def DOE(w_arr):
reinf1 = Reinforcement(
r=0.00345, #r=RV('uniform', loc=0.002, scale=0.002),
tau=RV('uniform', loc=.2, scale=1.),
V_f=0.1,
E_f=200e3,
xi=RV('weibull_min', shape=5., scale=.02),
n_int=100)
ccb = CompositeCrackBridge(E_m=25e3,
reinforcement_lst=[reinf1],
Ll=100.,
Lr=100.)
def eps_w(w_arr):
eps = []
ccb.iters = 6
for w in w_arr:
# print 'w_ctrl=',
ccb.w = w
ccb.damage = np.zeros_like(ccb.sorted_E_f)
eps.append(ccb.profile[3])
plt.plot(w_arr, eps, color='black', lw=2, label=str(ccb.iters))
eps_w(w_arr)
def rand_tau():
E_f, V_f, r, m, sV0 = 200e3, 0.01, 0.01, 7.0, 3.e-3
Pf = RV('uniform', loc=0.0, scale=1.0)
w_arr = np.linspace(0, 1., 200)
cb = CBResidual(include_pullout=True)
for i, taui in enumerate([
RV('uniform', loc=.0999, scale=.0002), #COV = 0.01
RV('uniform', loc=.05, scale=.1), #COV = 0.3
RV('uniform', loc=.01, scale=0.18)
]): #COV = 0.5
total = SPIRRID(q=cb,
sampling_type='MCS',
evars=dict(w=w_arr),
tvars=dict(tau=taui,
E_f=E_f,
V_f=V_f,
r=r,
m=m,
sV0=sV0,
Pf=Pf),
n_int=300)
if isinstance(r, RV):
r_arr = np.linspace(r.ppf(0.001), r.ppf(0.999), 300)
Er = np.trapz(r_arr**2 * r.pdf(r_arr), r_arr)
else:
Er = r**2
result = total.mu_q_arr / Er
plt.plot(w_arr, result, lw=2, color='black')
plt.xlabel('$w\, [\mathrm{mm}]$')
plt.ylabel('$\mu_{\sigma_\mathrm{c},\\xi \\tau}\,[\mathrm{MPa}]$')
plt.ylim(0, 10)
plt.xlim(0, 1.)
plt.show()
def general_diagram():
E_f, V_f, r, tau, m, sV0 = 200e3, 0.01, 0.01, .1, 7., 3.e-3
Pf = RV('uniform', loc=0.0, scale=1.0)
w_arr = np.linspace(0, 1.2, 200)
cb = CBResidual(include_pullout=True)
total = SPIRRID(q=cb,
sampling_type='TGrid',
evars=dict(w=w_arr),
tvars=dict(tau=tau,
E_f=E_f,
V_f=V_f,
r=r,
m=m,
sV0=sV0,
Pf=Pf),
n_int=1000)
if isinstance(r, RV):
r_arr = np.linspace(r.ppf(0.001), r.ppf(0.999), 300)
Er = np.trapz(r_arr**2 * r.pdf(r_arr), r_arr)
else:
Er = r**2
total = total.mu_q_arr / Er
plt.plot(w_arr, total, lw=2, color='black')
cb = CBResidual(include_pullout=False)
broken = SPIRRID(q=cb,
sampling_type='PGrid',
evars=dict(w=w_arr),
tvars=dict(tau=tau,
E_f=E_f,
V_f=V_f,
r=r,
m=m,
sV0=sV0,
Pf=Pf),
n_int=1000)
if isinstance(r, RV):
r_arr = np.linspace(r.ppf(0.001), r.ppf(0.999), 300)
Er = np.trapz(r_arr**2 * r.pdf(r_arr), r_arr)
else:
Er = r**2
broken = broken.mu_q_arr / Er
plt.plot(w_arr, broken, lw=2, ls='dashed', color='black')
plt.plot(w_arr, total - broken, lw=2, ls='dashed', color='black')
plt.ylim(0, 10)
plt.xlim(0, .8)
plt.xlabel('$w\, [\mathrm{mm}]$')
plt.ylabel('$\mu_{\sigma_\mathrm{c},\mathbf{X}}\,[\mathrm{MPa}]$')
plt.show()
# statistical characteristics (mean, stdev)
m_la, std_la = 10., 1.0
m_xi, std_xi = 1.0, 0.1
# discretize the control variable (x-axis)
e_arr = np.linspace(0, 1.2, 40)
# Exact solution
def mu_q_ex(e, m_xi, std_xi, m_la):
return e * (0.5 - 0.5 * erf(0.5 * math.sqrt(2) *
(e - m_xi) / std_xi)) * m_la
mu_q_ex_arr = mu_q_ex(e_arr, m_xi, std_xi, m_la)
g_la = RV('norm', m_la, std_la)
g_xi = RV('norm', m_xi, std_xi)
s = SPIRRID(
q=fiber_tt_2p,
e_arr=e_arr,
n_int=10,
tvars=dict(la=g_la, xi=g_xi),
)
mu_q_ex_arr = mu_q_ex(e_arr, m_xi, std_xi, m_la)
slab = SPIRRIDLAB(s=s,
save_output=False,
show_output=True,
exact_arr=mu_q_ex(e_arr, m_xi, std_xi, m_la))
from quaducom.micro.resp_func.cb_emtrx_clamped_fiber_stress import \
CBEMClampedFiberStress
from quaducom.micro.resp_func.cb_emtrx_clamped_fiber_stress_residual import \
CBEMClampedFiberStressResidual
from stats.spirrid.spirrid import SPIRRID
from stats.spirrid.rv import RV
from matplotlib import pyplot as plt
import numpy as np
if __name__ == '__main__':
# filaments
r = 0.00345
V_f = 0.0103
tau = RV('uniform', loc=0.1, scale=.3)
E_f = 200e3
E_m = 25e3
l = RV('uniform', scale=10., loc=2.)
