.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/PhaseField/Tension.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_examples_PhaseField_Tension.py: Tension ======= Damage simulation for a plate subjected to tension. .. GENERATED FROM PYTHON SOURCE LINES 12-287 .. image-sg:: /examples/PhaseField/images/sphx_glr_Tension_001.gif :alt: Tension :srcset: /examples/PhaseField/images/sphx_glr_Tension_001.gif :class: sphx-glr-single-img .. rst-class:: sphx-glr-horizontal * .. image-sg:: /examples/PhaseField/images/sphx_glr_Tension_002.png :alt: $\phi$ :srcset: /examples/PhaseField/images/sphx_glr_Tension_002.png :class: sphx-glr-multi-img * .. image-sg:: /examples/PhaseField/images/sphx_glr_Tension_003.png :alt: TRI3: Ne = 2059, Nn = 1100 :srcset: /examples/PhaseField/images/sphx_glr_Tension_003.png :class: sphx-glr-multi-img * .. image-sg:: /examples/PhaseField/images/sphx_glr_Tension_004.png :alt: Tension :srcset: /examples/PhaseField/images/sphx_glr_Tension_004.png :class: sphx-glr-multi-img * .. image-sg:: /examples/PhaseField/images/sphx_glr_Tension_005.png :alt: Boundary conditions :srcset: /examples/PhaseField/images/sphx_glr_Tension_005.png :class: sphx-glr-multi-img * .. image-sg:: /examples/PhaseField/images/sphx_glr_Tension_006.png :alt: Summary :srcset: /examples/PhaseField/images/sphx_glr_Tension_006.png :class: sphx-glr-multi-img .. rst-class:: sphx-glr-script-out .. code-block:: none /home/docs/checkouts/readthedocs.org/user_builds/easyfea/checkouts/stable/examples/PhaseField/results/Tension2D/Test/Bourdin_AT1_optimMesh 1: 0.000µm, [0.00e+00;0.00e+00], 1:0.026s, tol=0.00e+00 2: 0.100µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 3: 0.200µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 4: 0.300µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 5: 0.400µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 6: 0.500µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 7: 0.600µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 8: 0.700µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 9: 0.800µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 10: 0.900µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 11: 1.000µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 12: 1.100µm, 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[0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 152: 5.200µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 153: 5.210µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 154: 5.220µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 155: 5.230µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 156: 5.240µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 157: 5.250µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 158: 5.260µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 159: 5.270µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 160: 5.280µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 161: 5.290µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 162: 5.300µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 163: 5.310µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 164: 5.320µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 165: 5.330µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 166: 5.340µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 167: 5.350µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 168: 