Tetrahedra microFE pipeline - non-linear simulation in Calculix

Created on: 23.05.2021
Last update: 14.01.2023

By: Gianluca Iori, 2023
The specimen scanned for this example is courtesy of Prof. Dr.-Ing. Claudia Fleck, Institut für Werkstoffwissenschaften und technologien, TU Berlin
For more info on the dataset see the paper: Kaya et al. (2019), Foams of Gray Cast Iron as Efficient Energy Absorption Structures: A Feasibility Study.
Adv. Eng. Mater., 21: 1900080. https://doi.org/10.1002/adem.201900080
Code license: MIT
Narrative license: CC-BY-NC-SA

Command line execution

The pipeline can be executed from the command line using the ciclope command:

python ciclope.py input.tif output.inp -vs 0.0065 0.0065 0.0065 --smooth -r 1.2 -t 90 --vol_mesh --tetrafe --template input_templates/tmp_example02_tens_Nlgeom_steel.inp -v

For info on the solver see the Calculix homepage

Configuration and imports

import sys
sys.path.append('./../../')

import numpy as np
import matplotlib
import matplotlib.pyplot as plt

import mcubes
from scipy import ndimage, misc
from skimage.filters import threshold_otsu, gaussian
from skimage import measure, morphology

from ciclope.utils.recon_utils import read_tiff_stack, plot_midplanes
from ciclope.utils.preprocess import remove_unconnected
import ciclope

matplotlib.rcParams['figure.dpi'] = 300

font = {'weight' : 'normal',
        'size'   : 8}

plt.rc('font', **font)

astropy module not found

Uncomment and run the following cell for visualizations using itkwidgets

# import vtk
# import itk
# from itkwidgets import view

ccx2paraview, dat2txt, and pandas are needed for the postprocessing of results

import ccx2paraview
import dat2txt
import pandas as pd

%%html
<style>
table {float:left}
</style>

Load input data

input_file = './../../test_data/steel_foam/rec_8bit_0_rescale_025/B_matrix_01_0000.tif'

Input data description

Scan parameters
Beamline	TOMCAT@SLS
Sample	Sintered steel foam strut from Kaya_2016
Energy	34 keV
Camera	PCO.edge5
Optics	4x
Voxel size	1.625 micron
Preliminary operations	downsampled (5X; quadratic interpolation)

data_3D = read_tiff_stack(input_file)
vs = np.ones(3)*1.625e-3*4 # [mm]

data_3D = data_3D[100:300, 100:300, 100:300]

# Inspect dataset
plot_midplanes(data_3D)
plt.show()

../_images/e49b293ae95ace3bf1cbc9c24d024f9974efbda24289dd3eb5d8ef50008b9088.png

Inspect the dataset with itkwidgets

# viewer = view(data_3D, ui_collapsed=True)
# viewer.interpolation = False

Launch the itk viewer

# viewer

Pre-processing

Gaussian smooth (optional)

data_3D = gaussian(data_3D, sigma=1, preserve_range=True)

Resize (optional)

resampling = 1.2

# resize the 3D data using spline interpolation of order 2
data_3D = ndimage.zoom(data_3D, 1/resampling, output=None, order=2)

# correct voxelsize
vs = vs * resampling

# Inspect again the dataset
plot_midplanes(data_3D)
plt.show()

../_images/d92e3c4633b87a0d0effbbc1bc74e4fc298d141fba2880a47ce924d5c75682a5.png

Thresholding

# use Otsu's method
T = threshold_otsu(data_3D)
print("Threshold: {}".format(T))

Threshold: 88

# plot the input image histogram
fig2, ax2 = plt.subplots()
plt.hist(data_3D.ravel(), bins=40)
plt.show()

../_images/aa3d4fff804ff76bd60556a50e396491c7b478c6a440bb9a74941c11e1152394.png

# apply the threshold
# BW = data_3D > T
BW = data_3D > 90

Morphological close of binary image

BW = morphology.closing(BW, morphology.cube(5))

