def lacor():
from stats.misc.random_field.random_field_1D import RandomField
rf = RandomField()
x = np.linspace(0,30, 200)
y = rf.acor(x,10.)
yy = rf.acor(x,3.0)
plt.plot(x, y, color = 'black', lw = 2)
plt.plot(x, yy, color = 'black', lw = 2)
plt.xticks(fontsize = 20)
plt.yticks(fontsize = 20)
plt.show()
def random_field():
rf = RandomField(lacor=3.,
length=500.,
nx=500,
distr_type='Weibull',
shape=12.,
scale=5.0,
loc=0.0)
plt.plot(rf.xgrid, rf.random_field, lw=1, color='grey', label='Weibull')
rf.lacor = 10.0
plt.plot(rf.xgrid, rf.random_field, lw=2, color='black', label='Weibull')
plt.ylim(0)
def random_field():
rf = RandomField(lacor=3.,
length=500.,
nx=500,
distr_type='Weibull',
shape=12.,
scale=5.0,
loc=0.0)
plt.plot(rf.xgrid, rf.random_field, lw=1, color='grey', label='Weibull')
rf.lacor = 10.0
plt.plot(rf.xgrid, rf.random_field, lw=2, color='black', label='Weibull')
plt.ylim(0)
def strength():
length = 2000.
nx = 2000
cracks = []
strengths = []
maxsigma = [12., 15., 20., 22., 24.]
Vfs = [0.05, 0.01, 0.013, 0.017, 0.02]
for i, Vf in enumerate(Vfs):
random_field = RandomField(
seed=False,
lacor=5.0,
length=length,
nx=800,
nsim=1,
loc=.0,
shape=8.,
scale=3.2,
)
reinf1 = ContinuousFibers(r=0.0035,
tau=RV('weibull_min',
loc=0.0,
shape=1.,
scale=0.03),
V_f=Vf,
E_f=180e3,
xi=fibers_MC(m=5.0, sV0=0.003),
label='carbon',
n_int=500)
CB_model = CompositeCrackBridge(
E_m=25e3,
reinforcement_lst=[reinf1],
)
scm = SCM(
length=length,
nx=nx,
random_field=random_field,
CB_model=CB_model,
load_sigma_c_arr=np.linspace(0.01, maxsigma[i], 100),
)
scm_view = SCMView(model=scm)
scm_view.model.evaluate()
eps, sigma = scm_view.eps_sigma
plt.plot(eps, sigma, lw=1, label=str(Vf))
strengths.append(np.max(sigma))
cracks.append(len(scm_view.model.cracks_list[-1]))
plt.legend(loc='best')
plt.xlabel('composite strain [-]')
plt.ylabel('composite stress [MPa]')
plt.figure()
plt.plot(Vfs, strengths, label='strengths')
plt.figure()
plt.plot(Vfs, cracks, label='cracks')
print strengths
print cracks
def mtrx_shape():
# shapes: 1000, 16.5, 8.0; scales: 3.0 3.1, 3.2
length = 2000.
nx = 2000
random_field = RandomField(seed=False,
lacor=5.,
length=length,
nx=1000,
nsim=1,
loc=.0,
shape=8.,
scale=3.2,
distr_type='Weibull')
plt.plot(random_field.xgrid,
random_field.random_field,
lw=1,
color='black')
plt.ylim(0)
plt.show()
reinf1 = ContinuousFibers(
r=0.0035,
tau=0.03, #RV('weibull_min', loc=0.0, shape=3., scale=0.03),
V_f=0.01,
E_f=180e3,
xi=fibers_MC(m=5.0, sV0=10.003),
label='carbon',
n_int=500)
CB_model = CompositeCrackBridge(
E_m=25e3,
reinforcement_lst=[reinf1],
)
scm = SCM(
length=length,
nx=nx,
random_field=random_field,
CB_model=CB_model,
load_sigma_c_arr=np.linspace(0.01, 8., 100),
)
scm_view = SCMView(model=scm)
scm_view.model.evaluate()
eps, sigma = scm_view.eps_sigma
plt.figure()
plt.plot(eps, sigma, color='black', lw=2, label='model')
plt.legend(loc='best')
plt.xlabel('composite strain [-]')
plt.ylabel('composite stress [MPa]')
def sigmamu_shape_study():
length = 2000.
