cauchy strain')
plt.xlabel('probe %s' % label, fontsize=8)
plt.legend(loc='best', prop=fm.FontProperties(size=8))
plt.subplot(313)
pars, vals = results['cauchy_stress']
for ic in range(vals.shape[1]):
plt.plot(pars, vals[:,ic], label=r'$\sigma_{%s}$' % sym_indices[ic],
lw=1, ls='-', marker='+', ms=3)
plt.ylabel('Cauchy stress')
plt.xlabel('probe %s' % label, fontsize=8)
plt.legend(loc='best', prop=fm.FontProperties(size=8))
return plt.gcf(), results
materials['Asphalt'][0].update({'D' : stiffness_tensor_youngpoisson(2, young, poisson)})
# Update fields and variables to be able to use probes for tensors.
fields.update({
'sym_tensor': ('real', 3, 'Omega', 0),
})
variables.update({
's' : ('parameter field', 'sym_tensor', None),
})
options.update({
'output_format' : 'h5', # VTK reader cannot read cell data yet for probing
'post_process_hook' : 'stress_strain',
'gen_probes' : 'gen_lines',
'probe_hook' : 'probe_hook',
