Note

Go to the end to download the full example code.

LShape#

Damage simulation for a L-part.

LShape
  • $\phi$
  • TRI3: Ne = 4234, Nn = 2178
  • Boundary conditions
  • LShape
  • LShape
  • Summary
/home/docs/checkouts/readthedocs.org/user_builds/easyfea/checkouts/v1.7.0/examples/PhaseField/results/LShape2D/Test/Miehe_AT1_CP_optimMesh nL=50   1 : 0.000 mm, [0.00e+00; 0.00e+00], 1:0.142 s, tol=0.00e+00
   2 : 0.040 mm, [0.00e+00; 0.00e+00], 1:0.122 s, tol=1.00e+00  4.00 % -> 2.93 s
   3 : 0.080 mm, [0.00e+00; 0.00e+00], 1:0.123 s, tol=9.95e-01  8.00 % -> 2.83 s
   4 : 0.120 mm, [0.00e+00; 0.00e+00], 1:0.123 s, tol=5.56e-01  12.00 % -> 2.71 s
   5 : 0.160 mm, [0.00e+00; 0.00e+00], 1:0.127 s, tol=4.38e-01  16.00 % -> 2.66 s
   6 : 0.200 mm, [0.00e+00; 0.00e+00], 1:0.128 s, tol=3.60e-01  20.00 % -> 2.56 s
   7 : 0.240 mm, [0.00e+00; 0.00e+00], 1:0.122 s, tol=3.06e-01  24.00 % -> 2.32 s
   8 : 0.280 mm, [0.00e+00; 8.98e-03], 1:0.137 s, tol=2.65e-01  28.00 % -> 2.46 s
   9 : 0.320 mm, [0.00e+00; 4.57e-02], 1:0.131 s, tol=2.32e-01  32.00 % -> 2.22 s
  10 : 0.360 mm, [0.00e+00; 1.10e-01], 1:0.125 s, tol=2.07e-01  36.00 % -> 2.00 s
  11 : 0.400 mm, [0.00e+00; 2.07e-01], 1:0.121 s, tol=1.86e-01  40.00 % -> 1.82 s
  12 : 0.440 mm, [0.00e+00; 3.48e-01], 1:0.121 s, tol=1.69e-01  44.00 % -> 1.69 s
  13 : 0.480 mm, [0.00e+00; 5.46e-01], 1:0.121 s, tol=1.55e-01  48.00 % -> 1.57 s
  14 : 0.520 mm, [0.00e+00; 7.78e-01], 1:0.122 s, tol=1.62e-01  52.00 % -> 1.46 s
  15 : 0.540 mm, [0.00e+00; 9.48e-01], 1:0.120 s, tol=2.22e-01  54.00 % -> 1.43 s
  16 : 0.560 mm, [0.00e+00; 9.93e-01], 1:0.123 s, tol=3.80e-01  56.00 % -> 1.44 s
  17 : 0.580 mm, [0.00e+00; 1.00e+00], 1:0.120 s, tol=4.44e-01  58.00 % -> 1.39 s
  18 : 0.600 mm, [0.00e+00; 1.00e+00], 1:0.122 s, tol=3.82e-01  60.00 % -> 1.38 s
  19 : 0.620 mm, [0.00e+00; 1.00e+00], 1:0.122 s, tol=3.28e-01  62.00 % -> 1.35 s
  20 : 0.640 mm, [0.00e+00; 1.00e+00], 1:0.122 s, tol=2.91e-01  64.00 % -> 1.30 s
  21 : 0.660 mm, [0.00e+00; 1.00e+00], 1:0.127 s, tol=2.78e-01  66.00 % -> 1.30 s