nx = 3000
lacor = 1.0
sigmamumin = 3.0
reinf = ContinuousFibers(r=0.0035,
tau=RV('gamma', shape=0.2, scale=0.5),
V_f=0.01,
E_f=180e3,
xi=1000.,
label='carbon',
n_int=500)
ccb = CompositeCrackBridge(E_m=25e3,
reinforcement_lst=[reinf],
)
#for mm in [5., 10., 15., 20., 25., 30., 35.]:
for mm in [5., 10., 15., 20., 30.]:
fLc = (lacor/(lacor+length))**(1./mm)
sm = sigmamumin / (fLc * gamma(1. + 1 / mm))
random_field = RandomField(seed=True,
lacor=1.,
length=length,
nx=500,
nsim=1,
loc=.0,
shape=mm,
scale=sm,
distr_type='Weibull')
scm = SCM(length=length,
nx=nx,
random_field=random_field,
CB_model=ccb,
load_sigma_c_arr=np.linspace(0.01, 20., 200),
n_BC_CB=15)
scm_view = SCMView(model=scm)
scm_view.model.evaluate()
eps, sigma = scm_view.eps_sigma
plt.plot(eps, sigma, label='mm = ' + str(mm) + ' sm = ' + str(sm))
plt.xlabel('composite strain [-]')
plt.ylabel('composite stress [MPa]')
plt.legend(loc='best')
plt.xlim(0)
plt.ylim(0)
plt.show()
def p_tau():
length = 5000.
nx = 5000
for tau_shape in [1.0, 2.0, 1000.]:
random_field = RandomField(seed=False,
lacor=5.0,
length=length,
nx=1000,
nsim=1,
loc=.0,
shape=8.,
scale=3.2,
distribution='Weibull')
reinf1 = ContinuousFibers(r=0.0035,
tau=RV('weibull_min',
loc=0.0,
shape=tau_shape,
scale=0.03),
V_f=0.01,
E_f=180e3,
xi=fibers_MC(m=5.0, sV0=10.003),
label='carbon',
n_int=500)
CB_model = CompositeCrackBridge(
E_m=25e3,
reinforcement_lst=[reinf1],
)
scm = SCM(
length=length,
nx=nx,
random_field=random_field,
CB_model=CB_model,
load_sigma_c_arr=np.linspace(0.01, 8., 100),
)
scm_view = SCMView(model=scm)
scm_view.model.evaluate()
eps, sigma = scm_view.eps_sigma
plt.plot(eps, sigma, lw=1, label=str(tau_shape))
plt.legend(loc='best')
plt.xlabel('composite strain [-]')
plt.ylabel('composite stress [MPa]')
def r_field():
from stats.misc.random_field.random_field_1D import RandomField
rf = RandomField(xgrid = np.linspace(0, 1000, 500))
rf.distribution = 'Weibull'
rf.lacor = 3.0
rf.shape = 10.
rf.scale = 5.
rf.loc = 0.0
x = rf.xgrid
y = rf.random_field
plt.plot(x,y, color = 'grey', lw = 1, label = 'lacor = %.1f' %rf.lacor)
rf.lacor = 10.
y = rf.random_field
plt.plot(x,y, color = 'black', lw = 2, label = 'lacor = %.1f' %rf.lacor)
plt.legend(loc = 'best')
plt.xticks(fontsize = 20)
plt.yticks(fontsize = 20)
plt.show()
def ld():
length = 1000.