5.360µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 169: 5.370µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 170: 5.380µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 171: 5.390µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 172: 5.400µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 173: 5.410µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 174: 5.420µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 175: 5.430µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 176: 5.440µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 177: 5.450µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 178: 5.460µm, [0.00e+00;0.00e+00], 1:0.019s, tol=0.00e+00 179: 5.470µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 180: 5.480µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 181: 5.490µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 182: 5.500µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 183: 5.510µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 184: 5.520µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 185: 5.530µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 186: 5.540µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 187: 5.550µm, [0.00e+00;0.00e+00], 1:0.019s, tol=0.00e+00 188: 5.560µm, [0.00e+00;0.00e+00], 1:0.018s, tol=0.00e+00 189: 5.570µm, [4.09e-12;1.37e-04], 1:0.018s, tol=1.00e+00 190: 5.580µm, [1.61e-11;5.60e-04], 1:0.018s, tol=9.40e-01 191: 5.590µm, [2.90e-11;1.05e-03], 1:0.018s, tol=7.15e-01 192: 5.600µm, [7.15e-11;1.70e-03], 1:0.018s, tol=6.51e-01 193: 5.610µm, [1.24e-10;2.64e-03], 1:0.018s, tol=5.57e-01 194: 5.620µm, [1.76e-10;3.63e-03], 1:0.018s, tol=4.58e-01 195: 5.630µm, [2.25e-10;4.62e-03], 1:0.018s, tol=3.80e-01 196: 5.640µm, [2.71e-10;5.62e-03], 1:0.018s, tol=3.22e-01 197: 5.650µm, [3.13e-10;6.62e-03], 1:0.018s, tol=2.79e-01 198: 5.660µm, [3.50e-10;7.62e-03], 1:0.018s, tol=2.46e-01 199: 5.670µm, [3.80e-10;8.62e-03], 1:0.018s, tol=2.19e-01 200: 5.680µm, [4.08e-10;9.62e-03], 1:0.018s, tol=1.98e-01 201: 5.690µm, [4.33e-10;1.06e-02], 1:0.018s, tol=1.80e-01 202: 5.700µm, [4.56e-10;1.16e-02], 1:0.018s, tol=1.66e-01 203: 5.710µm, [4.77e-10;1.26e-02], 1:0.018s, tol=1.53e-01 204: 5.720µm, [4.96e-10;1.36e-02], 1:0.018s, tol=1.42e-01 205: 5.730µm, [5.14e-10;1.46e-02], 1:0.018s, tol=1.33e-01 206: 5.740µm, [5.29e-10;1.56e-02], 1:0.018s, tol=1.25e-01 207: 5.750µm, [5.43e-10;1.65e-02], 1:0.018s, tol=1.18e-01 208: 5.760µm, [5.55e-10;1.75e-02], 1:0.018s, tol=1.11e-01 209: 5.770µm, [5.66e-10;1.85e-02], 1:0.018s, tol=1.05e-01 210: 5.780µm, [5.75e-10;1.95e-02], 1:0.018s, tol=1.00e-01 211: 5.790µm, [5.83e-10;2.05e-02], 1:0.018s, tol=9.55e-02 212: 5.800µm, [5.90e-10;2.15e-02], 1:0.019s, tol=9.13e-02 213: 5.810µm, [5.95e-10;2.24e-02], 1:0.019s, tol=8.73e-02 214: 5.820µm, [6.00e-10;2.34e-02], 1:0.018s, tol=8.38e-02 215: 5.830µm, [6.03e-10;2.44e-02], 1:0.018s, tol=8.05e-02 216: 5.840µm, [6.06e-10;2.54e-02], 1:0.018s, tol=7.74e-02 217: 5.850µm, [6.07e-10;2.63e-02], 1:0.018s, tol=7.46e-02 218: 5.860µm, [6.08e-10;2.73e-02], 1:0.018s, tol=7.20e-02 219: 5.870µm, [6.08e-10;2.83e-02], 1:0.018s, tol=6.95e-02 220: 5.880µm, [6.07e-10;2.92e-02], 1:0.018s, tol=6.72e-02 221: 5.890µm, [6.06e-10;3.02e-02], 1:0.019s, tol=6.51e-02 222: 5.900µm, [6.04e-10;3.12e-02], 1:0.018s, tol=6.31e-02 223: 5.910µm, [6.01e-10;3.21e-02], 1:0.018s, tol=6.12e-02 224: 5.920µm, [5.98e-10;3.31e-02], 1:0.018s, tol=5.94e-02 225: 5.930µm, [5.94e-10;3.40e-02], 