def model_free(self, tau_loc, tau_shape, tau_scale):
xi_shape = 6.7
#xi_scale = 3243. / (182e3 * (pi * 3.5e-3 **2 * 50.)**(-1./xi_shape)*gamma(1+1./xi_shape))
xi_scale = 7.6e-3
#CS=8.
#mu_tau = 1.3 * self.r * 3.6 * (1.-0.01) / (2. * 0.01 * CS)
#tau_scale = (mu_tau - tau_loc)/tau_shape
#xi_scale = 0.0077
#xi_shape = 6.7
#tau_scale = (mu_tau - tau_loc)/tau_shape
cb = CBClampedRandXi(pullout=False)
spirrid = SPIRRID(q=cb, sampling_type='LHS')
tau = RV('gamma', shape=tau_shape, scale=tau_scale, loc=tau_loc)
w = self.w
spirrid.eps_vars = dict(w=w)
spirrid.theta_vars = dict(tau=tau,
E_f=self.Ef,
V_f=self.V_f,
r=self.r,
m=xi_shape,
sV0=xi_scale)
spirrid.n_int = 5000
sigma_c = spirrid.mu_q_arr / self.r**2
plt.plot(w, sigma_c)
return sigma_c
def hybrid():
cb = CBClampedRandXi()
w = np.linspace(0.0, 2.5, 1000)
spirrid = SPIRRID(q=cb, sampling_type='PGrid',
eps_vars=dict(w=w),
theta_vars=dict(tau=0.5,
E_f=180e3,
V_f=0.01,
r=0.00345,
m=7.0,
sV0=0.0026,
lm=1000.),
n_int=100)
sigma_c1 = spirrid.mu_q_arr / spirrid.theta_vars['r'] ** 2
plt.plot(w, sigma_c1, label='1')
spirrid.theta_vars['E_f'] = 70e3
spirrid.theta_vars['r'] = 0.013
spirrid.theta_vars['sV0'] = 0.015
spirrid.theta_vars['m'] = 20.
sigma_c2 = spirrid.mu_q_arr / spirrid.theta_vars['r'] ** 2
plt.plot(w, sigma_c2, label='2')
plt.plot(w, sigma_c2 + sigma_c1)
plt.ylim(0, 20)
plt.legend()
plt.show()
def _get_model_extrapolate(self):
cb = CBClampedRandXi(pullout=False)
spirrid = SPIRRID(q=cb, sampling_type='LHS')
sV0 = self.sV0
V_f = 1.0
r = 3.5e-3
m = self.m
tau = RV('gamma',
shape=self.tau_shape,
scale=self.tau_scale,
loc=self.tau_loc)
n_int = self.n_int
w = self.w2
lm = self.lm
spirrid.eps_vars = dict(w=w)
spirrid.theta_vars = dict(tau=tau,
E_f=self.Ef,
V_f=V_f,
r=r,
m=m,
sV0=sV0,
lm=lm)
spirrid.n_int = n_int
sigma_c = spirrid.mu_q_arr / self.r**2
return sigma_c
def _get_model_extrapolate(self):
cb = CBClampedRandXi(pullout=False)
spirrid = SPIRRID(q=cb, sampling_type='LHS')
sV0 = self.sV0
V_f = 1.0
r = 3.5e-3
m = self.m
tau = RV('gamma', shape=self.tau_shape, scale=self.tau_scale, loc=self.tau_loc)
n_int = self.n_int
w = self.w2
lm = self.lm
spirrid.eps_vars = dict(w=w)
spirrid.theta_vars = dict(tau=tau, E_f=self.Ef, V_f=V_f, r=r, m=m, sV0=sV0, lm=lm)
spirrid.n_int = n_int
sigma_c = spirrid.mu_q_arr / self.r ** 2
return sigma_c
def model_clamped(self, tau_shape, tau_scale, tau_loc):
cb = CBClampedRandXi(pullout=True)
spirrid = SPIRRID(q=cb, sampling_type='LHS')
sV0 = self.sV0
V_f = self.V_f
r = self.r
m = self.m
tau = RV('gamma', shape=tau_shape, scale=tau_scale, loc=tau_loc)
n_int = self.n_int
w = self.w2
lm = self.lm
spirrid.eps_vars = dict(w=w)
spirrid.theta_vars = dict(tau=tau, E_f=self.Ef, V_f=V_f, r=r, m=m, sV0=sV0, lm=lm)
spirrid.n_int = n_int
sigma_c = spirrid.mu_q_arr / self.r ** 2
return sigma_c
def model_free(self, tau_loc, tau_shape, tau_scale):
xi_shape = 6.7
#xi_scale = 3243. / (182e3 * (pi * 3.5e-3 **2 * 50.)**(-1./xi_shape)*gamma(1+1./xi_shape))
xi_scale = 7.6e-3
#CS=8.