theta = 0.0
xi = RV('weibull_min', scale=0.02, shape=5)
phi = 1.
Ll = 20.
Lr = 30.
s0 = 0.0205
m = 5.0
Pf = RV('uniform', loc=0., scale=1.0)
w = np.linspace(0, 1.3, 100)
cb_emtrx = CBEMClampedFiberStress()
omega))
q = self.q(wD, tau, l, E_f, E_m, theta, xi, phi, Ll, Lr, V_f, r,
omega) * (1. - omega)
w_lst.append(wD)
q_lst.append(q)
return np.array(w_lst), np.array(q_lst)
if __name__ == '__main__':
from stats.spirrid.rv import RV
a = WAnalytIter()
# filaments
r = 0.00345
V_f = 0.04
tau = 0.5 #RV('uniform', loc=0.2, scale=1.)
E_f = 200e3
E_m = 25e3
l = 0.0
theta = 0.0
phi = 1.
Ll = 100.
Lr = 100.
xi = RV('weibull_min', shape=5., scale=.02)
ctrl_damage = np.linspace(0.0, .9999, 50)
w = np.linspace(0., 0.7, 100)
#q = a.damage_func(w, tau, l, E_f, E_m, theta, xi, phi, Ll, Lr, V_f, r, 0.3)
w, q = a.eval_w_q(tau, l, E_f, E_m, theta, xi, phi, Ll, Lr, V_f, r,
ctrl_damage)
plt.plot(w, q)
plt.show()
import numpy as np
from matplotlib import pyplot as plt
from stats.spirrid.rv import RV
import math
import numpy as np
###################
def same_length( l ):
return np.arccos( l[0] / l )
n_int = 200
phi = RV( 'sin2x', loc = 0., scale = 1. )
a_l = RV( 'uniform', loc = 0., scale = 1. )
discr_ppf = np.linspace( .0001 / n_int, 1. - .0001 / n_int, n_int )
phi = phi.ppf( discr_ppf )
a = a_l.ppf( discr_ppf )
#for ae in a:
# x = np.ones( len( a ) ) * ae
# print x, phi
# plt.plot( x , phi, 'ro' )
isol = np.linspace( a[5], a[-5], 5 )
'''
for i, il in enumerate( isol ):
x_l = np.linspace( il, np.max( a ), 200 )
y_l = same_length( x_l )
if i != 1:
plt.plot( x_l, y_l , 'k' )
else:
if isinstance(r, RV):
r_arr = np.linspace(r.ppf(0.001), r.ppf(0.999), 300)
Er = np.trapz(r_arr**2 * r.pdf(r_arr), r_arr)
else:
Er = r**2
sigma_c = spirrid.mu_q_arr / Er
plt.plot(w, sigma_c, lw=2, label='sigma c')
#plt.ylim(0, 35)
plt.xlabel('w [mm]')
plt.ylabel('sigma_c [MPa]')
plt.legend(loc='best')
plt.show()
w = np.linspace(0, .5, 300)
tau = 0.5 #RV('weibull_min', shape=3., scale=.03)
E_f = 200e3
V_f = 0.01
r = RV('uniform', loc=0.001, scale=0.004)
m = 7.
# sV0=XXX corresponds to sL0=0.02 at L0=100 and r=0.002
sV0 = 3.1e-3
Pf = RV('uniform', loc=0., scale=1.0)
n_int = 300
#cb = CBResidual()
#plt.plot(w, cb(w, 0.5, E_f, V_f, 0.001, m, sV0, 0.5) / 0.001 ** 2, label='r=0.001')
#plt.plot(w, cb(w, 0.5, E_f, V_f, 0.002, m, sV0, 0.5) / 0.002 ** 2, label='r=0.002')
#plt.plot(w, cb(w, 0.5, E_f, V_f, 0.003, m, sV0, 0.5) / 0.003 ** 2, label='r=0.003')
#plt.legend()
#plt.show()
CB_composite_stress(w, tau, E_f, V_f, r, m, sV0, Pf, n_int)