homogenization/nonlinear_homogenization.pyΒΆ
Description
missing description!
# -*- coding: utf-8 -*-
import numpy as nm
from sfepy.homogenization.utils import define_box_regions
import sfepy.homogenization.coefs_base as cb
import sfepy.discrete.fem.periodic as per
from sfepy.base.base import Struct
from sfepy.terms.terms_hyperelastic_ul import\
HyperElasticULFamilyData, NeoHookeanULTerm, BulkPenaltyULTerm
from sfepy.terms.extmods.terms import sym2nonsym
from sfepy.discrete.functions import ConstantFunctionByRegion
from sfepy import data_dir
import sfepy.linalg as la
def recovery_hook(pb, ncoors, region, ts,
naming_scheme='step_iel', recovery_file_tag=''):
from sfepy.base.ioutils import get_print_info
from sfepy.homogenization.recovery import get_output_suffix
import os.path as op
for ii, icell in enumerate(region.cells):
out = {}
pb.set_mesh_coors(ncoors[ii], update_fields=True,
clear_all=False, actual=True)
stress = pb.evaluate('ev_volume_integrate_mat.3.Y(mat_he.S, u)',
mode='el_avg')
out['cauchy_stress'] = Struct(name='output_data',
mode='cell',
data=stress,
dofs=None)
strain = pb.evaluate('ev_volume_integrate_mat.3.Y(mat_he.E, u)',
mode='el_avg')
out['green_strain'] = Struct(name='output_data',
mode='cell',
data=strain,
dofs=None)
out['displacement'] = Struct(name='output_data',
mode='vertex',
data=ncoors[ii] - pb.get_mesh_coors(),
dofs=None)
output_dir = pb.conf.options.get('output_dir', '.')
format = get_print_info(pb.domain.mesh.n_el, fill='0')[1]
suffix = get_output_suffix(icell, ts, naming_scheme, format,
pb.output_format)
micro_name = pb.get_output_name(extra='recovered_'
+ recovery_file_tag + suffix)
filename = op.join(output_dir, op.basename(micro_name))
fpv = pb.conf.options.get('file_per_var', False)
pb.save_state(filename, out=out, file_per_var=fpv)
def def_mat(ts, mode, coors, term, pb):
if not (mode == 'qp'):
return
if not hasattr(pb, 'family_data'):
pb.family_data = HyperElasticULFamilyData()
update_var = pb.conf.options.mesh_update_variable
if pb.equations is None:
state_u = pb.create_variables([update_var])[update_var]
else:
state_u = pb.get_variables()[update_var]
if state_u.data[0] is None:
state_u.init_data()
state_u.set_data(
pb.domain.get_mesh_coors(actual=True) - pb.domain.get_mesh_coors())
state_u.field.clear_mappings()
family_data = pb.family_data(state_u, term.region,
term.integral, term.integration)
if len(state_u.field.mappings0) == 0:
state_u.field.save_mappings()
n_el, n_qp, dim, n_en, n_c = state_u.get_data_shape(term.integral,
term.integration,
term.region.name)
conf_mat = pb.conf.materials
solid_key = [key for key in conf_mat.keys() if 'solid' in key][0]
solid_mat = conf_mat[solid_key].values
mat = {}
for mat_key in ['mu', 'K']:
if isinstance(solid_mat[mat_key], dict):
mat_fun = ConstantFunctionByRegion({mat_key: solid_mat[mat_key]})
mat[mat_key] = mat_fun.function(ts=ts, coors=coors, mode='qp',
term=term, problem=pb)[mat_key].reshape((n_el, n_qp, 1, 1))
else:
mat[mat_key] = nm.ones((n_el, n_qp, 1, 1)) * solid_mat[mat_key]
shape = family_data.green_strain.shape[:2]
sym = family_data.green_strain.shape[-2]
dim2 = dim**2
fargs = [family_data.get(name)
for name in NeoHookeanULTerm.family_data_names]
stress = nm.empty(shape + (sym, 1), dtype=nm.float64)