Detect largest isolated cluster of voxels

Label the BW 3D image

# [labels, n_labels] = measure.label(BW, None, True)
[labels, n_labels] = measure.label(BW, None, True, 1) # 1 connectivity hop

Inspect the labels with napari

# import napari
# viewer = napari.view_image(labels)

# count occurrences of each label label
occurrences = np.bincount(labels.reshape(labels.size))

# find largest unconnected label
largest_label_id = occurrences[1:].argmax()+1
L = labels == largest_label_id

You can do the same using the function remove_unconnected contained in preprocess

L = remove_unconnected(BW)

# Inspect dataset
# plot_midplanes(np.bitwise_xor(L, BW))
plot_midplanes(L)
plt.show()

../_images/41f90ffe0984f74752de4170499ee603094b1a1d5b16e194c7a03570ed8f7fac.png

Generate meshes for visualization

Create triangles mesh of the outer model shell (optional.. expensive!)

# vertices, triangles = ciclope.shell_mesh(L, method='pymcubes')

Write VTK mesh with meshio

# meshio.write_points_cells("pippo_shell.vtk", vertices.tolist(), [("triangle", triangles.tolist())])

Create tetrahedra mesh

Volume meshing using CGAL through pygalmesh

filename_mesh_out = '/home/gianthk/PycharmProjects/CT2FE/test_data/steel_foam/B_matrix_mesh.vtk'

# import pygalmesh
# mesh = pygalmesh.generate_from_array(np.transpose(L, [2, 1, 0]).astype('uint8'), tuple(vs), max_facet_distance=1.2*min(vs), max_cell_circumradius=5*1.2*min(vs))

Alternatively use the method ciclope.tetraFE.cgal_mesh For some reason this works only from script

mesh = ciclope.tetraFE.cgal_mesh(L, vs, 'tetra', 1.2*min(vs), 5*1.2*min(vs))

mesh.write(filename_mesh_out)

Visualize the mesh with itkwidgtes

# from itkwidgets import view

# reader = vtk.vtkUnstructuredGridReader()
# reader.SetFileName(filename_mesh_out)
# reader.Update()
# grid = reader.GetOutput()

# view(geometries=grid)

Write Abaqus input FE files

Generate tetrahedra-FE model with constant material properties

The method ciclope.tetraFE.mesh2tetrafe assumes that the material property definition is contained in the FE analysis .INP template file.

input_template = "./../../input_templates/tmp_example02_tens_static_steel.inp"

Inspect input template file

!cat {input_template}

** ----------------------------------------------------
** Material definition:
*MATERIAL, NAME=STEEL_4301
*ELASTIC
210000, 0.3333333333, 0
*DENSITY
7.85e-9
*SOLID SECTION, ELSET=SET1, MATERIAL=STEEL_4301
** ---------------------------------------------------
** Analysis definition. The Step module defines the analysis steps and associated output requests.
** More info at:
** https://abaqus-docs.mit.edu/2017/English/SIMACAECAERefMap/simacae-m-Sim-sb.htm#simacae-m-Sim-sb
** ---------------------------------------------------
*STEP
*STATIC
** All displacements fixed at bottom:
*BOUNDARY
NODES_B, 1, 3, 0.0
** Vertical displacement imposed at top:
*BOUNDARY
NODES_T, 3, 3, +0.1
** ---------------------------------------------------
** Output request:
*NODE FILE, OUTPUT=2D
U
*NODE PRINT, TOTALS=ONLY, NSET=NODES_B
RF
*EL FILE, OUTPUT=2D
S
*END STEP

filename_out = './../../test_data/steel_foam/B_matrix_tetraFE.inp'

Generate CalculiX FE input file

ciclope.tetraFE.mesh2tetrafe(mesh, input_template, filename_out, keywords=['NSET', 'ELSET'])

INFO:root:Converting mesh with fields:

