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_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_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 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()