1:0.018s, tol=5.78e-02 226: 5.940µm, [5.90e-10;3.50e-02], 1:0.019s, tol=5.62e-02 227: 5.950µm, [5.85e-10;3.60e-02], 1:0.019s, tol=5.47e-02 228: 5.960µm, [5.80e-10;3.69e-02], 1:0.019s, tol=5.33e-02 229: 5.970µm, [5.75e-10;3.79e-02], 1:0.019s, tol=5.19e-02 230: 5.980µm, [5.69e-10;3.88e-02], 1:0.018s, tol=5.07e-02 231: 5.990µm, [5.63e-10;3.98e-02], 1:0.018s, tol=4.94e-02 232: 6.000µm, [5.56e-10;4.07e-02], 1:0.018s, tol=4.83e-02 233: 6.010µm, [5.50e-10;4.17e-02], 1:0.018s, tol=4.72e-02 234: 6.020µm, [5.43e-10;4.26e-02], 1:0.018s, tol=4.61e-02 235: 6.030µm, [5.36e-10;4.36e-02], 1:0.018s, tol=4.51e-02 236: 6.040µm, [5.29e-10;4.45e-02], 1:0.018s, tol=4.42e-02 237: 6.050µm, [5.21e-10;4.54e-02], 1:0.018s, tol=4.32e-02 238: 6.060µm, [5.14e-10;4.64e-02], 1:0.018s, tol=4.24e-02 239: 6.070µm, [5.06e-10;4.73e-02], 1:0.018s, tol=4.15e-02 240: 6.080µm, [4.98e-10;4.82e-02], 1:0.018s, tol=4.07e-02 241: 6.090µm, [4.91e-10;4.92e-02], 1:0.018s, tol=3.99e-02 242: 6.100µm, [4.83e-10;5.01e-02], 1:0.018s, tol=3.92e-02 243: 6.110µm, [4.75e-10;5.11e-02], 1:0.018s, tol=3.84e-02 244: 6.120µm, [4.67e-10;5.20e-02], 1:0.018s, tol=3.77e-02 245: 6.130µm, [4.59e-10;5.29e-02], 1:0.018s, tol=3.71e-02 246: 6.140µm, [4.51e-10;5.38e-02], 1:0.018s, tol=3.64e-02 247: 6.150µm, [4.43e-10;5.48e-02], 1:0.018s, tol=3.58e-02 248: 6.160µm, [4.34e-10;5.57e-02], 1:0.018s, tol=3.52e-02 249: 6.170µm, [4.26e-10;5.66e-02], 1:0.018s, tol=3.46e-02 250: 6.180µm, [4.18e-10;5.75e-02], 1:0.018s, tol=3.40e-02 251: 6.190µm, [4.10e-10;5.85e-02], 1:0.018s, tol=3.35e-02 252: 6.200µm, [4.02e-10;5.94e-02], 1:0.018s, tol=3.30e-02 253: 6.210µm, [3.94e-10;6.03e-02], 1:0.018s, tol=3.24e-02 254: 6.220µm, [3.86e-10;6.12e-02], 1:0.018s, tol=3.20e-02 255: 6.230µm, [3.79e-10;6.21e-02], 1:0.018s, tol=3.15e-02 256: 6.240µm, [3.71e-10;6.30e-02], 1:0.018s, tol=3.10e-02 257: 6.250µm, [3.63e-10;6.39e-02], 1:0.018s, tol=3.06e-02 258: 6.260µm, [3.55e-10;6.49e-02], 1:0.018s, tol=3.01e-02 259: 6.270µm, [3.48e-10;6.58e-02], 1:0.018s, tol=2.97e-02 260: 6.280µm, [3.42e-10;6.70e-02], 1:0.018s, tol=3.85e-02 261: 6.290µm, [3.37e-10;6.85e-02], 1:0.018s, tol=4.46e-02 262: 6.300µm, [3.32e-10;7.02e-02], 1:0.018s, tol=4.71e-02 263: 6.310µm, [3.29e-10;7.20e-02], 1:0.018s, tol=5.24e-02 264: 6.320µm, [3.26e-10;7.40e-02], 1:0.018s, tol=5.68e-02 265: 6.330µm, [3.23e-10;7.61e-02], 1:0.018s, tol=5.91e-02 266: 6.340µm, [3.20e-10;7.83e-02], 1:0.018s, tol=5.98e-02 267: 6.350µm, [3.17e-10;8.05e-02], 1:0.018s, tol=5.97e-02 268: 6.360µm, [3.14e-10;8.28e-02], 1:0.018s, tol=5.91e-02 269: 6.370µm, [3.11e-10;8.51e-02], 1:0.018s, tol=5.82e-02 270: 6.380µm, [3.08e-10;8.74e-02], 1:0.018s, tol=5.71e-02 271: 6.390µm, [3.04e-10;8.97e-02], 1:0.018s, tol=5.60e-02 272: 6.400µm, [3.01e-10;9.20e-02], 1:0.018s, tol=5.49e-02 273: 6.410µm, [2.97e-10;9.43e-02], 1:0.018s, tol=5.38e-02 274: 6.420µm, [2.93e-10;9.66e-02], 1:0.018s, tol=5.27e-02 275: 6.430µm, [2.89e-10;9.89e-02], 1:0.018s, tol=5.16e-02 276: 6.440µm, [2.85e-10;1.01e-01], 1:0.018s, tol=5.06e-02 277: 6.450µm, [2.81e-10;1.03e-01], 1:0.018s, tol=4.96e-02 278: 6.460µm, [2.77e-10;1.06e-01], 1:0.018s, tol=4.86e-02 279: 6.470µm, [2.73e-10;1.08e-01], 1:0.018s, tol=4.77e-02 280: 6.480µm, [2.69e-10;1.10e-01], 1:0.018s, tol=4.68e-02 281: 6.490µm, [2.64e-10;1.13e-01], 1:0.018s, tol=4.60e-02 282: 6.500µm, [2.60e-10;1.15e-01], 1:0.018s, tol=4.52e-02 283: 6.510µm, [2.55e-10;1.17e-01], 1:0.019s, tol=4.44e-02 284: 6.520µm, [2.54e-10;1.20e-01], 