INFO:root:{'points': array([[ 1.0637777e-01,  2.7099030e+00,  1.2464654e+00],
       [ 3.1638098e+00,  2.4738045e+00,  8.2634044e-01],
       [-2.8007149e-04,  2.4925890e+00,  1.6835400e+00],
       ...,
       [ 1.7855428e+00,  3.3190203e+00,  1.1995814e+00],
       [ 6.9351017e-01,  3.2858081e+00,  2.6503036e+00],
       [ 2.7904041e+00,  2.9363434e+00,  2.7100861e+00]], dtype=float32), 'cells': [<meshio CellBlock, type: tetra, num cells: 122964>], 'point_data': {'medit:ref': array([1, 1, 1, ..., 1, 1, 1])}, 'cell_data': {'medit:ref': array([1, 1, 1, ..., 1, 1, 1])}, 'field_data': {}, 'point_sets': {}, 'cell_sets': {}, 'gmsh_periodic': None, 'info': None}
INFO:root:Reading Abaqus template file input_templates/tmp_example02_tens_static_steel.inp
INFO:root:Data written to file /home/gianthk/PycharmProjects/CT2FE/test_data/steel_foam/B_matrix_tetraFE.inp

Solve FE model in calculix

The following section assumes that you have the Calculix solver installed and accessible with the command ccx_2.17 or for multithread option ccx_2.17_MT
The multithread option in CalculiX is activated by defining the number of threads (default=1) used for the calculation.
This is done by setting the env variable OMP_NUM_THREADS with: export OMP_NUM_THREADS=8

# !export OMP_NUM_THREADS=8; ccx_2.17_MT "trabecular_sample_voxelfe"

Postprocessing

Convert Calculix output to Paraview

The following sections assume that you have ccx2paraview and Paraview installed and working.
For more info visit:
https://www.paraview.org/
https://github.com/calculix/ccx2paraview

filename_out_base, ext_out = os.path.splitext(filename_out)
ccx2paraview.Converter(filename_out_base + '.frd', ['vtk']).run()

Visualize results in Paraview

!paraview filename_out_base + '.vtk'

Generate tetrahedra-FE model for non-linear analysis

input_template = "./../../input_templates/tmp_example02_tens_Nlgeom_steel.inp"

Inspect .INP template file for non-linear analysis

!cat {input_template}

** -----------------`----------------------------------
** Material definition:
*MATERIAL, NAME=STEEL_4301
*ELASTIC
210000, 0.3333333333, 0
*DENSITY
7.85e-9
*PLASTIC
2000, 0, 0
3000, 1, 0
*SOLID SECTION, ELSET=SET1, MATERIAL=STEEL_4301
** ---------------------------------------------------
** Analysis definition:
*TIME POINTS, NAME=t10, GENERATE
0, 1, 0.05
*STEP, AMPLITUDE=RAMP, UNSYMM=YES, NLGEOM=YES
*STATIC
0.2, 1, 1e-04, 0.2
** All displacements fixed at bottom:
*BOUNDARY, TYPE=DISPLACEMENT
NODES_B, 1, 3, 0
** Vertical displacement imposed at top:
*BOUNDARY, TYPE=DISPLACEMENT
NODES_T, 3, 3, +0.5
** ---------------------------------------------------
** Output request:
*EL FILE, OUTPUT=2D, TIME POINTS=t10
S,PEEQ
*NODE FILE, OUTPUT=2D
U
*NODE PRINT, TOTALS=ONLY, NSET=NODES_B
RF
*END STEP

filename_out = './../../test_data/steel_foam/B_matrix_tetraFE_Nlgeom.inp'

ciclope.mesh2tetrafe(mesh, input_template, filename_out, keywords=['NSET', 'ELSET'])

Generate CalculiX FE input file

filename_out_base, ext_out = os.path.splitext(filename_out)
ccx2paraview.Converter(filename_out_base + '.frd', ['vtk']).run()

