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A simple software for constructing artificial binary microstructures in 2D or 3D
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larsblatny/GRFsaw
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GRFsaw is a simple software for artificially constructing binary microstructures (in two or three spatial dimensions) with user-defined
- porosity (solid volume fraction)
- heterogeinity ("grain" size distribution)
- anisotropy (preferred "grain" elongation)
It is based on thresholding Gaussian random fields (GRFs).
Several post-processing schemes are available for
- computing the angular-averaged two-point correlation function using Fast Fourier Transforms
- computing the one-dimensional two-point correlation function in different directions
- finding the spanning (percolating) cluster(s) using the Burning Method
- finding the shortest path through the structure
- plotting and visualizing in 2D and 3D
- saving structures as CSV- or VTK-files
This code relies only on the standard librariesnumpy,scipy,matplotlib andmultiprocessing
Use ofPyVista is optional, but needed for visualizing 3D microstructures and saving structures as VTK-files.
Tested on Python >= 3.6.
fromgrfsaw.microstructureimportMicrostructure
shape= [200,200]solid_fraction=0.65m=Microstructure(shape,solid_fraction)m.create()m.plot()
These are all the options the user may specify for the desired microstructure.
Only two parameters are required,shape andphi, the rest are given their default values below:
shape=<REQUIRED># list of 2 (if 2D structure) or 3 (if 3D) integers# the size of the structure as number of mesh points in each directionphi=<REQUIRED># float# desired solid volume fraction = 1 - porosityfolder="output/"# str# name of directory to save data and plotssingle_cut=True# boolean# decides if generate single-cut or double-cut structureN=10000# int# number of waves to use, the more the better but slowerdistr='n'# char# type of distribution to use for wavevector magnitude sampling,# 'n' for normal or 'g' for gamma distributionm_mean=3# float# average number of microstructural elements per length in the x-direction# = a measure of the grain size of the structurem_std=0.001# float# the standard deviation of manitype='i'# char# type of preferred orientation (type of anisotropy)# 'h' for horizontal or 'v' for vertical, anything else means fully isotropica=1# float# measure of the anisotropy level between 0 and 1, meaning isotropic (default 1)seed=numpy.random.randint(1,1e5)# int# seed for RNGprocs=multiprocessing.cpu_count()# int# number of cpus to use for the computations (default is all cpus on computer)m=Microstructure(shape,phi,folder,single_cut,N,distr,m_mean,m_std,anitype,a,seed,procs)
From left to right (all usingN = 10000 anddistr = 'g'):
phi = 0.63,single_cut = True,m_mean = 13,m_std = 1.8,anitype = 'i'phi = 0.63,single_cut = True,m_mean = 13,m_std = 7.5,anitype = 'i'phi = 0.63,single_cut = True,m_mean = 13,m_std = 1.8,anitype = 'h',a = 0.6phi = 0.35,single_cut = False,m_mean = 9,m_std = 1.3,anitype = 'i'phi = 0.35,single_cut = False,m_mean = 9,m_std = 5.2,anitype = 'i'
Both structures:phi = 0.42,single_cut = True,N = 10000,distr = 'g',anitype = 'i' andm_mean = 9
Left:m_std = 1.3, Right:m_std = 5.2
In all the below methods, the argumentcleaning (defaultFalse) refers to if you are using the cleaned version of the structure or not. In the cleaned version, all parts of the structure that do not belong to a spanning cluster have been removed.In addition, the argumentsfigsize,dpi andfontsize refer to size, resolution and font size, respectively, of the plots to be generated.
m.create()# creates the structuresm.save_parameters()# saves setup parameters to file for future referencem.save(cleaned=False,vtk=False)# saves the structure as CSV-file or as VTK-file (if vtk=True)m.plot(slicelist=[0],cleaned=False,figsize=(13,8),dpi=100,fontsize=22)# plots the structure, or, if 3D structure, a slices of the structuregiven by the arg slicelistm.visualize_3d(cleaned=False,pyvista=True,from_file=False)# visualizes the 3D structure using PyVista (if pyvista=True, recommended) or matplotlibm.plot_distributions(figsize=(13,8),dpi=100,fontsize=22)# plots histograms of the samples of the wave lengths and directionm.autocorrelation(cleaned=False,one_dim=False,figsize=(13,8),dpi=100,fontsize=22)# computes and plots the autocorrelation (two-point correlation) of the structure using FFT# if one-dim=True, it also computes the 1D autocorrelation in the x-, y- and z-directionsm.find_shortest_path(cleaned=False)# calculates the shortest path of the spanning clusterm.cleaning()# removes parts of the structure that do not belong to any side-to-side spanning clustersm.analytic_ssa()# calculates the analytic specific surface area per unit solid volume (SSA)
The functions are further documented here:https://larsblatny.github.io/GRFsaw/
A microstructure before (left) and after (right) applyingcleaning(). We see that stand-alone clusters are removed.
A plot of the two-point correlation function (aka spatial autocorrelation function) produced byautocorrelation(one_dim=True). The angular-averaged two-point correlation as obtained from FFT is plotted in black. This was a highly anisotropic structure, noticed by the differing 1D correlations in the x- and y directions.
Pull requests are welcome. Or feel free to open an issue to discuss what can be changed.
This code is licensed under theMIT License.
Please consider citing the methods used inthis paper when making use of this software.
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A simple software for constructing artificial binary microstructures in 2D or 3D