1:0.019s, tol=5.01e-02 285: 6.530µm, [2.53e-10;1.23e-01], 1:0.018s, tol=5.34e-02 286: 6.540µm, [2.52e-10;1.26e-01], 1:0.018s, tol=5.49e-02 287: 6.550µm, [2.52e-10;1.30e-01], 1:0.019s, tol=5.53e-02 288: 6.560µm, [2.52e-10;1.33e-01], 1:0.018s, tol=5.51e-02 289: 6.570µm, [2.51e-10;1.37e-01], 1:0.018s, tol=5.53e-02 290: 6.580µm, [2.52e-10;1.41e-01], 1:0.018s, tol=6.30e-02 291: 6.590µm, [2.54e-10;1.46e-01], 1:0.018s, tol=6.97e-02 292: 6.600µm, [2.57e-10;1.52e-01], 1:0.019s, tol=7.45e-02 293: 6.610µm, [2.60e-10;1.58e-01], 1:0.018s, tol=7.76e-02 294: 6.620µm, [2.64e-10;1.64e-01], 1:0.018s, tol=7.95e-02 295: 6.630µm, [2.68e-10;1.71e-01], 1:0.018s, tol=8.06e-02 296: 6.640µm, [2.71e-10;1.78e-01], 1:0.018s, tol=8.09e-02 297: 6.650µm, [2.71e-10;1.85e-01], 1:0.020s, tol=8.08e-02 298: 6.660µm, [2.69e-10;1.92e-01], 1:0.019s, tol=8.04e-02 299: 6.670µm, [2.67e-10;2.00e-01], 1:0.019s, tol=7.97e-02 300: 6.680µm, [2.66e-10;2.08e-01], 1:0.018s, tol=7.89e-02 301: 6.690µm, [2.64e-10;2.16e-01], 1:0.018s, tol=7.79e-02 302: 6.700µm, [2.61e-10;2.24e-01], 1:0.019s, tol=7.70e-02 303: 6.710µm, [2.59e-10;2.32e-01], 1:0.019s, tol=7.60e-02 304: 6.720µm, [2.57e-10;2.40e-01], 1:0.018s, tol=7.50e-02 305: 6.730µm, [2.54e-10;2.48e-01], 1:0.018s, tol=7.40e-02 306: 6.740µm, [2.52e-10;2.57e-01], 1:0.018s, tol=7.31e-02 307: 6.750µm, [2.49e-10;2.66e-01], 1:0.018s, tol=7.22e-02 308: 6.760µm, [2.46e-10;2.74e-01], 1:0.018s, tol=7.13e-02 309: 6.770µm, [2.43e-10;2.83e-01], 1:0.018s, tol=7.06e-02 310: 6.780µm, [2.40e-10;2.92e-01], 1:0.018s, tol=6.99e-02 311: 6.790µm, [2.36e-10;3.01e-01], 1:0.018s, tol=6.92e-02 312: 6.800µm, [2.33e-10;3.11e-01], 1:0.018s, tol=6.86e-02 313: 6.810µm, [2.32e-10;3.21e-01], 1:0.018s, tol=7.33e-02 314: 6.820µm, [2.32e-10;3.32e-01], 1:0.018s, tol=7.88e-02 315: 6.830µm, [2.34e-10;3.45e-01], 1:0.018s, tol=8.37e-02 316: 6.840µm, [2.36e-10;3.58e-01], 1:0.019s, tol=8.81e-02 317: 6.850µm, [2.39e-10;3.73e-01], 1:0.019s, tol=9.20e-02 318: 6.860µm, [2.42e-10;3.89e-01], 1:0.019s, tol=9.54e-02 319: 6.870µm, [2.46e-10;4.05e-01], 1:0.019s, tol=9.84e-02 320: 6.880µm, [2.50e-10;4.23e-01], 1:0.018s, tol=1.01e-01 321: 6.890µm, [2.54e-10;4.41e-01], 1:0.018s, tol=1.03e-01 322: 6.900µm, [2.58e-10;4.61e-01], 1:0.018s, tol=1.05e-01 323: 6.910µm, [2.62e-10;4.81e-01], 1:0.018s, tol=1.07e-01 324: 6.920µm, [2.66e-10;5.02e-01], 1:0.018s, tol=1.09e-01 325: 6.930µm, [2.70e-10;5.24e-01], 1:0.019s, tol=1.11e-01 326: 6.940µm, [2.74e-10;5.47e-01], 1:0.018s, tol=1.12e-01 327: 6.950µm, [2.77e-10;5.71e-01], 1:0.018s, tol=1.13e-01 328: 6.960µm, [2.80e-10;5.94e-01], 1:0.018s, tol=1.13e-01 329: 6.970µm, [2.82e-10;6.19e-01], 1:0.018s, tol=1.15e-01 330: 6.980µm, [2.84e-10;6.44e-01], 1:0.019s, tol=1.25e-01 331: 6.990µm, [2.85e-10;6.72e-01], 1:0.019s, tol=1.44e-01 332: 7.000µm, [2.88e-10;7.04e-01], 1:0.019s, tol=1.74e-01 333: 7.010µm, [2.89e-10;7.42e-01], 1:0.018s, tol=2.14e-01 334: 7.020µm, [2.90e-10;7.85e-01], 1:0.018s, tol=2.74e-01 335: 7.030µm, [2.89e-10;8.36e-01], 1:0.018s, tol=3.58e-01 336: 7.040µm, [2.89e-10;8.94e-01], 1:0.018s, tol=4.44e-01 337: 7.050µm, [2.90e-10;9.46e-01], 1:0.018s, tol=4.77e-01 338: 7.060µm, [2.94e-10;9.78e-01], 1:0.019s, tol=4.26e-01 339: 7.070µm, [2.98e-10;9.89e-01], 1:0.018s, tol=3.22e-01 340: 7.080µm, [2.99e-10;9.90e-01], 1:0.018s, tol=2.43e-01 341: 7.090µm, [2.99e-10;9.90e-01], 1:0.018s, tol=2.10e-01 342: 7.100µm, [3.01e-10;9.93e-01], 1:0.018s, tol=1.79e-01 343: 7.110µm, [3.03e-10;9.95e-01], 1:0.018s, tol=1.49e-01 