  22 : 0.680 mm, [0.00e+00; 1.00e+00], 1:0.129 s, tol=2.54e-01  68.00 % -> 1.27 s
  23 : 0.700 mm, [0.00e+00; 1.00e+00], 1:0.125 s, tol=2.53e-01  70.00 % -> 1.18 s
  24 : 0.720 mm, [0.00e+00; 1.00e+00], 1:0.129 s, tol=2.02e-01  72.00 % -> 1.15 s
  25 : 0.740 mm, [0.00e+00; 1.00e+00], 1:0.131 s, tol=1.76e-01  74.00 % -> 1.11 s
  26 : 0.760 mm, [0.00e+00; 1.00e+00], 1:0.128 s, tol=1.87e-01  76.00 % -> 1.01 s
  27 : 0.780 mm, [0.00e+00; 1.00e+00], 1:0.134 s, tol=1.72e-01  78.00 % -> 981.43 ms
  28 : 0.800 mm, [0.00e+00; 1.00e+00], 1:0.127 s, tol=1.65e-01  80.00 % -> 859.46 ms
  29 : 0.820 mm, [0.00e+00; 1.00e+00], 1:0.128 s, tol=1.90e-01  82.00 % -> 788.69 ms
  30 : 0.840 mm, [0.00e+00; 1.00e+00], 1:0.128 s, tol=1.65e-01  84.00 % -> 706.82 ms
  31 : 0.860 mm, [0.00e+00; 1.00e+00], 1:0.138 s, tol=1.51e-01  86.00 % -> 672.21 ms
  32 : 0.880 mm, [0.00e+00; 1.00e+00], 1:0.133 s, tol=1.15e-01  88.00 % -> 561.70 ms
  33 : 0.900 mm, [0.00e+00; 1.00e+00], 1:0.125 s, tol=1.10e-01  90.00 % -> 444.21 ms
  34 : 0.920 mm, [0.00e+00; 1.00e+00], 1:0.134 s, tol=9.93e-02  92.00 % -> 383.12 ms
  35 : 0.940 mm, [0.00e+00; 1.00e+00], 1:0.132 s, tol=9.94e-02  94.00 % -> 285.94 ms
  36 : 0.960 mm, [0.00e+00; 1.00e+00], 1:0.135 s, tol=9.12e-02  96.00 % -> 196.58 ms
  37 : 0.980 mm, [0.00e+00; 1.00e+00], 1:0.137 s, tol=1.02e-01  98.00 % -> 100.79 ms
  38 : 1.000 mm, [0.00e+00; 1.00e+00], 1:0.137 s, tol=9.35e-02  100.00 % -> -0.00 µs
Saved:
/home/docs/checkouts/readthedocs.org/user_builds/easyfea/checkouts/v1.7.0/examples/PhaseField/results/LShape2D/Test/Miehe_AT1_CP_optimMesh nL=50/force-displacement.pickle
Saved:
/home/docs/checkouts/readthedocs.org/user_builds/easyfea/checkouts/v1.7.0/examples/PhaseField/results/LShape2D/Test/Miehe_AT1_CP_optimMesh nL=50/simulation.pickle
Saved:
/home/docs/checkouts/readthedocs.org/user_builds/easyfea/checkouts/v1.7.0/examples/PhaseField/results/LShape2D/Test/Miehe_AT1_CP_optimMesh nL=50/summary.txt
Loaded:
/home/docs/checkouts/readthedocs.org/user_builds/easyfea/checkouts/v1.7.0/examples/PhaseField/results/LShape2D/Test/Miehe_AT1_CP_optimMesh nL=50/force-displacement.pickle