INFO:root:Reading B_matrix_tetraFE_Nlgeom.frd
INFO:root:38341 nodes
INFO:root:122964 cells
INFO:root:Step 1, time 5.00e-02, U, 3 components, 38341 values
INFO:root:Step 1, time 5.00e-02, S, 6 components, 38341 values
INFO:root:Step 1, time 5.00e-02, PEEQ, 1 components, 38341 values
INFO:root:Step 1, time 5.00e-02, ERROR, 1 components, 38341 values
INFO:root:Step 2, time 1.00e-01, U, 3 components, 38341 values
INFO:root:Step 2, time 1.00e-01, S, 6 components, 38341 values
INFO:root:Step 2, time 1.00e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 2, time 1.00e-01, ERROR, 1 components, 38341 values
INFO:root:Step 3, time 1.50e-01, U, 3 components, 38341 values
INFO:root:Step 3, time 1.50e-01, S, 6 components, 38341 values
INFO:root:Step 3, time 1.50e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 3, time 1.50e-01, ERROR, 1 components, 38341 values
INFO:root:Step 4, time 2.00e-01, U, 3 components, 38341 values
INFO:root:Step 4, time 2.00e-01, S, 6 components, 38341 values
INFO:root:Step 4, time 2.00e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 4, time 2.00e-01, ERROR, 1 components, 38341 values
INFO:root:Step 5, time 2.50e-01, U, 3 components, 38341 values
INFO:root:Step 5, time 2.50e-01, S, 6 components, 38341 values
INFO:root:Step 5, time 2.50e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 5, time 2.50e-01, ERROR, 1 components, 38341 values
INFO:root:Step 6, time 3.00e-01, U, 3 components, 38341 values
INFO:root:Step 6, time 3.00e-01, S, 6 components, 38341 values
INFO:root:Step 6, time 3.00e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 6, time 3.00e-01, ERROR, 1 components, 38341 values
INFO:root:Step 7, time 3.50e-01, U, 3 components, 38341 values
INFO:root:Step 7, time 3.50e-01, S, 6 components, 38341 values
INFO:root:Step 7, time 3.50e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 7, time 3.50e-01, ERROR, 1 components, 38341 values
INFO:root:Step 8, time 4.00e-01, U, 3 components, 38341 values
INFO:root:Step 8, time 4.00e-01, S, 6 components, 38341 values
INFO:root:Step 8, time 4.00e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 8, time 4.00e-01, ERROR, 1 components, 38341 values
INFO:root:Step 9, time 4.50e-01, U, 3 components, 38341 values
INFO:root:Step 9, time 4.50e-01, S, 6 components, 38341 values
INFO:root:Step 9, time 4.50e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 9, time 4.50e-01, ERROR, 1 components, 38341 values
INFO:root:Step 10, time 5.00e-01, U, 3 components, 38341 values
INFO:root:Step 10, time 5.00e-01, S, 6 components, 38341 values
INFO:root:Step 10, time 5.00e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 10, time 5.00e-01, ERROR, 1 components, 38341 values
INFO:root:Step 11, time 5.50e-01, U, 3 components, 38341 values
INFO:root:Step 11, time 5.50e-01, S, 6 components, 38341 values
INFO:root:Step 11, time 5.50e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 11, time 5.50e-01, ERROR, 1 components, 38341 values
INFO:root:Step 12, time 6.00e-01, U, 3 components, 38341 values
INFO:root:Step 12, time 6.00e-01, S, 6 components, 38341 values
INFO:root:Step 12, time 6.00e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 12, time 6.00e-01, ERROR, 1 components, 38341 values
INFO:root:Step 13, time 6.50e-01, U, 3 components, 38341 values
INFO:root:Step 13, time 6.50e-01, S, 6 components, 38341 values
INFO:root:Step 13, time 6.50e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 13, time 6.50e-01, ERROR, 1 components, 38341 values
INFO:root:Step 14, time 7.00e-01, U, 3 components, 38341 values
INFO:root:Step 14, time 7.00e-01, S, 6 components, 38341 values
INFO:root:Step 14, time 7.00e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 14, time 7.00e-01, ERROR, 1 components, 38341 values
INFO:root:Step 15, time 7.50e-01, U, 3 components, 38341 values
INFO:root:Step 15, time 7.50e-01, S, 6 components, 38341 values
INFO:root:Step 15, time 7.50e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 15, time 7.50e-01, ERROR, 1 components, 38341 values
INFO:root:Step 16, time 8.00e-01, U, 3 components, 38341 values
INFO:root:Step 16, time 8.00e-01, S, 6 components, 38341 values
INFO:root:Step 16, time 8.00e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 16, time 8.00e-01, ERROR, 1 components, 38341 values
INFO:root:Step 17, time 8.50e-01, U, 3 components, 38341 values
INFO:root:Step 17, time 8.50e-01, S, 6 components, 38341 values
INFO:root:Step 17, time 8.50e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 17, time 8.50e-01, ERROR, 1 components, 38341 values
INFO:root:Step 18, time 9.00e-01, U, 3 components, 38341 values
INFO:root:Step 18, time 9.00e-01, S, 6 components, 38341 values
INFO:root:Step 18, time 9.00e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 18, time 9.00e-01, ERROR, 1 components, 38341 values
INFO:root:Step 19, time 9.50e-01, U, 3 components, 38341 values
INFO:root:Step 19, time 9.50e-01, S, 6 components, 38341 values
INFO:root:Step 19, time 9.50e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 19, time 9.50e-01, ERROR, 1 components, 38341 values
INFO:root:Step 20, time 1.0, U, 3 components, 38341 values
INFO:root:Step 20, time 1.0, S, 6 components, 38341 values
INFO:root:Step 20, time 1.0, PEEQ, 1 components, 38341 values
INFO:root:Step 20, time 1.0, ERROR, 1 components, 38341 values
INFO:root:20 time increments
INFO:root:Writing B_matrix_tetraFE_Nlgeom.01.vtk