344: 7.120µm, [3.03e-10;9.96e-01], 1:0.018s, tol=1.20e-01 345: 7.130µm, [3.02e-10;9.96e-01], 1:0.018s, tol=1.22e-01 346: 7.140µm, [3.03e-10;9.97e-01], 1:0.018s, tol=1.39e-01 347: 7.150µm, [3.05e-10;1.00e+00], 1:0.018s, tol=1.33e-01 348: 7.160µm, [3.07e-10;1.00e+00], 1:0.019s, tol=1.18e-01 349: 7.170µm, [3.10e-10;1.00e+00], 1:0.019s, tol=1.12e-01 350: 7.180µm, [3.13e-10;1.00e+00], 1:0.019s, tol=1.02e-01 351: 7.190µm, [3.15e-10;1.00e+00], 1:0.019s, tol=8.29e-02 352: 7.200µm, [3.17e-10;1.00e+00], 1:0.019s, tol=7.83e-02 353: 7.210µm, [3.19e-10;1.00e+00], 1:0.019s, tol=8.43e-02 354: 7.220µm, [3.21e-10;1.00e+00], 1:0.018s, tol=8.60e-02 355: 7.230µm, [3.24e-10;1.01e+00], 1:0.018s, tol=8.44e-02 356: 7.240µm, [3.28e-10;1.01e+00], 1:0.018s, tol=8.16e-02 357: 7.250µm, [3.31e-10;1.01e+00], 1:0.018s, tol=7.04e-02 358: 7.260µm, [3.33e-10;1.01e+00], 1:0.019s, tol=5.79e-02 359: 7.270µm, [3.36e-10;1.01e+00], 1:0.019s, tol=5.54e-02 360: 7.280µm, [3.39e-10;1.00e+00], 1:0.018s, tol=5.91e-02 361: 7.290µm, [3.41e-10;1.01e+00], 1:0.018s, tol=6.38e-02 362: 7.300µm, [3.43e-10;1.01e+00], 1:0.018s, tol=6.45e-02 363: 7.310µm, [3.46e-10;1.01e+00], 1:0.019s, tol=6.60e-02 364: 7.320µm, [3.50e-10;1.01e+00], 1:0.019s, tol=6.62e-02 365: 7.330µm, [3.53e-10;1.00e+00], 1:0.018s, tol=5.95e-02 366: 7.340µm, [3.56e-10;1.00e+00], 1:0.018s, tol=5.54e-02 367: 7.350µm, [3.61e-10;1.00e+00], 1:0.018s, tol=5.61e-02 368: 7.360µm, [3.65e-10;1.00e+00], 1:0.018s, tol=5.44e-02 369: 7.370µm, [3.68e-10;1.00e+00], 1:0.018s, tol=5.46e-02 370: 7.380µm, [3.73e-10;1.00e+00], 1:0.018s, tol=5.51e-02 371: 7.390µm, [3.78e-10;1.00e+00], 1:0.018s, tol=5.44e-02 372: 7.400µm, [3.83e-10;1.00e+00], 1:0.018s, tol=5.56e-02 373: 7.410µm, [3.89e-10;1.00e+00], 1:0.018s, tol=5.27e-02 374: 7.420µm, [3.94e-10;1.00e+00], 1:0.018s, tol=4.99e-02 375: 7.430µm, [3.98e-10;1.00e+00], 1:0.018s, tol=5.17e-02 376: 7.440µm, [4.01e-10;1.00e+00], 1:0.019s, tol=4.99e-02 377: 7.450µm, [4.06e-10;1.00e+00], 1:0.018s, tol=4.77e-02 378: 7.460µm, [4.15e-10;1.00e+00], 1:0.018s, tol=4.65e-02 379: 7.470µm, [4.22e-10;1.00e+00], 1:0.018s, tol=4.06e-02 380: 7.480µm, [4.32e-10;1.00e+00], 1:0.018s, tol=4.13e-02 381: 7.490µm, [4.42e-10;1.00e+00], 1:0.018s, tol=4.07e-02 382: 7.500µm, [4.50e-10;1.00e+00], 1:0.018s, tol=3.34e-02 383: 7.510µm, [4.64e-10;1.00e+00], 1:0.018s, tol=3.10e-02 384: 7.520µm, [4.77e-10;1.00e+00], 1:0.018s, tol=3.15e-02 385: 7.530µm, [4.87e-10;1.00e+00], 1:0.018s, tol=3.42e-02 386: 7.540µm, [4.96e-10;1.01e+00], 1:0.018s, tol=3.76e-02 387: 7.550µm, [5.07e-10;1.01e+00], 1:0.019s, tol=3.69e-02 388: 7.560µm, [5.20e-10;1.01e+00], 1:0.018s, tol=3.22e-02 389: 7.570µm, [5.35e-10;1.01e+00], 1:0.018s, tol=3.09e-02 390: 7.580µm, [5.48e-10;1.01e+00], 1:0.018s, tol=3.01e-02 391: 7.590µm, [5.56e-10;1.01e+00], 1:0.019s, tol=2.99e-02 392: 7.600µm, [5.69e-10;1.01e+00], 1:0.018s, tol=3.41e-02 393: 7.610µm, [5.85e-10;1.01e+00], 1:0.019s, tol=3.63e-02 394: 7.620µm, [6.00e-10;1.01e+00], 1:0.018s, tol=3.22e-02 395: 7.630µm, [6.17e-10;1.01e+00], 1:0.019s, tol=2.91e-02 396: 7.640µm, [6.27e-10;1.01e+00], 1:0.019s, tol=2.61e-02 397: 7.650µm, [6.39e-10;1.01e+00], 1:0.019s, tol=2.85e-02 398: 7.660µm, [6.56e-10;1.01e+00], 1:0.018s, tol=3.32e-02 399: 7.670µm, [6.74e-10;1.01e+00], 1:0.018s, tol=3.36e-02 400: 7.680µm, [6.94e-10;1.01e+00], 1:0.019s, tol=3.29e-02 401: 7.690µm, [7.07e-10;1.01e+00], 1:0.018s, tol=2.93e-02 402: 7.700µm, [7.20e-10;1.01e+00], 1:0.018s, tol=3.09e-02 403: 