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Merge branch '256-grid-geometry-displacement-reconstruction' into 'development' 

Resolve "grid geometry/displacement reconstruction"

Closes #256

See merge request damask/DAMASK!762
This commit is contained in:
Sharan Roongta 2023-06-13 08:48:35 +00:00
parent bafbba4b58 137c4e3b03
commit f424d54f5e
3 changed files with 117 additions and 64 deletions
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2
PRIVATE

@ -1 +1 @@
Subproject commit 4cd6c7350b0a9d4ad3efcb5fe6c6cfffa99c426f Subproject commit 486e66396f57abe970f01337b9b3967993dd601f

6
python/damask/grid_filters.py
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@ -186,8 +186,6 @@ def displacement_fluct_point(size: _FloatSequence,
Fluctuating part of the cell center displacements. Fluctuating part of the cell center displacements.
""" """
integrator = 0.5j*_np.array(size,float)/_np.pi
k_s = _ks(size,F.shape[:3],False) k_s = _ks(size,F.shape[:3],False)
k_s_squared = _np.einsum('...l,...l',k_s,k_s) k_s_squared = _np.einsum('...l,...l',k_s,k_s)
k_s_squared[0,0,0] = 1.0 k_s_squared[0,0,0] = 1.0
@ -195,8 +193,8 @@ def displacement_fluct_point(size: _FloatSequence,
displacement = -_np.einsum('ijkml,ijkl,l->ijkm', displacement = -_np.einsum('ijkml,ijkl,l->ijkm',
_np.fft.rfftn(F,axes=(0,1,2)), _np.fft.rfftn(F,axes=(0,1,2)),
k_s, k_s,
integrator, _np.array([0.5j/_np.pi]*3),
) / k_s_squared[...,_np.newaxis] ) / k_s_squared[...,_np.newaxis]
return _np.fft.irfftn(displacement,axes=(0,1,2),s=F.shape[:3]) return _np.fft.irfftn(displacement,axes=(0,1,2),s=F.shape[:3])