nx = 3000
random_field = RandomField(seed=True,
lacor=1.,
length=length,
nx=1000,
nsim=1,
loc=.0,
shape=45.,
scale=3.360,
distr_type='Weibull')
reinf_cont = ContinuousFibers(r=3.5e-3,
tau=RV('gamma', loc=0.0, scale=1.534, shape=.0615),
V_f=0.01,
E_f=181e3,
xi=fibers_MC(m=8.6, sV0=11.4e-3),
label='carbon',
n_int=100)
CB_model = CompositeCrackBridge(E_m=25e3,
reinforcement_lst=[reinf_cont],
)
scm = SCM(length=length,
nx=nx,
random_field=random_field,
CB_model=CB_model,
load_sigma_c_arr=np.linspace(0.01, 30., 200),
n_BC_CB = 12)
scm_view = SCMView(model=scm)
scm_view.model.evaluate()
eps, sigma = scm_view.eps_sigma
plt.plot(eps, sigma, color='black', lw=2, label='continuous fibers')
plt.legend(loc='best')
plt.xlabel('composite strain [-]')
plt.ylabel('composite stress [MPa]')
plt.show()
cb = NonLinearCB(
A_c=9. * 95.,
tstepper=ts,
max_w_p=r * 1.84 * 18 * 1500, # [N]
slip=[
0., 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1., 1.1, 1.2,
1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.
],
bond=bond_18,
n_BC=100)
random_field = RandomField(seed=False,
lacor=1.,
length=2000,
nx=1000,
nsim=1,
loc=.0,
stdev=0.05,
mean=5.,
distr_type='Gauss')
ctt = CompositeTensileTest(n_x=1000,
L=2000,
cb=cb,
sig_mu_x=random_field.random_field,
strength=r * 1.84 * 18. * 1500. / 9. / 95.)
sig_c_i, z_x_i, BC_x_i, sig_c_u, n_crack = ctt.get_cracking_history()
load_arr1 = np.unique(
np.hstack((np.linspace(0, sig_c_u, 100), sig_c_i)))
eps_c_arr1 = ctt.get_eps_c_arr(sig_c_i, z_x_i, BC_x_i, load_arr1)
plt.savefig(savepath)
plt.clf()
return eps_arr
if __name__ == '__main__':
cb = NonLinearCB(slip=[0, 0.1, 0.2, 0.3, 0.4, 0.5],
bond=[0., 10., 20., 30., 40., 50.],
n_BC=100)
random_field = RandomField(seed=False,
lacor=1.,
length=500,
nx=1000,
nsim=1,
loc=.0,
shape=60.,
scale=1.5,
distr_type='Weibull')
ctt = CompositeTensileTest(n_x=1000,
L=500,
cb=cb,
sig_mu_x=random_field.random_field)
sig_c_i, z_x_i, BC_x_i, sig_c_u, n_crack = ctt.get_cracking_history()
load_arr = np.unique(np.hstack((np.linspace(0, sig_c_u, 100), sig_c_i)))
eps_c_arr = ctt.get_eps_c_arr(sig_c_i, z_x_i, BC_x_i, load_arr)
plt.plot(eps_c_arr, load_arr, 'k', lw=2, label='v_f=1.5%')
plt.show()
raise ValueError('''got stuck in loop,
try to adapt x, w, BC ranges''')
last_pos = float(crack_position)
if __name__ == '__main__':
from quaducom.meso.homogenized_crack_bridge.elastic_matrix.reinforcement import ContinuousFibers, ShortFibers
from stats.pdistrib.weibull_fibers_composite_distr import fibers_MC
from matplotlib import pyplot as plt
length = 100.
nx = 500
random_field = RandomField(seed=True,
lacor=1.,
length=length,
nx=500,
nsim=1,
loc=.0,
shape=15.,
scale=4.0,
distr_type='Weibull')
reinf1 = ContinuousFibers(r=3.5e-3,
tau=RV('weibull_min',
loc=0.01,
scale=.01,
shape=2.),
V_f=0.05,
E_f=200e3,
xi=fibers_MC(m=7., sV0=0.01),
label='carbon',
n_int=100)
sigc_max = new_sigc_max
if float(crack_position) == last_pos:
raise ValueError('''got stuck in loop,
try to adapt x, w, BC ranges''')
last_pos = float(crack_position)
print sigc_min
if __name__ == '__main__':
length = 2000.