7.710µm, [7.37e-10;1.01e+00], 1:0.018s, tol=3.25e-02 404: 7.720µm, [7.54e-10;1.01e+00], 1:0.018s, tol=2.79e-02 405: 7.730µm, [7.71e-10;1.01e+00], 1:0.018s, tol=2.58e-02 406: 7.740µm, [7.83e-10;1.01e+00], 1:0.018s, tol=2.51e-02 407: 7.750µm, [7.94e-10;1.01e+00], 1:0.018s, tol=2.91e-02 408: 7.760µm, [8.11e-10;1.01e+00], 1:0.018s, tol=3.03e-02 409: 7.770µm, [8.29e-10;1.01e+00], 1:0.018s, tol=2.73e-02 410: 7.780µm, [8.44e-10;1.01e+00], 1:0.018s, tol=2.62e-02 411: 7.790µm, [8.54e-10;1.01e+00], 1:0.018s, tol=2.62e-02 412: 7.800µm, [8.66e-10;1.01e+00], 1:0.018s, tol=2.88e-02 413: 7.810µm, [8.81e-10;1.01e+00], 1:0.018s, tol=2.61e-02 414: 7.820µm, [8.95e-10;1.01e+00], 1:0.018s, tol=2.47e-02 415: 7.830µm, [9.06e-10;1.01e+00], 1:0.019s, tol=2.51e-02 416: 7.840µm, [9.13e-10;1.01e+00], 1:0.018s, tol=2.74e-02 417: 7.850µm, [9.22e-10;1.01e+00], 1:0.018s, tol=2.85e-02 418: 7.860µm, [9.31e-10;1.01e+00], 1:0.018s, tol=2.75e-02 419: 7.870µm, [9.39e-10;1.01e+00], 1:0.018s, tol=2.85e-02 420: 7.880µm, [9.43e-10;1.01e+00], 1:0.019s, tol=3.22e-02 421: 7.890µm, [9.48e-10;1.01e+00], 1:0.019s, tol=3.54e-02 422: 7.900µm, [9.52e-10;1.01e+00], 1:0.019s, tol=3.92e-02 423: 7.910µm, [9.56e-10;1.01e+00], 1:0.019s, tol=5.05e-02 424: 7.920µm, [9.58e-10;1.01e+00], 1:0.019s, tol=8.86e-02 425: 7.930µm, [9.60e-10;1.01e+00], 1:0.019s, tol=1.66e-01 426: 7.940µm, [9.62e-10;1.00e+00], 1:0.019s, tol=4.95e-02 427: 7.950µm, [9.62e-10;1.00e+00], 1:0.019s, tol=1.54e-02 428: 7.960µm, [9.62e-10;1.00e+00], 1:0.019s, tol=2.55e-03 429: 7.970µm, [9.62e-10;1.00e+00], 1:0.019s, tol=1.50e-03 430: 7.980µm, [9.62e-10;1.00e+00], 1:0.019s, tol=1.43e-03 431: 7.990µm, [9.62e-10;1.00e+00], 1:0.019s, tol=1.43e-03 432: 8.000µm, [9.62e-10;1.00e+00], 1:0.018s, tol=1.43e-03 433: 8.010µm, [9.62e-10;1.00e+00], 1:0.018s, tol=1.46e-03 434: 8.020µm, [9.62e-10;1.00e+00], 1:0.019s, tol=1.50e-03 435: 8.030µm, [9.62e-10;1.00e+00], 1:0.019s, tol=1.49e-03 Saved mesh data in: /home/docs/checkouts/readthedocs.org/user_builds/easyfea/checkouts/stable/examples/PhaseField/results/Tension2D/Test/Bourdin_AT1_optimMesh/Meshes Saved simulation and summary in: /home/docs/checkouts/readthedocs.org/user_builds/easyfea/checkouts/stable/examples/PhaseField/results/Tension2D/Test/Bourdin_AT1_optimMesh Generate movie 01/21 (4.76 %) 2.94 s Generate movie 02/21 (9.52 %) 2.59 s Generate movie 03/21 (14.29 %) 2.41 s Generate movie 04/21 (19.05 %) 2.27 s Generate movie 05/21 (23.81 %) 2.15 s Generate movie 06/21 (28.57 %) 2.03 s Generate movie 07/21 (33.33 %) 1.89 s Generate movie 08/21 (38.10 %) 1.75 s Generate movie 09/21 (42.86 %) 1.60 s Generate movie 10/21 (47.62 %) 1.58 s Generate movie 11/21 (52.38 %) 1.36 s Generate movie 12/21 (57.14 %) 1.25 s Generate movie 13/21 (61.90 %) 1.09 s Generate movie 14/21 (66.67 %) 953.14 ms Generate movie 15/21 (71.43 %) 818.75 ms Generate movie 16/21 (76.19 %) 680.95 ms Generate movie 17/21 (80.95 %) 548.82 ms Generate movie 18/21 (85.71 %) 416.97 ms Generate movie 19/21 (90.48 %) 270.30 ms Generate movie 20/21 (95.24 %) 136.80 ms Generate movie 21/21 (100.00 %) 0.00 µs Mesh: 42.125 ms Boundary Conditions: 4.292 ms Matrix: 4.334 s Split: 12.751 ms PostProcessing: 114.028 ms Solver: 4.176 s Resolution phase field: 7.942 s Display: 581.734 ms PyVista_Interface: 4.561 s | .. code-block:: Python :lineno-start: 13 import matplotlib.pyplot as plt import numpy as np from EasyFEA import ( Display, Folder, Models, Tic, ElemType, Simulations, PyVista, Paraview, ) from