173
python/tests/test_grid_filters.py
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@ -2,98 +2,153 @@ import pytest
import numpy as np import numpy as np
from damask import grid_filters from damask import grid_filters
from damask import mechanics
from damask import Grid from damask import Grid
from damask import seeds from damask import seeds
class TestGridFilters: class TestGridFilters:
def test_coordinates0_point(self): def test_coordinates0_point(self):
size = np.random.random(3) # noqa size = np.random.random(3) # noqa
cells = np.random.randint(8,32,(3)) cells = np.random.randint(8,32,(3))
coord = grid_filters.coordinates0_point(cells,size) coord = grid_filters.coordinates0_point(cells,size)
assert np.allclose(coord[0,0,0],size/cells*.5) and coord.shape == tuple(cells) + (3,) assert np.allclose(coord[0,0,0],size/cells*.5) and coord.shape == tuple(cells) + (3,)
def test_coordinates0_node(self): def test_coordinates0_node(self):
size = np.random.random(3) # noqa size = np.random.random(3) # noqa
cells = np.random.randint(8,32,(3)) cells = np.random.randint(8,32,(3))
coord = grid_filters.coordinates0_node(cells,size) coord = grid_filters.coordinates0_node(cells,size)
assert np.allclose(coord[-1,-1,-1],size) and coord.shape == tuple(cells+1) + (3,) assert np.allclose(coord[-1,-1,-1],size) and coord.shape == tuple(cells+1) + (3,)
def test_coord0(self): def test_coord0(self):
size = np.random.random(3) # noqa size = np.random.random(3) # noqa
cells = np.random.randint(8,32,(3)) cells = np.random.randint(8,32,(3))
c = grid_filters.coordinates0_point(cells+1,size+size/cells) c = grid_filters.coordinates0_point(cells+1,size+size/cells)
n = grid_filters.coordinates0_node(cells,size) + size/cells*.5 n = grid_filters.coordinates0_node(cells,size) + size/cells*.5
assert np.allclose(c,n) assert np.allclose(c,n)
@pytest.mark.parametrize('mode',['point','node']) @pytest.mark.parametrize('mode',['point','node'])
def test_grid_DNA(self,mode): def test_grid_DNA(self,mode):
"""Ensure that cellsSizeOrigin_coordinates0_xx is the inverse of coordinates0_xx.""" # noqa """Ensure that cellsSizeOrigin_coordinates0_xx is the inverse of coordinates0_xx.""" # noqa
cells = np.random.randint(8,32,(3)) cells = np.random.randint(8,32,(3))
size = np.random.random(3) size = np.random.random(3)
origin = np.random.random(3) origin = np.random.random(3)
coord0 = eval(f'grid_filters.coordinates0_{mode}(cells,size,origin)') # noqa coord0 = eval(f'grid_filters.coordinates0_{mode}(cells,size,origin)') # noqa
_cells,_size,_origin = eval(f'grid_filters.cellsSizeOrigin_coordinates0_{mode}(coord0.reshape(-1,3,order="F"))') _cells,_size,_origin = eval(f'grid_filters.cellsSizeOrigin_coordinates0_{mode}(coord0.reshape(-1,3,order="F"))')
assert np.allclose(cells,_cells) and np.allclose(size,_size) and np.allclose(origin,_origin) assert np.allclose(cells,_cells) and np.allclose(size,_size) and np.allclose(origin,_origin)
def test_displacement_fluct_equivalence(self): def test_displacement_fluct_periodic(self):
"""Ensure that fluctuations are periodic.""" # noqa """Ensure that fluctuations are periodic.""" # noqa
size = np.random.random(3) size = np.random.random(3)
cells = np.random.randint(8,32,(3)) cells = np.random.randint(8,32,(3))
F = np.random.random(tuple(cells)+(3,3)) F = np.random.random(tuple(cells)+(3,3))
assert np.allclose(grid_filters.displacement_fluct_node(size,F), assert np.allclose(grid_filters.displacement_fluct_node(size,F),
grid_filters.point_to_node(grid_filters.displacement_fluct_point(size,F))) grid_filters.point_to_node(grid_filters.displacement_fluct_point(size,F)))
def test_interpolation_to_node(self): def test_interpolation_to_node(self):
size = np.random.random(3) # noqa size = np.random.random(3) # noqa
cells = np.random.randint(8,32,(3)) cells = np.random.randint(8,32,(3))
F = np.random.random(tuple(cells)+(3,3)) F = np.random.random(tuple(cells)+(3,3))
assert np.allclose(grid_filters.coordinates_node(size,F) [1:-1,1:-1,1:-1], assert np.allclose(grid_filters.coordinates_node(size,F) [1:-1,1:-1,1:-1],
grid_filters.point_to_node(grid_filters.coordinates_point(size,F))[1:-1,1:-1,1:-1]) grid_filters.point_to_node(grid_filters.coordinates_point(size,F))[1:-1,1:-1,1:-1])
def test_interpolation_to_cell(self): def test_interpolation_to_cell(self):
cells = np.random.randint(1,30,(3)) # noqa cells = np.random.randint(1,30,(3)) # noqa
coordinates_node_x = np.linspace(0,np.pi*2,num=cells[0]+1) coordinates_node_x = np.linspace(0,np.pi*2,num=cells[0]+1)
node_field_x = np.cos(coordinates_node_x) node_field_x = np.cos(coordinates_node_x)
node_field = np.broadcast_to(node_field_x.reshape(-1,1,1),cells+1) node_field = np.broadcast_to(node_field_x.reshape(-1,1,1),cells+1)
coordinates0_point_x = coordinates_node_x[:-1]+coordinates_node_x[1]*.5 coordinates0_point_x = coordinates_node_x[:-1]+coordinates_node_x[1]*.5
cell_field_x = np.interp(coordinates0_point_x,coordinates_node_x,node_field_x,period=np.pi*2.) cell_field_x = np.interp(coordinates0_point_x,coordinates_node_x,node_field_x,period=np.pi*2.)
cell_field = np.broadcast_to(cell_field_x.reshape(-1,1,1),cells) cell_field = np.broadcast_to(cell_field_x.reshape(-1,1,1),cells)