INFO:root:Step 1, time 5.00e-02, U, 3 components, 38341 values
INFO:root:Step 1, time 5.00e-02, S, 6 components, 38341 values
INFO:root:Step 1, time 5.00e-02, S_Mises, 1 components, 38341 values
INFO:root:Step 1, time 5.00e-02, S_Principal, 3 components, 38341 values
INFO:root:Step 1, time 5.00e-02, PEEQ, 1 components, 38341 values
INFO:root:Step 1, time 5.00e-02, ERROR, 1 components, 38341 values
INFO:root:Writing B_matrix_tetraFE_Nlgeom.02.vtk
INFO:root:Step 2, time 1.00e-01, U, 3 components, 38341 values
INFO:root:Step 2, time 1.00e-01, S, 6 components, 38341 values
INFO:root:Step 2, time 1.00e-01, S_Mises, 1 components, 38341 values
INFO:root:Step 2, time 1.00e-01, S_Principal, 3 components, 38341 values
INFO:root:Step 2, time 1.00e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 2, time 1.00e-01, ERROR, 1 components, 38341 values
INFO:root:Writing B_matrix_tetraFE_Nlgeom.03.vtk
INFO:root:Step 3, time 1.50e-01, U, 3 components, 38341 values
INFO:root:Step 3, time 1.50e-01, S, 6 components, 38341 values
INFO:root:Step 3, time 1.50e-01, S_Mises, 1 components, 38341 values
INFO:root:Step 3, time 1.50e-01, S_Principal, 3 components, 38341 values
INFO:root:Step 3, time 1.50e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 3, time 1.50e-01, ERROR, 1 components, 38341 values
INFO:root:Writing B_matrix_tetraFE_Nlgeom.04.vtk
INFO:root:Step 4, time 2.00e-01, U, 3 components, 38341 values
INFO:root:Step 4, time 2.00e-01, S, 6 components, 38341 values
INFO:root:Step 4, time 2.00e-01, S_Mises, 1 components, 38341 values
INFO:root:Step 4, time 2.00e-01, S_Principal, 3 components, 38341 values
INFO:root:Step 4, time 2.00e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 4, time 2.00e-01, ERROR, 1 components, 38341 values
INFO:root:Writing B_matrix_tetraFE_Nlgeom.05.vtk
INFO:root:Step 5, time 2.50e-01, U, 3 components, 38341 values
INFO:root:Step 5, time 2.50e-01, S, 6 components, 38341 values
INFO:root:Step 5, time 2.50e-01, S_Mises, 1 components, 38341 values
INFO:root:Step 5, time 2.50e-01, S_Principal, 3 components, 38341 values
INFO:root:Step 5, time 2.50e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 5, time 2.50e-01, ERROR, 1 components, 38341 values
INFO:root:Writing B_matrix_tetraFE_Nlgeom.06.vtk
INFO:root:Step 6, time 3.00e-01, U, 3 components, 38341 values
INFO:root:Step 6, time 3.00e-01, S, 6 components, 38341 values
INFO:root:Step 6, time 3.00e-01, S_Mises, 1 components, 38341 values
INFO:root:Step 6, time 3.00e-01, S_Principal, 3 components, 38341 values
INFO:root:Step 6, time 3.00e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 6, time 3.00e-01, ERROR, 1 components, 38341 values
INFO:root:Writing B_matrix_tetraFE_Nlgeom.07.vtk
INFO:root:Step 7, time 3.50e-01, U, 3 components, 38341 values
INFO:root:Step 7, time 3.50e-01, S, 6 components, 38341 values
INFO:root:Step 7, time 3.50e-01, S_Mises, 1 components, 38341 values
INFO:root:Step 7, time 3.50e-01, S_Principal, 3 components, 38341 values