#mu_tau = 1.3 * self.r * 3.6 * (1.-0.01) / (2. * 0.01 * CS)
#tau_scale = (mu_tau - tau_loc)/tau_shape
#xi_scale = 0.0077
#xi_shape = 6.7
#tau_scale = (mu_tau - tau_loc)/tau_shape
cb = CBClampedRandXi(pullout=False)
spirrid = SPIRRID(q=cb, sampling_type='LHS')
tau = RV('gamma', shape=tau_shape, scale=tau_scale, loc=tau_loc)
w = self.w
spirrid.eps_vars = dict(w=w)
spirrid.theta_vars = dict(tau=tau, E_f=self.Ef, V_f=self.V_f,
r=self.r, m=xi_shape, sV0=xi_scale)
spirrid.n_int = 5000
sigma_c = spirrid.mu_q_arr / self.r ** 2
plt.plot(w, sigma_c)
return sigma_c
def _get_model_rand(self):
cb = CBResidualRandXi()
spirrid = SPIRRID(q=cb, sampling_type='PGrid')
sV0 = self.sV0
tau_scale = self.tau_scale
V_f = 1.0
r = 3.5e-3
m = self.m
tau = RV('weibull_min', shape=self.tau_shape, scale=tau_scale, loc=self.tau_loc)
n_int = self.n_int
w = self.w
spirrid.eps_vars=dict(w=w)
spirrid.theta_vars=dict(tau=tau, E_f=self.Ef, V_f=V_f, r=r, m=m, sV0=sV0)
spirrid.n_int=n_int
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
return sigma_c
def hybrid():
cb = CBClampedRandXi()
w = np.linspace(0.0, 2.5, 1000)
spirrid = SPIRRID(q=cb,
sampling_type='PGrid',
eps_vars=dict(w=w),
theta_vars=dict(tau=0.5,
E_f=180e3,
V_f=0.01,
r=0.00345,
m=7.0,
sV0=0.0026,
lm=1000.),
n_int=100)
sigma_c1 = spirrid.mu_q_arr / spirrid.theta_vars['r']**2
plt.plot(w, sigma_c1, label='1')
spirrid.theta_vars['E_f'] = 70e3
spirrid.theta_vars['r'] = 0.013
spirrid.theta_vars['sV0'] = 0.015
spirrid.theta_vars['m'] = 20.
sigma_c2 = spirrid.mu_q_arr / spirrid.theta_vars['r']**2
plt.plot(w, sigma_c2, label='2')
plt.plot(w, sigma_c2 + sigma_c1)
plt.ylim(0, 20)
plt.legend()
plt.show()
def simplified():
cb = CBClampedRandXi()
spirrid = SPIRRID(q=cb,
sampling_type='PGrid',
theta_vars=dict(tau=RV('gamma',
loc=0.0055,
scale=0.7,
shape=0.2),
E_f=200e3,
V_f=0.01,
r=0.00345,
m=7.0,
sV0=0.0042,
lm=1000.),
n_int=200)
def sigmac(w, lm):
spirrid.eps_vars['w'] = np.array([w])
spirrid.theta_vars['lm'] = lm
sigma_c = spirrid.mu_q_arr / spirrid.theta_vars['r']**2
return sigma_c
def maxsigma(lm):
def minfunc(w):
res = sigmac(w, lm)
return -res * (w < 200.) + 1e-5 * w**2
w_max = minimize_scalar(minfunc, bracket=(0.0001, 0.0002))
return w_max.x, sigmac(w_max.x, lm) / spirrid.theta_vars['V_f']
sigmaf = []
w_lst = []
lcs = 1. / np.linspace(8.4, 300.0, 20)
for lcsi in lcs:
print lcsi
wi, sigi = maxsigma(1. / lcsi)
sigmaf.append(sigi)
w_lst.append(wi)
plt.plot(lcs, sigmaf)
plt.plot(1. / 13.7, 1201, 'ro')
plt.plot(1. / 9.7, 1373, 'bo')
plt.errorbar(1. / 13.7, 1201, 104.4)
plt.errorbar(1. / 9.7, 1373, 36.4)
plt.ylim(0)
plt.figure()
plt.plot(lcs, w_lst)
plt.plot(1. / 13.7, 0.088, 'ro')
plt.plot(1. / 9.7, 0.05, 'bo')
plt.errorbar(1. / 13.7, 0.088, 0.003)
plt.errorbar(1. / 9.7, 0.05, 0.005)
plt.ylim(0)
plt.show()
def mechanisms():
m = 5.15004407
sV0 = 0.00915595
r = 3.5e-3
Ef = 181e3
cb = CBClampedRandXi(pullout=False)
spirrid = SPIRRID(q=cb,
sampling_type='LHS',
theta_vars=dict(E_f=Ef,
sV0=sV0,
V_f=1.0,
r=r,
m=m,
tau=RV('gamma', shape=0.03684979, scale=3.75278102, loc=0.0),
lm=1000.),
n_int=100,
)
lm_arr = np.linspace(1000., 3., 20)
sigma_u_hommech = []
for lm_i in lm_arr:
spirrid.theta_vars['lm'] = lm_i
max_w = min(30., lm_i * 0.07)
w_arr = np.linspace(0.0, max_w, 200)
spirrid.eps_vars = dict(w=w_arr)
sig_w = spirrid.mu_q_arr / r ** 2
plt.plot(w_arr, sig_w)
plt.show()
sigma_u_hommech.append(np.max(sig_w))
sigma_u_hommech = np.array(sigma_u_hommech)
plt.plot(lm_arr, sigma_u_hommech)#/np.min(sigma_u_hommech))
plt.xlabel('crack spacing')
plt.ylabel('normalized strength')
plt.show()
def short_fibers_CHOB():
cb = CBShortFiber()
Ef = 200e3
Vf = 0.015
r = 0.088
Lc = 400.