EasyFEA.Geoms import Point, Points, Domain, Line, Contour if __name__ == "__main__": # ---------------------------------------------- # Configurations # ---------------------------------------------- dim = 2 # simu options doSimu = True meshTest = True openCrack = True optimMesh = True # outputs folder = Folder.Results_Dir() + f"{dim}D" plotMesh = False plotEnergy = False makeParaview = False makeMovie = True # phasefield maxIter = 1000 tolConv = 1e-0 # 1e-1, 1e-2, 1e-3 pfmSolver = Models.PhaseField.SolverType.History # Available splits: Bourdin, Amor, Miehe, Stress (isotropic) # He, AnisotStrain, AnisotStress, Zhang (anisotropic) split = Models.PhaseField.SplitType.Bourdin # Available regus: AT1, AT2 regu = Models.PhaseField.ReguType.AT1 # ---------------------------------------------- # Geometry # ---------------------------------------------- L = 1e-3 # m l0 = 8.5e-6 thickness = 1 if dim == 2 else 0.1 / 1000 # ---------------------------------------------- # Material # ---------------------------------------------- E = 210e9 # Pa v = 0.3 Gc = 2.7e3 # J/m2 folder_save = Simulations.PhaseField.Folder( folder, "", split, regu, "", tolConv, pfmSolver, meshTest, optimMesh, not openCrack, ) Display.MyPrint(folder_save, "green", end="\n") if doSimu: # ---------------------------------------------- # Mesh # ---------------------------------------------- clC = l0 * 2 if meshTest else l0 / 2 if optimMesh: clD = clC * 4 gap = L * 0.05 refineDomain = Domain( Point(L / 2 - gap, L / 2 - gap), Point(L, L / 2 + gap, thickness), clC, ) else: clD = clC refineDomain = None pt1 = Point() pt2 = Point(L) pt3 = Point(L, L) pt4 = Point(0, L) contour = Points([pt1, pt2, pt3, pt4], clD) if dim == 2: ptC1 = Point(0, L / 2, isOpen=openCrack) ptC2 = Point(L / 2, L / 2) cracks = [Line(ptC1, ptC2, clC, isOpen=openCrack)] elif dim == 3: meshSize = clD if optimMesh else clC ptC1 = Point(0, L / 2, 0, isOpen=openCrack) ptC2 = Point(L / 2, L / 2, 0) ptC3 = Point(L / 2, L / 2, thickness) ptC4 = Point(0, L / 2, thickness, isOpen=openCrack) l1 = Line(ptC1, ptC2, meshSize, openCrack) l2 = Line(ptC2, ptC3, meshSize, False) l3 = Line(ptC3, ptC4, meshSize, openCrack) l4 = Line(ptC4, ptC1, meshSize, openCrack) cracks = [Contour([l1, l2, l3, l4])] if dim == 2: mesh = contour.Mesh_2D([], ElemType.TRI3, cracks, [refineDomain]) elif dim == 3: mesh = contour.Mesh_Extrude( [], [0, 0, thickness], [3], ElemType.TETRA4, cracks, [refineDomain] ) # Nodes nodes_upper = mesh.Nodes_Conditions(lambda x, y, z: y == L) nodes_lower = mesh.Nodes_Conditions(lambda x, y, z: y == 0) nodes_right = mesh.Nodes_Conditions( lambda x, y, z: (x == L) & (y > 0) & (y < L) ) nodes_crack = mesh.Nodes_Conditions(lambda x, y, z: (y == L / 2) & (x <= L / 2)) if openCrack: nodes_detect = mesh.nodes.copy() else: nodes_detect = np.array(list(set(mesh.nodes) - set(nodes_crack))) # Builds edge nodes nodes_edges = [] for nodes in [nodes_lower, nodes_right, nodes_upper]: nodes_edges.extend(nodes) # ---------------------------------------------- # Material # ---------------------------------------------- material = Models.Elastic.Isotropic( dim, E=E, v=v, planeStress=False, thickness=thickness ) pfm = Models.PhaseField(material, split, regu, Gc=Gc, l0=l0, solver=pfmSolver) # ---------------------------------------------- # Boundary conditions # ---------------------------------------------- uinc0 = 1e-7 if meshTest else 1e-8 N0 = 40 