INFO:root:Step 7, time 3.50e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 7, time 3.50e-01, ERROR, 1 components, 38341 values
INFO:root:Writing B_matrix_tetraFE_Nlgeom.08.vtk
INFO:root:Step 8, time 4.00e-01, U, 3 components, 38341 values
INFO:root:Step 8, time 4.00e-01, S, 6 components, 38341 values
INFO:root:Step 8, time 4.00e-01, S_Mises, 1 components, 38341 values
INFO:root:Step 8, time 4.00e-01, S_Principal, 3 components, 38341 values
INFO:root:Step 8, time 4.00e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 8, time 4.00e-01, ERROR, 1 components, 38341 values
INFO:root:Writing B_matrix_tetraFE_Nlgeom.09.vtk
INFO:root:Step 9, time 4.50e-01, U, 3 components, 38341 values
INFO:root:Step 9, time 4.50e-01, S, 6 components, 38341 values
INFO:root:Step 9, time 4.50e-01, S_Mises, 1 components, 38341 values
INFO:root:Step 9, time 4.50e-01, S_Principal, 3 components, 38341 values
INFO:root:Step 9, time 4.50e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 9, time 4.50e-01, ERROR, 1 components, 38341 values
INFO:root:Writing B_matrix_tetraFE_Nlgeom.10.vtk
INFO:root:Step 10, time 5.00e-01, U, 3 components, 38341 values
INFO:root:Step 10, time 5.00e-01, S, 6 components, 38341 values
INFO:root:Step 10, time 5.00e-01, S_Mises, 1 components, 38341 values
INFO:root:Step 10, time 5.00e-01, S_Principal, 3 components, 38341 values
INFO:root:Step 10, time 5.00e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 10, time 5.00e-01, ERROR, 1 components, 38341 values
INFO:root:Writing B_matrix_tetraFE_Nlgeom.11.vtk
INFO:root:Step 11, time 5.50e-01, U, 3 components, 38341 values
INFO:root:Step 11, time 5.50e-01, S, 6 components, 38341 values
INFO:root:Step 11, time 5.50e-01, S_Mises, 1 components, 38341 values
INFO:root:Step 11, time 5.50e-01, S_Principal, 3 components, 38341 values
INFO:root:Step 11, time 5.50e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 11, time 5.50e-01, ERROR, 1 components, 38341 values
INFO:root:Writing B_matrix_tetraFE_Nlgeom.12.vtk
INFO:root:Step 12, time 6.00e-01, U, 3 components, 38341 values
INFO:root:Step 12, time 6.00e-01, S, 6 components, 38341 values
INFO:root:Step 12, time 6.00e-01, S_Mises, 1 components, 38341 values
INFO:root:Step 12, time 6.00e-01, S_Principal, 3 components, 38341 values
INFO:root:Step 12, time 6.00e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 12, time 6.00e-01, ERROR, 1 components, 38341 values
INFO:root:Writing B_matrix_tetraFE_Nlgeom.13.vtk
INFO:root:Step 13, time 6.50e-01, U, 3 components, 38341 values
INFO:root:Step 13, time 6.50e-01, S, 6 components, 38341 values
INFO:root:Step 13, time 6.50e-01, S_Mises, 1 components, 38341 values
INFO:root:Step 13, time 6.50e-01, S_Principal, 3 components, 38341 values
INFO:root:Step 13, time 6.50e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 13, time 6.50e-01, ERROR, 1 components, 38341 values
INFO:root:Writing B_matrix_tetraFE_Nlgeom.14.vtk
INFO:root:Step 14, time 7.00e-01, U, 3 components, 38341 values
INFO:root:Step 14, time 7.00e-01, S, 6 components, 38341 values
