grain growth not maintained and has issues
the grain growth model is based on the Voronoi Implicit Interface Method (https://doi.org/10.1016/j.jcp.2012.04.004). The last step in this algorithm is the assignment of the new phase/material ID to the voxels in the 'thick boundary' which is done with distance_transform_edt from ndimage. This problem can have multiple solution and can lead to the translation of grains. In the original publication, the position of the boundary is calculated with subvoxel resolution by solving the eikonal equation. The following python packages might help: https://pypi.org/project/eikonalfm https://pypi.org/project/scikit-fmm https://github.com/malcolmw/pykonal
This commit is contained in:
Martin Diehl
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#!/usr/bin/env python3
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import os
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import sys
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from io import StringIO
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from optparse import OptionParser
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import numpy as np
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from scipy import ndimage
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import damask
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scriptName = os.path.splitext(os.path.basename(__file__))[0]
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scriptID = ' '.join([scriptName,damask.version])
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getInterfaceEnergy = lambda A,B: np.float32((A != B)*1.0) # 1.0 if A & B are distinct, 0.0 otherwise
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struc = ndimage.generate_binary_structure(3,1) # 3D von Neumann neighborhood
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#--------------------------------------------------------------------------------------------------
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# MAIN
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#--------------------------------------------------------------------------------------------------
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parser = OptionParser(option_class=damask.extendableOption, usage='%prog option(s) [geomfile(s)]', description = """
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Smoothen interface roughness by simulated curvature flow.
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This is achieved by the diffusion of each initially sharply bounded grain volume within the periodic domain
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up to a given distance 'd' voxels.
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The final geometry is assembled by selecting at each voxel that grain index for which the concentration remains largest.
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References 10.1073/pnas.1111557108 (10.1006/jcph.1994.1105)
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""", version = scriptID)
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parser.add_option('-d', '--distance',
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dest = 'd',
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type = 'float', metavar = 'float',
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help = 'diffusion distance in voxels [%default]')
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parser.add_option('-N', '--iterations',
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dest = 'N',
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type = 'int', metavar = 'int',
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help = 'curvature flow iterations [%default]')
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parser.add_option('-i', '--immutable',
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action = 'extend', dest = 'immutable', metavar = '<int LIST>',
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help = 'list of immutable material indices')
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parser.add_option('--ndimage',
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dest = 'ndimage', action='store_true',
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help = 'use ndimage.gaussian_filter in lieu of explicit FFT')
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parser.set_defaults(d = 1,
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N = 1,
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immutable = [],
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ndimage = False,
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)
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(options, filenames) = parser.parse_args()
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options.immutable = list(map(int,options.immutable))
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if filenames == []: filenames = [None]
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for name in filenames:
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damask.util.report(scriptName,name)
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geom = damask.Grid.load(StringIO(''.join(sys.stdin.read())) if name is None else name)
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grid_original = geom.cells
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damask.util.croak(geom)
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material = np.tile(geom.material,np.where(grid_original == 1, 2,1)) # make one copy along dimensions with grid == 1
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grid = np.array(material.shape)
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# --- initialize support data ---------------------------------------------------------------------
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# store a copy of the initial material indices to find locations of immutable indices
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material_original = np.copy(material)
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if not options.ndimage:
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X,Y,Z = np.mgrid[0:grid[0],0:grid[1],0:grid[2]]
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# Calculates gaussian weights for simulating 3d diffusion
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gauss = np.exp(-(X*X + Y*Y + Z*Z)/(2.0*options.d*options.d),dtype=np.float32) \
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/np.power(2.0*np.pi*options.d*options.d,(3.0 - np.count_nonzero(grid_original == 1))/2.,dtype=np.float32)
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gauss[:,:,:grid[2]//2:-1] = gauss[:,:,1:(grid[2]+1)//2] # trying to cope with uneven (odd) grid size
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gauss[:,:grid[1]//2:-1,:] = gauss[:,1:(grid[1]+1)//2,:]
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gauss[:grid[0]//2:-1,:,:] = gauss[1:(grid[0]+1)//2,:,:]
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gauss = np.fft.rfftn(gauss).astype(np.complex64)
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for smoothIter in range(options.N):