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 12 from EasyFEA import (
 13     Display,
 14     Folder,
 15     Models,
 16     plt,
 17     np,
 18     Tic,
 19     ElemType,
 20     Simulations,
 21     Paraview,
 22     PyVista,
 23 )
 24 from EasyFEA.Geoms import Point, Points, Domain, Circle
 25
 26 if __name__ == "__main__":
 27     Display.Clear()
 28
 29     # ----------------------------------------------
 30     # Configuration
 31     # ----------------------------------------------
 32
 33     # simu options
 34     doSimu = True
 35     meshTest = True
 36     optimMesh = True
 37
 38     # outputs
 39     folder = Folder.Results_Dir()
 40     pltIter = False
 41     pltLoad = False
 42     makeMovie = True
 43     makeParaview = False
 44
 45     # geom
 46     dim = 2
 47     L = 250  # mm
 48     nL = 50
 49     ep = 100
 50
 51     # model
 52     E = 2e4  # MPa
 53     v = 0.18
 54
 55     split = "Miehe"
 56     regu = "AT1"
 57     Gc = 130  # J/m2
 58     Gc *= 1000 / 1e6  # mJ/mm2
 59
 60     # convergence
 61     tolConv = 1e-0
 62     convOption = 2
 63
 64     # load
 65     uMax = 1  # mm
 66     inc0 = uMax / 25
 67     inc1 = inc0 / 2
 68
 69     config = f"""
 70     uMax = {uMax}
 71
 72     inc0 = {inc0}
 73     inc1 = {inc1}
 74
 75     while ud <= uMax:
 76
 77     ud += inc0 if simu.damage.max() < 0.6 else inc1
 78
 79     simu.add_dirichlet(nodes_circle, [0], ['d'], "damage")
 80     simu.add_dirichlet(nodes_y0, [0]*dim, simu.Get_dofs())
 81     simu.add_dirichlet(nodes_load, [ud], ['y'])
 82     """
 83
 84     # ----------------------------------------------
 85     # Mesh
 86     # ----------------------------------------------
 87     l0 = L / nL
 88
 89     if meshTest:
 90         hC = l0
 91     else:
 92         hC = 0.5
 93         # hC = 0.25
 94
 95     p1 = Point()
 96     p2 = Point(L, 0)
 97     p3 = Point(L, L)
 98     p4 = Point(2 * L - 30, L)
 99     p5 = Point(2 * L, L)
100     p6 = Point(2 * L, 2 * L)
101     p7 = Point(0, 2 * L)
102     if optimMesh:
103         # hauteur zone rafinée
104         h = 100
105         refineDomain = Domain(Point(0, L - h / 3), Point(L + h / 3, L + h), hC)
106         hD = hC * 5
107     else:
108         refineDomain = None
109         hD = hC
110
111     contour = Points([p1, p2, p3, p4, p5, p6, p7], hD)
112
113     circle = Circle(p5, 100)
114
115     if dim == 2:
116         mesh = contour.Mesh_2D([], ElemType.TRI3, refineGeoms=[refineDomain])
117     else:
118         mesh = contour.Mesh_Extrude(
119             [], [0, 0, -ep], [3], ElemType.HEXA8, refineGeoms=[refineDomain]
120         )
121
122     # Display.Plot_Mesh(mesh)
123     # Display.Plot_Tags(mesh)
124     # from EasyFEA import PyVista
125     # PyVista.Plot_Mesh(mesh).show()
126
127     nodes_y0 = mesh.Nodes_Conditions(lambda x, y, z: y == 0)
128     nodes_load = mesh.Nodes_Conditions(lambda x, y, z: (y == L) & (x >= 2 * L - 30))
129     node3 = mesh.Nodes_Point(p3)
130     node4 = mesh.Nodes_Point(p4)
131     nodes_circle = mesh.Nodes_Cylinder(circle, [0, 0, ep])
132     nodes_edges = mesh.Nodes_Conditions(lambda x, y, z: (x == 0) | (y == 0))
133
134     # ----------------------------------------------
135     # Simulation
136     # ----------------------------------------------
137     material = Models.Elastic.Isotropic(dim, E, v, True, ep)
138     pfm = Models.PhaseField(material, split, regu, Gc, l0)
139
140     folder_save = Simulations.PhaseField.Folder(
141         f"{folder}{dim}D",
142         "",
143         pfm.split,
144         pfm.regularization,
145         "CP",
146         tolConv,
147         "",
148         meshTest,
149         optimMesh,
150         nL=nL,
151     )
152
153     Display.MyPrint(folder_save, "green")
154
155     if doSimu:
156         simu = Simulations.PhaseField(mesh, pfm)
157         simu.Results_Set_Bc_Summary(config)
158
159         dofsY_load = simu.Bc_dofs_nodes(nodes_load, ["y"])
160