INFO:root:Step 14, time 7.00e-01, S_Mises, 1 components, 38341 values
INFO:root:Step 14, time 7.00e-01, S_Principal, 3 components, 38341 values
INFO:root:Step 14, time 7.00e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 14, time 7.00e-01, ERROR, 1 components, 38341 values
INFO:root:Writing B_matrix_tetraFE_Nlgeom.15.vtk
INFO:root:Step 15, time 7.50e-01, U, 3 components, 38341 values
INFO:root:Step 15, time 7.50e-01, S, 6 components, 38341 values
INFO:root:Step 15, time 7.50e-01, S_Mises, 1 components, 38341 values
INFO:root:Step 15, time 7.50e-01, S_Principal, 3 components, 38341 values
INFO:root:Step 15, time 7.50e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 15, time 7.50e-01, ERROR, 1 components, 38341 values
INFO:root:Writing B_matrix_tetraFE_Nlgeom.16.vtk
INFO:root:Step 16, time 8.00e-01, U, 3 components, 38341 values
INFO:root:Step 16, time 8.00e-01, S, 6 components, 38341 values
INFO:root:Step 16, time 8.00e-01, S_Mises, 1 components, 38341 values
INFO:root:Step 16, time 8.00e-01, S_Principal, 3 components, 38341 values
INFO:root:Step 16, time 8.00e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 16, time 8.00e-01, ERROR, 1 components, 38341 values
INFO:root:Writing B_matrix_tetraFE_Nlgeom.17.vtk
INFO:root:Step 17, time 8.50e-01, U, 3 components, 38341 values
INFO:root:Step 17, time 8.50e-01, S, 6 components, 38341 values
INFO:root:Step 17, time 8.50e-01, S_Mises, 1 components, 38341 values
INFO:root:Step 17, time 8.50e-01, S_Principal, 3 components, 38341 values
INFO:root:Step 17, time 8.50e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 17, time 8.50e-01, ERROR, 1 components, 38341 values
INFO:root:Writing B_matrix_tetraFE_Nlgeom.18.vtk
INFO:root:Step 18, time 9.00e-01, U, 3 components, 38341 values
INFO:root:Step 18, time 9.00e-01, S, 6 components, 38341 values
INFO:root:Step 18, time 9.00e-01, S_Mises, 1 components, 38341 values
INFO:root:Step 18, time 9.00e-01, S_Principal, 3 components, 38341 values
INFO:root:Step 18, time 9.00e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 18, time 9.00e-01, ERROR, 1 components, 38341 values
INFO:root:Writing B_matrix_tetraFE_Nlgeom.19.vtk
INFO:root:Step 19, time 9.50e-01, U, 3 components, 38341 values
INFO:root:Step 19, time 9.50e-01, S, 6 components, 38341 values
INFO:root:Step 19, time 9.50e-01, S_Mises, 1 components, 38341 values
INFO:root:Step 19, time 9.50e-01, S_Principal, 3 components, 38341 values
INFO:root:Step 19, time 9.50e-01, PEEQ, 1 components, 38341 values
INFO:root:Step 19, time 9.50e-01, ERROR, 1 components, 38341 values
INFO:root:Writing B_matrix_tetraFE_Nlgeom.20.vtk
INFO:root:Step 20, time 1.0, U, 3 components, 38341 values
INFO:root:Step 20, time 1.0, S, 6 components, 38341 values
INFO:root:Step 20, time 1.0, S_Mises, 1 components, 38341 values
INFO:root:Step 20, time 1.0, S_Principal, 3 components, 38341 values
INFO:root:Step 20, time 1.0, PEEQ, 1 components, 38341 values
INFO:root:Step 20, time 1.0, ERROR, 1 components, 38341 values