tanmod = nm.empty(shape + (sym, sym), dtype=nm.float64)
NeoHookeanULTerm.stress_function(stress, mat['mu'], *fargs)
NeoHookeanULTerm.tan_mod_function(tanmod, mat['mu'], *fargs)
fargs = [family_data.get(name)
for name in BulkPenaltyULTerm.family_data_names]
stress_p = nm.empty(shape + (sym, 1), dtype=nm.float64)
tanmod_p = nm.empty(shape + (sym, sym), dtype=nm.float64)
BulkPenaltyULTerm.stress_function(stress_p, mat['K'], *fargs)
BulkPenaltyULTerm.tan_mod_function(tanmod_p, mat['K'], *fargs)
stress_ns = nm.zeros(shape + (dim2, dim2), dtype=nm.float64)
tanmod_ns = nm.zeros(shape + (dim2, dim2), dtype=nm.float64)
sym2nonsym(stress_ns, stress + stress_p)
sym2nonsym(tanmod_ns, tanmod + tanmod_p)
npts = nm.prod(shape)
J = family_data.det_f
mtx_f = family_data.mtx_f.reshape((npts, dim, dim))
out = {
'E': 0.5 * (la.dot_sequences(mtx_f, mtx_f, 'ATB') - nm.eye(dim)),
'A': ((tanmod_ns + stress_ns) / J).reshape((npts, dim2, dim2)),
'S': ((stress + stress_p) / J).reshape((npts, sym, 1)),
}
return out
filename_mesh = data_dir + '/meshes/2d/special/circle_in_square_small.mesh'
dim = 2
options = {
'coefs': 'coefs',
'requirements': 'requirements',
'volume': {'expression': 'd_volume.5.Y(u)'},
'output_dir': './output',
'coefs_filename': 'coefs_hyper_homog',
'multiprocessing': True,
'chunks_per_worker': 2,
'micro_update': {'coors': [('corrs_rs', 'u', 'mtx_e')]},
'mesh_update_variable': 'u',
'recovery_hook': 'recovery_hook',
'store_micro_idxs': [49, 81],
}
fields = {
'displacement': ('real', 'vector', 'Y', 1),
}
functions = {
'match_x_plane': (per.match_x_plane,),
'match_y_plane': (per.match_y_plane,),
'mat_fce': (lambda ts, coors, mode=None, term=None, problem=None, **kwargs:
def_mat(ts, mode, coors, term, problem),),
}
materials = {
'mat_he': 'mat_fce',
'solid': ({'K': 1000,
'mu': {'Ym': 100, 'Yc': 10},
},),
}
variables = {
'u': ('unknown field', 'displacement'),
'v': ('test field', 'displacement', 'u'),
'Pi': ('parameter field', 'displacement', 'u'),
'Pi1u': ('parameter field', 'displacement', '(set-to-None)'),
'Pi2u': ('parameter field', 'displacement', '(set-to-None)'),
}
regions = {
'Y': 'all',
'Ym': 'cells of group 1',
'Yc': 'cells of group 2',
}
regions.update(define_box_regions(dim, (0., 0.), (1., 1.)))
ebcs = {
'fixed_u': ('Corners', {'u.all': 0.0}),
}
epbcs = {
'periodic_ux': (['Left', 'Right'], {'u.all': 'u.all'}, 'match_x_plane'),
'periodic_uy': (['Bottom', 'Top'], {'u.all': 'u.all'}, 'match_y_plane'),
}
coefs = {
'A': {
'requires': ['pis', 'corrs_rs'],
'expression': 'dw_nonsym_elastic.3.Y(mat_he.A, Pi1u, Pi2u)',
'set_variables': [('Pi1u', ('pis', 'corrs_rs'), 'u'),
('Pi2u', ('pis', 'corrs_rs'), 'u')],
'class': cb.CoefNonSymNonSym,
},
'S': {
'expression': 'ev_volume_integrate_mat.3.Y(mat_he.S, u)',
'class': cb.CoefOne,
}
}
requirements = {
'pis': {
'variables': ['u'],
'class': cb.ShapeDimDim,
},
'corrs_rs': {
'requires': ['pis'],
'ebcs': ['fixed_u'],
'epbcs': ['periodic_ux', 'periodic_uy'],
'equations': {
'balance_of_forces':
"""dw_nonsym_elastic.3.Y(mat_he.A, v, u)
= - dw_nonsym_elastic.3.Y(mat_he.A, v, Pi)"""
},
'set_variables': [('Pi', 'pis', 'u')],
'class': cb.CorrDimDim,
'save_name': 'corrs_hyper_homog',
},
}
solvers = {
'ls': ('ls.scipy_direct', {}),
'newton': ('nls.newton', {
'i_max': 1,
'eps_a': 1e-4,
'problem': 'nonlinear',
}),
}