def evaluate(self):
'''evaluates the cracking history and saves it in a list'''
if len(self.CB_objects_lst) == 0:
# first crack
position_first_crack = self.x_arr[np.argmin(self.matrix_strength)]
sigmac_pre_crack = np.min(
self.matrix_strength) / self.CB_model.E_m * self.CB_model.E_c
pre_cracking_W = sigmac_pre_crack / self.CB_model.E_c * self.length
first_CB = CB(
position=position_first_crack,
cracking_stress=sigmac_pre_crack,
pre_cracking_W=pre_cracking_W,
CB_model=CompositeCrackBridge(
reinforcement_lst=self.CB_model.reinforcement_lst,
E_m=self.CB_model.E_m,
Gf=self.CB_model.Gf,
ft=float(self.matrix_strength[np.argwhere(
position_first_crack == self.x_arr)]) * 0.99))
self.CB_objects_lst.append(first_CB)
while True:
try:
s = t.clock()
sigmac_pre_crack, position_new_crack, pre_cracking_W, pre_cracking_w_lst = self.find_next_crack(
)
cb_lst = []
for i, cb_i in enumerate(self.sorted_CB_lst):
if cb_i.CB_model.w_unld < pre_cracking_w_lst[i]:
cb_i.CB_model.w_unld = pre_cracking_w_lst[i]
cb_lst.append(cb_i)
self.CB_objects_lst = cb_lst
new_CB = CB(
position=position_new_crack,
cracking_stress=sigmac_pre_crack,
pre_cracking_W=pre_cracking_W,
CB_model=CompositeCrackBridge(
reinforcement_lst=self.CB_model.reinforcement_lst,
E_m=self.CB_model.E_m,
Gf=self.CB_model.Gf,
ft=float(self.matrix_strength[np.argwhere(
position_new_crack == self.x_arr)]) * 0.99))
self.CB_objects_lst.append(new_CB)
print 'crack #' + str(len(self.CB_objects_lst) +
1), 'evaluated, time: ', t.clock(
) - s, 's, Gf = ', self.CB_model.Gf
except:
# #plt.plot(np.hstack((0.0,self.cracking_W_lst)), np.hstack((0.0,self.cracking_stresses_lst)), color='blue', lw=2)
# #plt.show()
print 'composite saturated'
break
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 evaluate(self):
# seek for the minimum strength redundancy to find the position
# of the next crack
while True:
#try:
s = t.clock()
sigmac_pre_crack, position_new_crack, W_pre_crack = self.find_next_crack(
)
print 'evaluation of the matrix crack #' + str(
len(self.cracking_stresses_lst) + 1), t.clock() - s, 's'
if len(self.cracking_W_lst) > 1000:
plt.plot(self.x_arr,
self.sigma_m(W=W_pre_crack) / self.CB_model.E_m,
color='blue',
lw=2)
plt.plot(self.x_arr,
self.matrix_strength / self.CB_model.E_m,
color='black',
lw=2)
plt.show()
self.crack_positions_lst.append(position_new_crack)
self.cracking_stresses_lst.append(sigmac_pre_crack)
self.cracking_W_lst.append(W_pre_crack)
#append the last crack object
self.CB_objects_lst.append(
CB(position=self.crack_positions_lst[-1],
cracking_stress=self.cracking_stresses_lst[-1],
CB_model=CompositeCrackBridge(
reinforcement_lst=self.CB_model.reinforcement_lst,
E_m=self.CB_model.E_m,
Gf=self.CB_model.Gf,
ft=float(self.matrix_strength[np.argwhere(
self.crack_positions_lst[-1] == self.x_arr)]) *
0.99)))
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 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 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()
tau_scale = (mu_tau - tau_loc) / tau_shape
reinf_cont = ContinuousFibers(r=3.5e-3,
tau=RV('gamma',
loc=tau_loc,
scale=tau_scale,
shape=tau_shape),
V_f=0.01,
E_f=181e3,
xi=fibers_MC(m=xi_shape, sV0=xi_scale),
label='carbon',
n_int=500)
model = CompositeCrackBridge(
E_m=25e3,
reinforcement_lst=[reinf_cont],
Ll=50.,
Lr=200.,
)
ccb_view = CompositeCrackBridgeView(model=model)
def profile(w):
ccb_view.model.w = w
plt.plot(ccb_view.x_arr,
ccb_view.epsm_arr,
lw=2,
label='Ll=' + str(ccb_view.model.Ll))
plt.plot(ccb_view.x_arr, ccb_view.epsf_arr, color='red', lw=2)
plt.xlabel('position [mm]')
plt.ylabel('strain')
E_f=200e3,
xi=fibers_MC(m=7., sV0=0.011),
label='carbon',
n_int=100)
reinf_short = ShortFibers(bond_law='plastic',
r=.2,
tau=1.5,
V_f=0.01,
E_f=200e3,
xi=10.,
snub=0.5,
phi=RV('sin2x', scale=1.0, shape=0.0),
Lf=20.,
label='carbon',
n_int=50)
CB_model = CompositeCrackBridge(E_m=25e3,
reinforcement_lst=[reinf1],
ft=1.0,
Gf=0.5)
scm = SCM(length=length,
nx=nx,
random_field=random_field,
CB_model=CB_model,
load_sigma_c_arr=np.linspace(0.01, 20., 100),
n_BC_CB=3)
scm.evaluate()
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)
reinf_short = ShortFibers(bond_law = 'plastic',
r=.2,
tau=1.,
V_f=0.01,
E_f=200e3,
xi=10.,
snub=0.5,
phi=RV('sin2x', scale=1.0, shape=0.0),
Lf=20.,
label='short steel fibers',
n_int=50)
model = CompositeCrackBridge(E_m=25e3,
reinforcement_lst=[reinf_cont],
Ll=10.,
Lr=10.,
ft=3.0,
Gf=.3
)
ccb_view = CompositeCrackBridgeView(model=model)
def profile(w):
ccb_view.model.w = w
plt.plot(ccb_view.x_arr, ccb_view.epsm_arr, lw=2, label='Ll=' + str(ccb_view.model.Ll))
plt.plot(ccb_view.x_arr, ccb_view.epsf_arr, color='red', lw=2)
plt.xlabel('position [mm]')
plt.ylabel('strain')
def sigma_c_w(w_arr):
sigma_c_arr, u_arr, damage_arr = ccb_view.sigma_c_arr(w_arr, damage=False, u=True)
n_int=100)
reinf_short = ShortFibers(bond_law='plastic',
r=.2,
tau=1.,
V_f=0.01,
E_f=200e3,
xi=10.,
snub=0.5,
phi=RV('sin2x', scale=1.0, shape=0.0),
Lf=20.,
label='short steel fibers',
n_int=50)
CB_model = CompositeCrackBridge(
E_m=25e3,
reinforcement_lst=[reinf_cont, reinf_short],
)
scm = SCM(length=length,
nx=nx,
random_field=random_field,
CB_model=CB_model,
load_sigma_c_arr=np.linspace(0.01, 20., 200),
n_BC_CB=10)
scm_view = SCMView(model=scm)
scm_view.model.evaluate()
def plot():
eps, sigma = scm_view.eps_sigma
plt.plot(eps, sigma, color='black', lw=2, label='model')
plt.legend(loc='best')