Equivalent Plastic Strain (PEEQ) animation created in Paraview:

Post-process non-linear FE analysis results

We use the helper script dat2txt.py from Martin Kraska to clean and convert the CalculiX FE output .DAT file to a text file containing only data:

filename_dat = './../../test_data/steel_foam/B_matrix_tetraFE_Nlgeom.dat'

dat2txt.dat2txt(filename_dat, True)

INFO:root:Reading file /home/gianthk/PycharmProjects/CT2FE/test_data/steel_foam/B_matrix_tetraFE_Nlgeom.dat.
INFO:root:Written total force fx,fy,fz for group NODES_B to file: total force fx,fy,fz_NODES_B.txt.
Total time points: 59.

('total force fx,fy,fz', 'NODES_B', 59)

Load and plot results with pandas

%matplotlib inline

header = ['time', 'fx', 'fy', 'fz']
filename_txt = './../../test_data/steel_foam/total force fx,fy,fz_NODES_B.txt'
data = pd.read_table(filename_txt, delim_whitespace=True, names=header, index_col=0)

Have a look at the data produced by CalculiX

data

	fx	fy	fz
time
0.05	6.246617e-09	-9.647296e-10	-63.92774
0.10	1.269526e-10	2.538340e-10	-97.62540
0.15	3.104711e-09	1.066627e-09	-116.32770
0.20	9.618676e-10	-4.711595e-10	-129.88530
0.25	-4.597598e-07	-8.556020e-08	-141.77580
0.30	3.020426e-07	3.076565e-07	-152.58380
0.35	-4.586224e-09	1.690051e-08	-161.88950
0.40	1.673068e-09	2.573413e-09	-168.59850
0.45	3.774273e-07	1.899347e-07	-174.08460
0.50	-1.608090e-07	-1.298831e-07	-177.40930
0.55	7.836687e-09	1.665111e-10	-178.39990
0.60	-9.815839e-09	-6.166009e-09	-179.22490
0.65	6.769719e-09	9.593283e-09	-178.20100
0.70	-1.156836e-09	1.002093e-08	-176.15900
0.75	-7.059488e-07	-2.223455e-07	-173.43490
0.80	-1.720688e-07	-9.126840e-08	-170.56940
0.85	-9.886431e-09	-6.904714e-09	-167.71290
0.90	-2.093420e-08	-4.455112e-08	-165.11650
0.95	-7.948244e-09	-5.174397e-09	-162.54210
1.00	-8.049240e-08	-8.431905e-08	-160.17860

Plot Force-Displacement curve

fig, axs = plt.subplots()

data['fz'].abs().plot(ax=axs, grid=True)
axs.set_ylabel("Total force Fz")

# fig.savefig("no2_concentrations.png")

Text(0, 0.5, 'Total force Fz')

../_images/44b7a4f2d1e46f382bf5dd233fc414c183d0d13f2ad254690ad3211805e9d5d4.png