Module weac.tools
Helper functions for the WEak Layer AntiCrack nucleation model.
Expand source code
# pylint: disable=C0103
"""Helper functions for the WEak Layer AntiCrack nucleation model."""
# Standard library imports
from timeit import default_timer as timer
# Third party imports
import numpy as np
def time():
"""Return current time in milliseconds."""
return 1e3*timer()
def isnotebook():
"""Identify shell environment."""
try:
shell = get_ipython().__class__.__name__
if shell == 'ZMQInteractiveShell':
return True # Jupyter notebook or qtconsole
if shell == 'TerminalInteractiveShell':
return False # Terminal running IPython
# None of the above: other type ?
return False
except NameError:
return False # Probably standard Python interpreter
def load_dummy_profile(profile_id):
"""Define standard layering types for comparison."""
# Layers [density (kg/m^3), thickness (mm), Young's modulus (N/mm^2)]
soft = [120., 120., 0.3]
medium = [180., 120., 1.5]
hard = [270., 120., 7.5]
# Database (top to bottom)
database = {
# Layered
'a': [hard, medium, soft],
'b': [soft, medium, hard],
'c': [hard, soft, hard],
'd': [soft, hard, soft],
'e': [hard, soft, soft],
'f': [soft, soft, hard],
# Homogeneous
'soft': [soft, soft, soft],
'medium': [medium, medium, medium],
'hard': [hard, hard, hard],
# Comparison
'comp': [[240., 200., 5.23], ]
}
# Load profile
try:
profile = np.array(database[profile_id.lower()])
except KeyError:
raise ValueError(f'Profile {profile_id} is not defined.') from None
# Prepare output
layers = profile[:, 0:2]
E = profile[:, 2]
return layers, E
def calc_center_of_gravity(layers):
"""
Calculate z-coordinate of the center of gravity.
Arguments
---------
layers : list
2D list of layer densities and thicknesses. Columns are
density (kg/m^3) and thickness (mm). One row corresponds
to one layer.
Returns
-------
H : float
Total slab thickness (mm).
zs : float
Z-coordinate of center of gravity (mm).
"""
# Layering info for center of gravity calculation (bottom to top)
n = layers.shape[0] # Number of layers
rho = np.flipud(layers[:, 0]) # Layer densities
h = np.flipud(layers[:, 1]) # Layer thicknesses
H = sum(h) # Total slab thickness
# Layer center coordinates (bottom to top)
zi = [H/2 - sum(h[0:j]) - h[j]/2 for j in range(n)]
# Z-coordinate of the center of gravity
zs = sum(zi*h*rho)/sum(h*rho)
# Return slab thickness and center of gravity
return H, zs
def scapozza(rho):
"""
Compute Young's modulus (MPa) from density (kg/m^3).
Arguments
---------
rho : float or ndarray
Density (kg/m^3).
Returns
-------
E : float or ndarray
Young's modulus (MPa).
"""
rho = rho*1e-12 # Convert to t/mm^3
rho0 = 917e-12 # Desity of ice in t/mm^3
E = 5.07e3*(rho/rho0)**5.13 # Young's modulus in MPa
return E
def gerling(rho, C0=6.0, C1=4.6):
"""
Compute Young's modulus density according to Gerling et al. 2017.
Arguments
---------
rho : float or ndarray
Density (kg/m^3).
C0 : float, optional
Multiplicative constant of Young modulus parametrization
according to Gerling et al. (2017). Default is 6.0.
C1 : float, optional
Exponent of Young modulus parameterization according to
Gerling et al. (2017). Default is 4.6.
Returns
-------
E : float or ndarray
Young's modulus (MPa).
"""
return C0*1e-10*rho**C1Functions
def calc_center_of_gravity(layers)-
Calculate z-coordinate of the center of gravity.
Arguments
layers:list- 2D list of layer densities and thicknesses. Columns are density (kg/m^3) and thickness (mm). One row corresponds to one layer.
Returns
H:float- Total slab thickness (mm).
zs:float- Z-coordinate of center of gravity (mm).
