forked from rubenftf/3D_cube
-
Notifications
You must be signed in to change notification settings - Fork 0
/
3D_ceramic_structure.py
150 lines (144 loc) · 6.84 KB
/
3D_ceramic_structure.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
import numpy as np
import random
import scipy.integrate as integrate
import lxml.etree as lxml
class material_properties():
def __init__(self,cube_data):
parser=lxml.XMLParser()
tree = lxml.parse(cube_data, parser)
root=tree.getroot()
self.cube_dimentions=np.asarray([int(i) for i in root[1][0].get('D').split(",")])
self.symmetry=str(root[0][0].get('symmetry'))
if self.symmetry=="Tetra":
self.tau=0.75e-11*2/1.3
self.eps=np.array([[1721,0,0],[0,1721,0],[0,0,382]])
self.Ea=33e6
self.Ps=0.3641
self.v=1.8
elif self.symmetry=="Rhombo":
self.tau=0.17e-11
self.eps=np.array([[529,0,0],[0,529,0],[0,0,295]])
self.Ea=25e6
self.Ps=0.455
self.v=1.4
elif self.symmetry=="Ortho":
self.tau=0.17e-12
self.eps=np.array([[160,0,0],[0,100,0],[0,0,55]])
self.Ea=8e6
self.Ps=0.42
self.v=1
self.v=1.8 if self.symmetry=="Tetra" else 1.4
self.Ea=33e6 if self.symmetry=="Tetra" else 25e6
self.Ps=0.3641 if self.symmetry=="Tetra" else 0.455
def assignpoldirection(self):
if self.symmetry=="Tetra":
#tetragonal
theta_r1=np.pi/4
theta_max=np.arcsin(np.sqrt(2.0/3.0))
def f1(x):
return 1.5/np.pi
def f2(x):
return 6*(np.pi/4-np.arccos(1/np.tan(x)))/np.pi**2
#print 2*np.pi*(integrate.quad(lambda x: f1(x)*np.sin(x),0,np.pi/4)[0]+integrate.quad(lambda x: f2(x)*np.sin(x),np.pi/4,np.arcsin(np.sqrt(2.0/3.0)))[0])
j=0
i=[]
f_theta_int=[]
theta=[]
while j<=theta_max:
if j<=np.pi/4:
f_theta_int.append(integrate.quad(lambda x: 2*np.pi*f1(x)*np.sin(x),0,j)[0])
theta.append(f1(j))
i.append(j)
else:
f_theta_int.append(integrate.quad(lambda x: 2*np.pi*f2(x)*np.sin(x),np.pi/4,j)[0]+integrate.quad(lambda x: 2*np.pi*f1(x)*np.sin(x),0,np.pi/4)[0])
theta.append(f2(j))
i.append(j)
j+=np.arcsin(np.sqrt(2.0/3.0))/10000.0
elif self.symmetry=="Rhombo":
#rhombohedra
theta_r1=np.arctan(1/np.sqrt(2))
theta_max=np.arctan(np.sqrt(2))
def f1(x):
return 2/np.pi
def f2(x):
return 6*(np.pi/3-np.arccos(1/(np.sqrt(2)*np.tan(x))))/np.pi**2
#print (2*np.pi*(integrate.quad(lambda x: f1(x)*np.sin(x),0,theta_r1)[0]+integrate.quad(lambda x: f2(x)*np.sin(x),theta_r1,theta_max)[0]))
j=0
i=[]
f_theta_int=[]
theta=[]
while j<=theta_max:
if j<=theta_r1:
f_theta_int.append(integrate.quad(lambda x: 2*np.pi*f1(x)*np.sin(x),0,j)[0])
theta.append(f1(j))
i.append(j)
else:
f_theta_int.append(integrate.quad(lambda x: 2*np.pi*f2(x)*np.sin(x),theta_r1,j)[0]+integrate.quad(lambda x: 2*np.pi*f1(x)*np.sin(x),0,theta_r1)[0])
theta.append(f2(j))
i.append(j)
j+=theta_max/10000.0
elif self.symmetry=="Ortho":
#orthorhombic
theta_max=np.pi/4