nx = 2000
random_field = RandomField(seed=True,
lacor=10.,
xgrid=np.linspace(0., length, 400),
nsim=1,
loc=.0,
shape=15.,
scale=6.,
non_negative_check=True,
distribution='Weibull')
reinf = Reinforcement(r=0.01,
tau=RV('uniform', loc=0.01, scale=.5),
V_f=0.05,
E_f=200e3,
xi=WeibullFibers(shape=5., sV0=0.00618983207723),
n_int=50,
label='carbon')
model = CompositeCrackBridge(
E_m=25e3,
max_w_p=1.84 * 8 * 2167, # [N]
slip=slip,
bond=bond,
n_BC=100)
'''
uncomment this loop in order to run multiple random simulations at once
'''
# n_crack_end = 0
# while n_crack_end < 3:
random_field = RandomField(
seed=False,
lacor=4,
length=350,
nx=1000,
nsim=1,
loc=.0,
# stdev=0.2,
# mean=3.22,
shape=5,
scale=8.60718591,
distr_type='Weibull')
ctt = CompositeTensileTest(n_x=1000,
L=350,
cb=cb,
sig_mu_x=random_field.random_field,
strength=21.26)
sig_c_i, z_x_i, BC_x_i, sig_c_u, n_crack = ctt.get_cracking_history()
# print n_crack
def valid(CS, param_set, w_max):
plt.figure()
TT()
from quaducom.meso.homogenized_crack_bridge.elastic_matrix.reinforcement import ContinuousFibers
from stats.pdistrib.weibull_fibers_composite_distr import fibers_MC
length = 250.
nx = 5000
tau_loc, tau_shape, xi_shape = param_set
E_f = 182e3
mu_tau = 1.3 * 3.5e-3 * 3.6 * (1. - 0.01) / (2. * 0.01 * CS)
tau_scale = (mu_tau - tau_loc) / tau_shape
xi_scale = 3243. / (182e3 * (pi * 3.5e-3**2 * 50.)**(-1. / xi_shape) *
gamma(1 + 1. / xi_shape))
#xi_scale = 1578. / (182e3 * (pi * 3.5e-3 **2 * 500. * e)**(-1./xi_shape))
n_CB = 8
ld = False
w_width = False
w_density = False
random_field1 = RandomField(seed=False,
lacor=1.,
length=length,
nx=800,
nsim=1,
loc=.0,
shape=45.,
scale=3.6,
distr_type='Weibull')
reinf1 = ContinuousFibers(r=3.5e-3,
tau=RV('gamma',
loc=tau_loc,
scale=tau_scale,
shape=tau_shape),
V_f=0.01,
E_f=E_f,
xi=fibers_MC(m=xi_shape, sV0=xi_scale),
label='carbon',
n_int=500)
CB_model1 = CompositeCrackBridge(
E_m=25e3,
reinforcement_lst=[reinf1],
)
scm1 = SCM(length=length,
nx=nx,
random_field=random_field1,
CB_model=CB_model1,
load_sigma_c_arr=np.linspace(0.01, 35., 100),
n_BC_CB=n_CB)
scm_view1 = SCMView(model=scm1)
scm_view1.model.evaluate()
eps1, sigma1 = scm_view1.eps_sigma
eps11, sigma11 = scm_view1.eps_sigma_altern
cr_lst1 = scm_view1.model.cracking_stress_lst
interp1 = interp1d(sigma1, eps1)
plt.plot(eps11,
sigma11,
color='red',
lw=2,
label='Vf=1.0, crack spacing = ' +
str(length / float(len(cr_lst1))))
#plt.plot(eps11, sigma11, color='black', ls='dashed', lw=2, label='altern eps')
plt.plot(interp1(np.array(cr_lst1) - np.max(sigma1) / 100.),
np.array(cr_lst1) - np.max(sigma1) / 100., 'ro')
if len(cr_lst1) > 2:
random_field2 = RandomField(seed=False,
lacor=1.,
length=length,
nx=700,
nsim=1,
loc=.0,
shape=45.,
scale=4.38,