161         if pltIter:
162             axIter = Display.Plot_Result(simu, "damage")
163
164             axLoad = Display.Init_Axes()
165             axLoad.set_xlabel("displacement [mm]")
166             axLoad.set_ylabel("load [kN]")
167
168         displacement = []
169         force = []
170         ud = -inc0
171         iter = -1
172
173         while ud <= uMax:
174             # update displacement
175             iter += 1
176             ud += inc0 if simu.damage.max() < 0.6 else inc1
177
178             # update boundary conditions
179             simu.Bc_Init()
180             simu.add_dirichlet(nodes_circle, [0], ["d"], "damage")
181             simu.add_dirichlet(nodes_y0, [0] * dim, simu.Get_unknowns())
182             simu.add_dirichlet(nodes_load, [ud], ["y"])
183
184             # solve
185             u, d, Ku, convergence = simu.Solve(tolConv, 500, convOption)
186             # calc load
187             fr = np.sum(Ku[dofsY_load, :] @ u)
188
189             # saves load and displacement
190             displacement.append(ud)
191             force.append(fr)
192
193             # print iter
194             simu.Results_Set_Iteration_Summary(iter, ud, "mm", ud / uMax, True)
195
196             # saves iteration
197             simu.Save_Iter()
198
199             if pltIter:
200                 plt.figure(axIter.figure)
201                 Display.Plot_Result(simu, "damage", ax=axIter)
202                 plt.pause(1e-12)
203
204                 plt.figure(axLoad.figure)
205                 axLoad.scatter(ud, fr / 1000, c="black")
206                 plt.pause(1e-12)
207
208             if not convergence or np.max(d[nodes_edges]) >= 1:
209                 # stops simulation if damage occurs on edges or convergence has not been reached
210                 break
211
212         # saves load and displacement
213         displacement = np.asarray(displacement)
214         force = np.asarray(force)
215         Simulations.Save_pickle(
216             (force, displacement), folder_save, "force-displacement"
217         )
218
219         # saves the simulation
220         simu.Save(folder_save)
221
222     else:
223         simu = Simulations.Load_Simu(folder_save)
224         mesh = simu.mesh
225
226     force, displacement = Simulations.Load_pickle(folder_save, "force-displacement")
227
228     # ----------------------------------------------
229     # Results
230     # ----------------------------------------------
231     Display.Plot_Result(simu, "damage", folder=folder_save)
232     Display.Plot_Mesh(simu)
233     Display.Plot_BoundaryConditions(simu)
234
235     axLoad = Display.Init_Axes()
236     axLoad.set_xlabel("displacement [mm]")
237     axLoad.set_ylabel("load [kN]")
238     axLoad.plot(displacement, force / 1000, c="blue")
239     Display.Save_fig(folder_save, "forcedep")
240
241     Display.Plot_Iter_Summary(simu, folder_save)
242
243     if makeMovie:
244         simu.Set_Iter(-1)
245         depMax = simu.Result("displacement_norm").max()
246         deformFactor = L * 0.05 / depMax
247
248         iterations = np.arange(0, simu.Niter, simu.Niter // 20)
249
250         def Func(plotter, iter):
251             simu.Set_Iter(iterations[iter])
252
253             grid = PyVista._pvMesh(simu, "damage", deformFactor)
254
255             tresh = grid.threshold((0, 0.8))
256
257             PyVista.Plot(
258                 tresh,
259                 "damage",
260                 deformFactor,
261                 plotMesh=True,
262                 plotter=plotter,
263                 clim=(0, 1),
264             )
265
266         PyVista.Movie_func(Func, iterations.size, folder_save, "damage.gif")
267
268     if makeParaview:
269         Paraview.Save_simu(simu, folder_save)
270
271     if doSimu:
272         Tic.Plot_History(folder_save, False)
273
274     plt.show()

Total running time of the script: (0 minutes 14.083 seconds)

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