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interfaceEnergy = np.zeros(material.shape,dtype=np.float32)
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for i in (-1,0,1):
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for j in (-1,0,1):
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for k in (-1,0,1):
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# assign interfacial energy to all voxels that have a differing neighbor (in Moore neighborhood)
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interfaceEnergy = np.maximum(interfaceEnergy,
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getInterfaceEnergy(material,np.roll(np.roll(np.roll(
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material,i,axis=0), j,axis=1), k,axis=2)))
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# periodically extend interfacial energy array by half a grid size in positive and negative directions
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periodic_interfaceEnergy = np.tile(interfaceEnergy,(3,3,3))[grid[0]//2:-grid[0]//2,
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grid[1]//2:-grid[1]//2,
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grid[2]//2:-grid[2]//2]
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# transform bulk volume (i.e. where interfacial energy remained zero), store index of closest boundary voxel
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index = ndimage.morphology.distance_transform_edt(periodic_interfaceEnergy == 0.,
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return_distances = False,
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return_indices = True)
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# want array index of nearest voxel on periodically extended boundary
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periodic_bulkEnergy = periodic_interfaceEnergy[index[0],
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index[1],
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index[2]].reshape(2*grid) # fill bulk with energy of nearest interface
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if options.ndimage:
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periodic_diffusedEnergy = ndimage.gaussian_filter(
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np.where(ndimage.morphology.binary_dilation(periodic_interfaceEnergy > 0.,
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structure = struc,
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iterations = int(round(options.d*2.))-1, # fat boundary
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),
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periodic_bulkEnergy, # ...and zero everywhere else
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0.),
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sigma = options.d)
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else:
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diffusedEnergy = np.fft.irfftn(np.fft.rfftn(
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np.where(
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ndimage.morphology.binary_dilation(interfaceEnergy > 0.,
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structure = struc,
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iterations = int(round(options.d*2.))-1),# fat boundary
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periodic_bulkEnergy[grid[0]//2:-grid[0]//2, # retain filled energy on fat boundary...
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grid[1]//2:-grid[1]//2,
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grid[2]//2:-grid[2]//2], # ...and zero everywhere else
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0.)).astype(np.complex64) *
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gauss).astype(np.float32)
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periodic_diffusedEnergy = np.tile(diffusedEnergy,(3,3,3))[grid[0]//2:-grid[0]//2,
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grid[1]//2:-grid[1]//2,
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grid[2]//2:-grid[2]//2] # periodically extend the smoothed bulk energy
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# transform voxels close to interface region
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index = ndimage.morphology.distance_transform_edt(periodic_diffusedEnergy >= 0.95*np.amax(periodic_diffusedEnergy),
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return_distances = False,
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return_indices = True) # want index of closest bulk grain
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periodic_material = np.tile(material,(3,3,3))[grid[0]//2:-grid[0]//2,
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grid[1]//2:-grid[1]//2,
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grid[2]//2:-grid[2]//2] # periodically extend the geometry
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material = periodic_material[index[0],
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index[1],
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index[2]].reshape(2*grid)[grid[0]//2:-grid[0]//2,
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grid[1]//2:-grid[1]//2,
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grid[2]//2:-grid[2]//2] # extent grains into interface region
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# replace immutable materials with closest mutable ones
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index = ndimage.morphology.distance_transform_edt(np.in1d(material,options.immutable).reshape(grid),
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return_distances = False,
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return_indices = True)
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material = material[index[0],
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index[1],
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index[2]]
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immutable = np.zeros(material.shape, dtype=np.bool)
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# find locations where immutable materials have been in original structure
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for micro in options.immutable:
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immutable += material_original == micro
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# undo any changes involving immutable materials
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material = np.where(immutable, material_original,material)
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damask.Grid(material = material[0:grid_original[0],0:grid_original[1],0:grid_original[2]],
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size = geom.size,
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origin = geom.origin,
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comments = geom.comments + [scriptID + ' ' + ' '.join(sys.argv[1:])],
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)\
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.save(sys.stdout if name is None else name)
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