Source code for simulators.links.models.links_lou
"""Links constitutive model: LOU.
Links (Large Strain Implicit Nonlinear Analysis of Solids Linking Scales) is
a finite element code developed by the CM2S research group at the Faculty of
Engineering, University of Porto.
Classes
-------
LinksLou(LinksConstitutiveModel)
Lou-Zhang-Yoon constitutive model.
"""
#
# Modules
# =============================================================================
# Third-party
import torch
# Local
from simulators.links.models.interface import LinksConstitutiveModel
#
# Authorship & Credits
# =============================================================================
__author__ = 'Bernardo Ferreira (bernardo_ferreira@brown.edu)'
__credits__ = ['Bernardo Ferreira', ]
__status__ = 'Alpha'
# =============================================================================
#
# =============================================================================
[docs]class LinksLou(LinksConstitutiveModel):
"""Lou-Zhang-Yoon constitutive model.
Lou-Zhang-Yoon model with general differentiable yield function and
isotropic hardening.
Attributes
----------
_name : str
Constitutive model name.
Methods
-------
_get_required_material_descriptors()
Get required constitutive model descriptors for Links input file.
_format_material_descriptors(self)
Format constitutive model descriptors to Links input file.
"""
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[docs] @staticmethod
def _get_required_material_descriptors():
"""Get required constitutive model descriptors for Links input file.
Returns
-------
material_descriptors : tuple[str]
Required constitutive model descriptors for Links input file.
"""
# Set required constitutive model descriptors
material_descriptors = ('name', 'density', 'young', 'poisson',
'yield_a_init', 'a_hard_slope',
'yield_b_init', 'b_hard_slope',
'yield_c_init', 'c_hard_slope',
'yield_d_init', 'd_hard_slope',
'n_hard_point', 'hardening_law',
'hardening_parameters')
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
return material_descriptors
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[docs] def _format_material_descriptors(self, mat_phase, descriptors):
"""Format constitutive model descriptors to Links input file.
Parameters
----------
mat_phase : int
Material phase identifier.
descriptors : str
Constitutive model descriptors.
Returns
-------
descriptors_input_lines : list[str]
Constitutive model descriptors formatted to Links input data file.
"""
# Check descriptors
required_descriptors = type(self)._get_required_material_descriptors()
if not set(required_descriptors).issubset(set(descriptors.keys())):
raise RuntimeError('Missing required constitutive model '
'descriptors.')
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Get descriptors
name = descriptors['name']
density = descriptors['density']
young = descriptors['young']
poisson = descriptors['poisson']
yield_a_init = descriptors['yield_a_init']
a_hard_slope = descriptors['a_hard_slope']
yield_b_init = descriptors['yield_b_init']
b_hard_slope = descriptors['b_hard_slope']
yield_c_init = descriptors['yield_c_init']
c_hard_slope = descriptors['c_hard_slope']
yield_d_init = descriptors['yield_d_init']
d_hard_slope = descriptors['d_hard_slope']
n_hard_point = descriptors['n_hard_point']
hardening_law = descriptors['hardening_law']
hardening_parameters = descriptors['hardening_parameters']
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Set spacing
spacing = (len(str(mat_phase)) + 1)*' '
# Initialize formatted constitutive model descriptors
descriptors_input_lines = \
[str(mat_phase) + ' ' + name + '\n'] + \
[spacing + '{:<16.8e}'.format(density) + '\n'] + \
[spacing + '{:<16.8e}'.format(young) +
'{:<16.8e}'.format(poisson) + '\n'] + \
[spacing + '{:<16.8e}'.format(yield_a_init) +
'{:<16.8e}'.format(a_hard_slope) + '\n'] + \
[spacing + '{:<16.8e}'.format(yield_b_init) +
'{:<16.8e}'.format(b_hard_slope) + '\n'] + \
[spacing + '{:<16.8e}'.format(yield_c_init) +
'{:<16.8e}'.format(c_hard_slope) + '\n'] + \
[spacing + '{:<16.8e}'.format(yield_d_init) +
'{:<16.8e}'.format(d_hard_slope) + '\n']
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Set formatted constitutive model descriptors (number of hardening
# points)
descriptors_input_lines += \
[spacing + '{:<4d}'.format(n_hard_point) + '\n']
# Set accumulated plastic strain hardening points
acc_p_strains = torch.linspace(0.0, 2.0, steps=n_hard_point)
# Loop over hardening points
for acc_p_strain in acc_p_strains:
# Compute yield stress
yield_stress, _ = \
hardening_law(hardening_parameters, acc_p_strain)
# Set formatted constitutive model descriptors (hardening law)
descriptors_input_lines += \
[spacing + '{:<16.8e}'.format(acc_p_strain)
+ '{:<16.8e}'.format(yield_stress) + '\n']
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
return descriptors_input_lines