distr_type='Weibull')
reinf2 = ContinuousFibers(r=3.5e-3,
tau=RV('gamma',
loc=tau_loc,
scale=tau_scale,
shape=tau_shape),
V_f=0.015,
E_f=E_f,
xi=fibers_MC(m=xi_shape, sV0=xi_scale),
label='carbon',
n_int=500)
CB_model2 = CompositeCrackBridge(
E_m=25e3,
reinforcement_lst=[reinf2],
)
scm2 = SCM(length=length,
nx=nx,
random_field=random_field2,
CB_model=CB_model2,
load_sigma_c_arr=np.linspace(0.01, 40., 100),
n_BC_CB=n_CB)
scm_view2 = SCMView(model=scm2)
scm_view2.model.evaluate()
eps2, sigma2 = scm_view2.eps_sigma
cr_lst2 = scm_view2.model.cracking_stress_lst
interp2 = interp1d(sigma2, eps2)
plt.plot(eps2,
sigma2,
color='blue',
lw=2,
label='Vf=1.5, crack spacing = ' +
str(length / float(len(cr_lst2))))
plt.plot(interp2(np.array(cr_lst2) - np.max(sigma2) / 100.),
np.array(cr_lst2) - np.max(sigma2) / 100., 'bo')
plt.xlabel('composite strain [-]')
plt.ylabel('composite stress [MPa]')
plt.xlim(0., np.max(eps1) * 1.15)
plt.legend(loc='best')
plt.savefig('validation_figsCS%1.f/w_max%.1f.png' % (CS, w_max))
plt.close()
if ld == True:
plt.plot(eps1,
sigma1,
color='red',
lw=2,
label='Vf=1.0, crack spacing = ' +
str(length / float(len(cr_lst1))))
#plt.plot(eps11, sigma11, color='black', ls='dashed', lw=2, label='altern eps')
plt.plot(interp1(np.array(cr_lst1) - np.max(sigma1) / 100.),
np.array(cr_lst1) - np.max(sigma1) / 100., 'ro')
plt.plot(eps2,
sigma2,
color='blue',
lw=2,
label='Vf=1.5, crack spacing = ' +
str(length / float(len(cr_lst2))))
plt.plot(interp2(np.array(cr_lst2) - np.max(sigma2) / 100.),
np.array(cr_lst2) - np.max(sigma2) / 100., 'bo')
plt.xlabel('composite strain [-]')
plt.ylabel('composite stress [MPa]')
plt.xlim(0., np.max(eps1) * 1.1)
plt.legend(loc='best')
if w_width == True:
plt.figure()
plt.plot(scm_view1.model.load_sigma_c_arr, scm_view1.w_mean)
plt.plot(scm_view1.model.load_sigma_c_arr, scm_view1.w_max)
# plt.plot(scm_view2.model.load_sigma_c_arr, scm_view2.w_mean)
# plt.plot(scm_view2.model.load_sigma_c_arr, scm_view2.w_max)
if w_density == True:
plt.figure()
plt.plot(scm_view1.model.load_sigma_c_arr, scm_view1.w_density)
plt.rcParams.update(params)
fig = p.figure(facecolor='white', figsize=(15.6 / 2.54, 7.8 / 2.54), dpi=100)
fig.subplots_adjust(left=0.1,
right=0.96,
bottom=0.18,
top=0.94,
wspace=0.3,
hspace=0.3)
for s, m in zip(s_arr, m_arr):
random_field = RandomField(seed=False,
lacor=l_rho,
length=length,
nx=1000,
nsim=1,
loc=.0,
scale=s,
shape=m,
distr_type='Weibull')
p.subplot(121)
p.plot(random_field.xgrid, random_field.random_field)
p.ylim(ymin=0.0)
p.subplot(122)
p.subplot(122).set_ylabel('Probability')
p.subplot(122).set_xlabel('Composite Stress [MPa]')
sig_pdf_arr = weibull_min.pdf(sig_arr, m, 0, s)
p.plot(sig_arr, sig_pdf_arr, label='m = %1.0f ' % random_field.shape)
p.legend()