assert np.allclose(cell_field,grid_filters.node_to_point(node_field)) assert np.allclose(cell_field,grid_filters.node_to_point(node_field))
@pytest.mark.parametrize('mode',['point','node']) @pytest.mark.parametrize('mode',['point','node'])
def test_coordinates0_origin(self,mode): def test_coordinates0_origin(self,mode):
origin= np.random.random(3) # noqa origin= np.random.random(3) # noqa
size = np.random.random(3) # noqa size = np.random.random(3) # noqa
cells = np.random.randint(8,32,(3)) cells = np.random.randint(8,32,(3))
shifted = eval(f'grid_filters.coordinates0_{mode}(cells,size,origin)') shifted = eval(f'grid_filters.coordinates0_{mode}(cells,size,origin)')
unshifted = eval(f'grid_filters.coordinates0_{mode}(cells,size)') unshifted = eval(f'grid_filters.coordinates0_{mode}(cells,size)')
if mode == 'cell': if mode == 'cell':
assert np.allclose(shifted,unshifted+np.broadcast_to(origin,tuple(cells) +(3,))) assert np.allclose(shifted,unshifted+np.broadcast_to(origin,tuple(cells) +(3,)))
elif mode == 'node': elif mode == 'node':
assert np.allclose(shifted,unshifted+np.broadcast_to(origin,tuple(cells+1)+(3,))) assert np.allclose(shifted,unshifted+np.broadcast_to(origin,tuple(cells+1)+(3,)))
@pytest.mark.parametrize('function',[grid_filters.displacement_avg_point, @pytest.mark.parametrize('function',[grid_filters.displacement_avg_point,
grid_filters.displacement_avg_node]) grid_filters.displacement_avg_node])
def test_displacement_avg_vanishes(self,function): def test_displacement_avg_vanishes(self,function):
"""Ensure that random fluctuations in F do not result in average displacement.""" # noqa """Ensure that random fluctuations in F do not result in average displacement.""" # noqa
size = np.random.random(3) size = np.random.random(3) + 1.0
cells = np.random.randint(8,32,(3)) cells = np.random.randint(8,32,(3))
F = np.random.random(tuple(cells)+(3,3)) F = np.random.random(tuple(cells)+(3,3))
F += np.eye(3) - np.average(F,axis=(0,1,2)) F += np.eye(3) - np.average(F,axis=(0,1,2))
assert np.allclose(function(size,F),0.0) assert np.allclose(function(size,F),0.0)
@pytest.mark.parametrize('function',[grid_filters.displacement_avg_point,
grid_filters.displacement_avg_node])
def test_displacement_avg_vanishes_simple(self,function):
F = np.eye(3)
size = np.random.random(3) + 1.0
F_c = F.copy()
F_t = F.copy()
F_c[0,0] = 0.8
F_t[0,0] = 1.2
F_no_avg = np.concatenate([np.broadcast_to(_,(10,20,20,3,3)) for _ in [F_t,F_c]])
assert np.allclose(function(size,F_no_avg),0.0)
@pytest.mark.parametrize('function',[grid_filters.displacement_fluct_point, @pytest.mark.parametrize('function',[grid_filters.displacement_fluct_point,
grid_filters.displacement_fluct_node]) grid_filters.displacement_fluct_node])
def test_displacement_fluct_vanishes(self,function): def test_displacement_fluct_vanishes_avg(self,function):
"""Ensure that constant F does not result in fluctuating displacement.""" # noqa """Ensure that constant F does not result in fluctuating displacement.""" # noqa
size = np.random.random(3) size = np.random.random(3)
cells = np.random.randint(8,32,(3)) cells = np.random.randint(8,32,(3))
F = np.broadcast_to(np.random.random((3,3)), tuple(cells)+(3,3)) F = np.broadcast_to(np.random.random((3,3)), tuple(cells)+(3,3))
assert np.allclose(function(size,F),0.0) assert np.allclose(function(size,F),0.0)
displacement_fluct_test_data = [
(['np.sin(np.pi*2*nodes[...,0]/size[0])', '0.0', '0.0',
'0.0', '0.0', '0.0',
'0.0', '0.0', '0.0'],
['-np.cos(np.pi*2*nodes[...,0]/size[0])/np.pi/2*size[0]', '0.0', '0.0']),
(['np.cos(np.pi*2*nodes[...,0]/size[0])', '0.0', '0.0',
'0.0', '0.0', '0.0',
'0.0', '0.0', 'np.cos(np.pi*2*nodes[...,2]/size[2])'],
['np.sin(np.pi*2*nodes[...,0]/size[0])/np.pi/2*size[0]',
'0.0',
'np.sin(np.pi*2*nodes[...,2]/size[2])/np.pi/2*size[2]'])]
@pytest.mark.parametrize('F_def,u_def',displacement_fluct_test_data)
def test_displacment_fluct_analytic(self,F_def,u_def):
size = np.random.random(3)+1.0
cells = np.random.randint(8,32,(3))
nodes = grid_filters.coordinates0_point(cells,size)
my_locals = locals() # needed for list comprehension
F = np.stack([np.broadcast_to(eval(F,globals(),my_locals),cells) for F in F_def],axis=-1).reshape(tuple(cells) + (3,3))
u = np.stack([np.broadcast_to(eval(u,globals(),my_locals),cells) for u in u_def],axis=-1).reshape(tuple(cells) + (3,))
assert np.allclose(u,grid_filters.displacement_fluct_point(size,F))
def test_coordinates(self):
cells = np.array([np.random.randint(40,100)*2,2,2])
size = (np.random.rand(3)+0.8)*cells
F = np.broadcast_to(np.eye(3),tuple(cells)+(3,3)).copy()
F[...,0,0] += np.expand_dims(0.1*np.sin(np.linspace(0,2*np.pi,cells[0],False))+
np.random.rand(cells[0])*0.05,(-1,-2))
c_n = grid_filters.coordinates_node(size,F)[:,0,0,0]
l_0 = (size/cells)[0]
l = c_n[1:] - c_n[:-1]
epsilon_reconstructed = (l-l_0)/l_0
epsilon_direct = mechanics.strain(F,'V',1)[:,0,0,0,0]
assert np.corrcoef(epsilon_reconstructed,epsilon_direct)[0,1] > 0.99
@pytest.mark.parametrize('function',[grid_filters.cellsSizeOrigin_coordinates0_point, @pytest.mark.parametrize('function',[grid_filters.cellsSizeOrigin_coordinates0_point,
grid_filters.cellsSizeOrigin_coordinates0_node]) grid_filters.cellsSizeOrigin_coordinates0_node])