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
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
|
#!/usr/bin/env python
# -*- coding: utf-8 -*-
# Python GetFEM interface
#
# Copyright (C) 2018-2020 Konstantinos Poulios.
#
# This file is a part of GetFEM
#
# GetFEM is free software; you can redistribute it and/or modify it
# under the terms of the GNU Lesser General Public License as published
# by the Free Software Foundation; either version 2.1 of the License, or
# (at your option) any later version.
# This program is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
# or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
# License for more details.
# You should have received a copy of the GNU Lesser General Public License
# along with this program; if not, write to the Free Software Foundation,
# Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA.
#
############################################################################
import os
import numpy as np
import getfem as gf
np.set_printoptions(threshold=100000)
gf.util_trace_level(1)
# Input data
NX = 60 # number of elements in horizontal direction
NY = 60 # number of elements in verical direction
LX = 1. # [mm] Length
LY = 1. # [mm] Height
E = 210e3 # [N/mm^2]
nu = 0.3
Gc0 = 2.7e0 # [N/mm]
ll = 0.015 # [mm] length scale
strain_rate = 2e-4
init_time_step = 1.
steps = 100
#------------------------------------
geotrans = "GT_QK(2,2)" # geometric transformation
disp_fem_order = 2 # displacements finite element order
phi_fem_order = 2 # phase field finite element order
integration_degree = 5 # 9 gauss points per quad
#------------------------------------
NX = int(2*((NX+1)/2))
NY = int(2*((NY+1)/2))
resultspath = "./demo_phase_field_results"
if not os.path.exists(resultspath):
os.makedirs(resultspath)
# auxiliary constants
B_BOUNDARY = 4
T_BOUNDARY = 6
TB_BOUNDARY = 7
NX_seed1 = np.linspace(-1., 0., int(NX/3+1))
NX_seed2 = np.linspace(0., 1., int((NX-NX/3)+1))[1:]
NY_seed = np.linspace(-1., 1., NY+1)
X_seed1 = LX/2*(0.2*NX_seed1+0.8*np.sign(NX_seed1)*np.power(np.abs(NX_seed1),1.5))
X_seed2 = LX/2*(0.6*NX_seed2+0.4*np.sign(NX_seed2)*np.power(np.abs(NX_seed2),1.5))
X_seed = np.concatenate((X_seed1,X_seed2))
Y_seed = LY/2*(0.2*NY_seed+0.8*np.sign(NY_seed)*np.power(np.abs(NY_seed),1.5))
m1 = gf.Mesh("cartesian", X_seed, Y_seed[0:int(NY/2+1)])
m2 = gf.Mesh("cartesian", X_seed, Y_seed[int(NY/2):])
gap = 1e-5
pts = m1.pts()
for i in range(pts.shape[1]):
if pts[0,i] < -1e-10:
pts[1,i] -= gap/2*(1+pts[1,i]/(LY/2))
m1.set_pts(pts)
pts = m2.pts()
for i in range(pts.shape[1]):
if pts[0,i] < -1e-10:
pts[1,i] += gap/2*(1-pts[1,i]/(LY/2))
m2.set_pts(pts)
mesh = m1
mesh.merge(m2)
N = mesh.dim()
bottom_faces = mesh.outer_faces_in_box([-LX/2-1e-5,-LY/2-1e-5],[LX/2+1e-5,-LY/2+1e-5])
top_faces = mesh.outer_faces_in_box([-LX/2-1e-5,LY/2-1e-5],[LX/2+1e-5,LY/2+1e-5])
mesh.set_region(B_BOUNDARY, bottom_faces)
mesh.set_region(T_BOUNDARY, top_faces)
mesh.region_merge(TB_BOUNDARY, T_BOUNDARY)
mesh.region_merge(TB_BOUNDARY, B_BOUNDARY)
mesh.export_to_vtk("%s/mesh.vtk" % resultspath)
# FEM
mfu = gf.MeshFem(mesh, N)
mfu.set_classical_fem(disp_fem_order)
mfdir = mfu
mfphi = gf.MeshFem(mesh, 1)
mfphi.set_classical_fem(phi_fem_order)
mfout = gf.MeshFem(mesh)
mfout.set_classical_discontinuous_fem(2)