Ac = 1600.
lf = 14.
spirrid = SPIRRID(q=cb,
sampling_type='PGrid',
eps_vars=dict(w=np.array([100.0])),
theta_vars=dict(tau=1.8,
E_f=Ef,
r=r,
le=RV('uniform', scale=lf / 2., loc=0.0),
phi=RV('sin2x', scale=1.0),
snub=.87,
xi=20e10),
n_int=100)
spirrid.codegen.implicit_var_eval = True
var_e = spirrid.var_q_arr
mu_e = spirrid.mu_q_arr
Af = pi * r**2
p = lf / 2. / Lc
n = Ac * Lc * Vf / Af / lf
mu_strength = Ef * Vf / 2. * mu_e
var_strength = (Ef * Vf / 2.)**2 / n / p * (var_e + (1. - p) * mu_e**2)
n = np.arange(10)
distr = norm(loc=mu_strength, scale=var_strength**(0.5))
sig_arr = np.linspace(mu_strength / 2., mu_strength * 1.5, 1000)
CDF1 = distr.cdf(sig_arr)
CDF2 = 1 - (1 - CDF1)**2
CDF10 = 1 - (1 - CDF1)**10
plt.figure()
plt.plot(sig_arr, CDF1, label='strength distr 1')
plt.plot(sig_arr, CDF2, label='strength distr 2')
plt.plot(sig_arr, CDF10, label='strength distr 10')
plt.figure()
cracks = np.linspace(1, 100, 500)
plt.plot(cracks, distr.ppf(1. - 0.5**(1. / cracks)), label='0.5')
plt.plot(cracks, distr.ppf(1. - 0.99999**(1. / cracks)), label='0.000001')
plt.ylim(1.0, 3.0)
plt.legend()
plt.show()
# print self.count / (30**3)*100, 'percent'
# print 'current params:', [sV0, m, tau], 'best params:', self.x0
# print 'current residuum:', resid, 'best:', self.residuum
return
if __name__ == '__main__':
from quaducom.micro.resp_func.CB_rigid_mtrx_rand_xi import CBResidualRandXi
from spirrid.spirrid import SPIRRID
from spirrid.rv import RV
from matplotlib import pyplot as plt
from scipy.special import gamma, gammainc
from math import pi
cb = CBResidualRandXi()
spirrid = SPIRRID(q=cb, sampling_type='PGrid')
def model_rand(params, *args):
w = args[0]
sV0, tau_scale = params
E_f = 180e3
V_f = 1.0
r = 3.45e-3
m = 4.
tau = RV('weibull_min', shape=.4, scale=tau_scale, loc=0.009)
# a_lower = 0.0
# tau = RV('piecewise_uniform', shape=0.0, scale=1.0)
# tau._distr.distr_type.distribution.a_lower = a_lower
# tau._distr.distr_type.distribution.a_upper = a_upper
# tau._distr.distr_type.distribution.b_lower = a_upper
# tau._distr.distr_type.distribution.b_upper = b_upper
from matplotlib import pyplot as plt
from scipy.stats import weibull_min
from stats.pdistrib.weibull_fibers_composite_distr import fibers_MC, fibers_CB_rigid, fibers_dry
from scipy.optimize import minimize_scalar
import pickle
from stats.spirrid import make_ogrid as orthogonalize
from mayavi import mlab
from math import pi
from scipy.stats import norm
cb = CBClampedRandXi()
spirrid = SPIRRID(q=cb,
sampling_type='PGrid',
theta_vars=dict(tau=0.1,
E_f=200e3,
V_f=0.01,
r=0.00345,
m=5.0,
sV0=0.0026,
lm=1000.),
n_int=100)
def fiber():
cb = CBClamped()
w = np.linspace(0.0, 1., 300)
sigmaCB = []
sigmaMC = []
for wi in w:
sigmaCB.append(cb(wi, .1, 240e3, 0.01, 0.0035, 7.0, 0.0046, 5000.,
0.5))
sigmaMC.append(cb(wi, .1, 240e3, 0.01, 0.0035, 7.0, 0.0046, 20., 0.5))
def _get_spirrid_filament(self):
resp_func = self.micro_model.FilamentCB()
spirrid = SPIRRID(q=resp_func)
return spirrid