if meshTest else 400 uinc1 = 1e-8 if meshTest else 1e-9 N1 = 400 if meshTest else 4000 threshold = uinc0 * N0 dep0 = threshold dep1 = dep0 + uinc1 * N1 config = f""" uinc0 = {uinc0:.1e} (dep < threshold={threshold:.2e}) uinc1 = {uinc1:.1e} while True: if not openCrack: simu.add_dirichlet(nodes_crack, [1], ["d"], problemType="damage") simu.add_dirichlet(nodes_upper, [0, dep], ["x", "y"]) simu.add_dirichlet(nodes_lower, [0], ["y"]) """ def Loading(dep): simu.Bc_Init() if not openCrack: simu.add_dirichlet(nodes_crack, [1], ["d"], problemType="damage") if dim == 2: simu.add_dirichlet(nodes_upper, [0, dep], ["x", "y"]) elif dim == 3: simu.add_dirichlet(nodes_upper, [0, dep, 0], ["x", "y", "z"]) simu.add_dirichlet(nodes_lower, [0], ["y"]) # ---------------------------------------------- # Simulation # ---------------------------------------------- simu = Simulations.PhaseField(mesh, pfm, folder=folder_save) simu.Results_Set_Bc_Summary(config) dofsY_upper = simu.Bc_dofs_nodes(nodes_upper, ["y"]) nDetect = 0 list_dep = [] list_f = [] dep = -uinc0 iter = -1 while True: iter += 1 dep += uinc0 if dep < threshold else uinc1 Loading(dep) u, _, converg = simu.Solve(tolConv, maxIter, convOption=1) simu.Save_Iter() simu.Results_Set_Iteration_Summary(iter, dep * 1e6, "µm", 0, True) if not converg: break f = np.sum(simu.Calc_Reaction(dofsY_upper, "elastic")) list_dep.append(dep) list_f.append(f) if simu.Detect_Damage(nodes_edges, 1): nDetect += 1 if nDetect == 10: break # ---------------------------------------------- # Saving # ---------------------------------------------- print() Simulations.Save_pickle((list_f, list_dep), folder_save, "force-displacement") simu.Save(folder_save) else: simu: Simulations.PhaseField = Simulations.Load_Simu(folder_save) list_f, list_dep = Simulations.Load_pickle(folder_save, "force-displacement") # ---------------------------------------------- # Results # ---------------------------------------------- Display.Plot_Result( simu, "damage", nodeValues=True, plotMesh=False, folder=folder_save, filename="damage", ) Display.Plot_Mesh(simu) Display.Plot_Iter_Summary(simu, folder_save, None, None) Display.Plot_BoundaryConditions(simu) # ax = Display.Init_Axes() # ax.plot(np.abs(list_dep) * 1e6, np.abs(list_f) * 1e-6, c="blue") # ax.set_xlabel("ud [µm]") # ax.set_ylabel("f [kN/mm]") # ax.grid() # Display.Save_fig(folder_save, "force-displacement") if plotMesh: Display.Plot_Mesh(simu.mesh) if plotEnergy: Display.Plot_Energy(simu, N=400, folder=folder_save) if makeParaview: Paraview.Save_simu(simu, folder_save, 400) if makeMovie: simu.Set_Iter(-1) deformFactor = L * 0.05 / simu.Result("displacement_norm").max() iterations = np.arange(0, simu.Niter, simu.Niter // 20) def Func(plotter, iter): simu.Set_Iter(iterations[iter]) thresh = PyVista._pvMesh(simu, "damage", deformFactor).threshold((0, 0.8)) PyVista.Plot(thresh, "damage", plotMesh=True, plotter=plotter, clim=(0, 1)) PyVista.Movie_func(Func, iterations.size, folder_save, "damage.gif") Tic.Resume() if doSimu: Tic.Plot_History(folder_save, False) plt.show() .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 15.599 seconds) .. _sphx_glr_download_examples_PhaseField_Tension.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: Tension.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: Tension.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: Tension.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_