# Integration method
mim = gf.MeshIm(mesh, integration_degree)
mimd1 = gf.MeshImData(mim, -1)
# Model
md = gf.Model("real")
md.add_fem_variable("u", mfu) # displacements
md.add_fem_variable("phi", mfphi) # phase field
md.add_fem_data("u_stored", mfu)
md.add_fem_data("phi_stored", mfphi)
md.add_im_data("psi0_max", mimd1)
md.add_initialized_data("kappa", E/(3.*(1.-2.*nu)))
md.add_initialized_data("mu", E/(2*(1+nu)))
md.add_initialized_data("Gc0", Gc0)
md.add_initialized_data("l", ll)
md.add_macro("damage", "max(1e-7,sqr(1-phi))")
md.add_macro("psi0", "(0.5*kappa*sqr(Trace(Grad_u))+mu*Norm_sqr((Sym(Grad_u)-Trace(Grad_u)/3*Id(2))))")
md.add_macro("Gc", "Gc0")
_sigma_ = "damage*(kappa*Trace(Grad_u)*Id(2)+2*mu*(Sym(Grad_u)-Trace(Grad_u)/3*Id(2)))"
md.add_nonlinear_term(mim, _sigma_+":Grad_Test_u")
md.add_nonlinear_term(mim, "(-2*(1-phi)*max(psi0_max,psi0)*Test_phi+Gc*(phi/l*Test_phi+l*Grad_phi.Grad_Test_phi))")
md.add_initialized_data("MM", 0)
md.add_nonlinear_term(mim, "MM*((u-u_stored).Test_u+1e2*(phi-phi_stored)*Test_phi)")
# Load
md.add_fem_data("dirichlet_data", mfu);
ibdir = md.add_Dirichlet_condition_with_multipliers(mim, "u", mfdir, TB_BOUNDARY, "dirichlet_data")
dirmultname = md.mult_varname_Dirichlet(ibdir)
mass_mat = gf.asm_mass_matrix(mim, mfout)
print("Displacement dofs: %i" % mfu.nbdof())
print("Total model dofs: %i" % md.nbdof())
time_step = init_time_step
eps = 0.
pseudodynamic = False
MM = 0.
with open("%s/demo_phase_field_forces.dat" % resultspath, "w") as f:
for step in range(steps):
eps_old = eps
while True:
if step > 0:
eps = eps_old + strain_rate*time_step
X = md.from_variables()
print("Step %i with eps=%e" % (step, eps))
md.set_variable("dirichlet_data", md.interpolation("{eps}*[0;X(2)]".format(eps=eps), mfu, -1))
if pseudodynamic:
print("With damping %e" % MM)
md.set_variable("MM",[MM])
iters = 20
try:
nit = \
md.solve("noisy", "lsolver", "mumps", "max_iter", iters, "max_res", 1e-7, #)[0]
"lsearch", "simplest", "alpha max ratio", 1.5, "alpha min", 0.4, "alpha mult", 0.6,
"alpha threshold res", 2)[0]
except (KeyboardInterrupt, SystemExit):
raise
except:
nit = iters
if nit >= iters:
if step == 0:
break
md.to_variables(X)
eps = eps_old
if time_step > init_time_step/50.:
time_step *= 0.5
else:
if pseudodynamic:
MM *= 100.
else:
pseudodynamic = True
MM = 10000.
else:
md.set_variable("u_stored", md.variable("u"))
md.set_variable("phi_stored", md.variable("phi"))
if pseudodynamic:
if MM < 1e-4:
MM = 0.
pseudodynamic = False
elif nit <= 6:
MM /= 2.
else:
TMP = md.interpolation("max(psi0_max,psi0)", mimd1, -1)
md.set_variable("psi0_max", TMP)
break
out = (mfu, md.variable("u"), "Displacements",
mfphi, md.variable("phi"), "phi")
for i,j in [[1,1],[2,2],[1,2]]:
sigma = gf.asm_generic(mim, 1, "{sigma}({i},{j})*Test_t".format(sigma=_sigma_, i=i, j=j),
-1, md, "t", True, mfout, np.zeros(mfout.nbdof()))\
[md.nbdof():]
sigma = np.transpose(gf.linsolve_mumps(mass_mat, sigma))
out += (mfout, sigma, "Cauchy Stress {i}{j}".format(i=i, j=j))
mfout.export_to_vtk("%s/demo_phase_field_%i.vtk" % (resultspath, step), *out)
DIRMULT = -md.variable(dirmultname)
DIRMULT = np.reshape(DIRMULT,[1,DIRMULT.size])
dfT = gf.asm_boundary_source(T_BOUNDARY, mim, mfu, md.mesh_fem_of_variable(dirmultname), DIRMULT)
f.write(("step=%i eps=%e fR=(%e,%e)\n") %
(step, eps, dfT[0::N].sum(), dfT[1::N].sum()))
f.flush()
|