Expand source code
def calc_center_of_gravity(layers): """ Calculate z-coordinate of the center of gravity. Arguments --------- layers : list 2D list of layer densities and thicknesses. Columns are density (kg/m^3) and thickness (mm). One row corresponds to one layer. Returns ------- H : float Total slab thickness (mm). zs : float Z-coordinate of center of gravity (mm). """ # Layering info for center of gravity calculation (bottom to top) n = layers.shape[0] # Number of layers rho = np.flipud(layers[:, 0]) # Layer densities h = np.flipud(layers[:, 1]) # Layer thicknesses H = sum(h) # Total slab thickness # Layer center coordinates (bottom to top) zi = [H/2 - sum(h[0:j]) - h[j]/2 for j in range(n)] # Z-coordinate of the center of gravity zs = sum(zi*h*rho)/sum(h*rho) # Return slab thickness and center of gravity return H, zs def gerling(rho, C0=6.0, C1=4.6)-
Compute Young's modulus density according to Gerling et al. 2017.
Arguments
rho:floatorndarray- Density (kg/m^3).
C0:float, optional- Multiplicative constant of Young modulus parametrization according to Gerling et al. (2017). Default is 6.0.
C1:float, optional- Exponent of Young modulus parameterization according to Gerling et al. (2017). Default is 4.6.
Returns
E:floatorndarray- Young's modulus (MPa).
Expand source code
def gerling(rho, C0=6.0, C1=4.6): """ Compute Young's modulus density according to Gerling et al. 2017. Arguments --------- rho : float or ndarray Density (kg/m^3). C0 : float, optional Multiplicative constant of Young modulus parametrization according to Gerling et al. (2017). Default is 6.0. C1 : float, optional Exponent of Young modulus parameterization according to Gerling et al. (2017). Default is 4.6. Returns ------- E : float or ndarray Young's modulus (MPa). """ return C0*1e-10*rho**C1 def isnotebook()-
Identify shell environment.
Expand source code
def isnotebook(): """Identify shell environment.""" try: shell = get_ipython().__class__.__name__ if shell == 'ZMQInteractiveShell': return True # Jupyter notebook or qtconsole if shell == 'TerminalInteractiveShell': return False # Terminal running IPython # None of the above: other type ? return False except NameError: return False # Probably standard Python interpreter def load_dummy_profile(profile_id)-
Define standard layering types for comparison.
Expand source code
def load_dummy_profile(profile_id): """Define standard layering types for comparison.""" # Layers [density (kg/m^3), thickness (mm), Young's modulus (N/mm^2)] soft = [120., 120., 0.3] medium = [180., 120., 1.5] hard = [270., 120., 7.5] # Database (top to bottom) database = { # Layered 'a': [hard, medium, soft], 'b': [soft, medium, hard], 'c': [hard, soft, hard], 'd': [soft, hard, soft], 'e': [hard, soft, soft], 'f': [soft, soft, hard], # Homogeneous 'soft': [soft, soft, soft], 'medium': [medium, medium, medium], 'hard': [hard, hard, hard], # Comparison 'comp': [[240., 200., 5.23], ] } # Load profile try: profile = np.array(database[profile_id.lower()]) except KeyError: raise ValueError(f'Profile {profile_id} is not defined.') from None # Prepare output layers = profile[:, 0:2] E = profile[:, 2] return layers, E def scapozza(rho)-
Compute Young's modulus (MPa) from density (kg/m^3).
Arguments
rho:floatorndarray- Density (kg/m^3).
Returns
E:floatorndarray- Young's modulus (MPa).
Expand source code
def scapozza(rho): """ Compute Young's modulus (MPa) from density (kg/m^3). Arguments --------- rho : float or ndarray Density (kg/m^3). Returns ------- E : float or ndarray Young's modulus (MPa). """ rho = rho*1e-12 # Convert to t/mm^3 rho0 = 917e-12 # Desity of ice in t/mm^3 E = 5.07e3*(rho/rho0)**5.13 # Young's modulus in MPa return E def time()-
Return current time in milliseconds.
Expand source code
def time(): """Return current time in milliseconds.""" return 1e3*timer()