theta_0=np.arctan(1/np.sqrt(2))
phi_0=np.arctan(np.sqrt(2))
def f1(x):
return 3/np.pi
def f2(x):
return 6*(np.pi/2-2*np.arccos(1/(np.sqrt(3)*np.tan(x))))/np.pi**2
def f3(x):
return 6*(phi_0-np.arccos(1/(np.sqrt(3)*np.tan(x))))/np.pi**2
print (integrate.quad(lambda x: 2*np.pi*f3(x)*np.sin(x),theta_0,np.pi/4)[0]+\
integrate.quad(lambda x: 2*np.pi*f2(x)*np.sin(x),np.pi/6,theta_0)[0]+\
integrate.quad(lambda x: 2*np.pi*f1(x)*np.sin(x),0,np.pi/6)[0])
j=0
i=[]
f_theta_int=[]
theta=[]
while j<=theta_max:
if j<=np.pi/6:
f_theta_int.append(integrate.quad(lambda x: 2*np.pi*f1(x)*np.sin(x),0,j)[0])
theta.append(f1(j))
i.append(j)
elif j>np.pi/6 and j<=theta_0:
f_theta_int.append(integrate.quad(lambda x: 2*np.pi*f2(x)*np.sin(x),np.pi/6,j)[0]+\
integrate.quad(lambda x: 2*np.pi*f1(x)*np.sin(x),0,np.pi/6)[0])
theta.append(f2(j))
i.append(j)
elif j>theta_0 and j<=np.pi/4:
f_theta_int.append(integrate.quad(lambda x: 2*np.pi*f3(x)*np.sin(x),theta_0,j)[0]+\
integrate.quad(lambda x: 2*np.pi*f2(x)*np.sin(x),np.pi/6,theta_0)[0]+\
integrate.quad(lambda x: 2*np.pi*f1(x)*np.sin(x),0,np.pi/6)[0])
theta.append(f2(j))
i.append(j)
j+=theta_max/10000.0
ang_sel_points=[]
random_point=np.random.random_sample((1,int(np.prod(self.cube_dimentions))))[0]
for i in range(np.prod(self.cube_dimentions)):
for j in range(len(f_theta_int)-1):
if random_point[i]>=f_theta_int[j] and random_point[i]<f_theta_int[j+1]:
ang_sel_points.append(j)
break
ones=np.ones(np.prod(self.cube_dimentions))
ones[:np.prod(self.cube_dimentions)/2]=-1
random.shuffle(ones)
self.one=ones
self.theta=np.array(ang_sel_points)*theta_max*ones/10000.0
self.phi=np.random.random_sample((1,np.prod(self.cube_dimentions)))[0]*np.pi*2
self.psi=np.random.random_sample((1,np.prod(self.cube_dimentions)))[0]*np.pi*2
p_direction=np.array([np.sin(self.theta)*np.cos(self.phi),np.sin(self.theta)*np.sin(self.phi),np.cos(self.theta)]).T
p_direction=np.reshape(p_direction,(self.cube_dimentions[2],self.cube_dimentions[1],self.cube_dimentions[0],3))
eps0=[]
for i,j,k in zip(self.phi,self.theta,self.psi):
eps0.append(self.eps_t(i,j,k))
epsilon=np.reshape(np.asarray(eps0),(self.cube_dimentions[2],self.cube_dimentions[1],self.cube_dimentions[0],3,3))
print (np.mean(np.cos(self.theta)))
return p_direction, epsilon
def eps_t(self,phi,theta,psi):
e=np.matrix(self.eps)
m_phi=np.array([[np.cos(phi),np.sin(phi),0],[-np.sin(phi),np.cos(phi),0],[0,0,1]])
e_phi=np.dot(np.dot(m_phi,e),m_phi.T)
m_theta=np.array([[1,0,0],[0,np.cos(theta),np.sin(theta)],[0,-np.sin(theta),np.cos(theta)]])
e_theta_phi= np.dot(np.dot(m_theta,e_phi),m_theta.T)
m_psi=np.array([[np.cos(psi),np.sin(psi),0],[-np.sin(psi),np.cos(psi),0],[0,0,1]])
return np.dot(np.dot(m_psi,e_theta_phi),m_psi.T)