def test_rotation(self):
for make_atoms, calc in [
# ( lambda a0,x :
# FaceCenteredCubic('He', size=[1,1,1],
# latticeconstant=3.5 if a0 is None else a0,
# directions=x),
# LJCut(epsilon=10.2, sigma=2.28, cutoff=5.0, shift=True) ),
( lambda a0,x : FaceCenteredCubic('Au', size=[1,1,1],
latticeconstant=a0, directions=x),
EAM('Au-Grochola-JCP05.eam.alloy') ),
# ( lambda a0,x : Diamond('Si', size=[1,1,1], latticeconstant=a0,
# directions=x),
# Kumagai() )
#( lambda a0,x : FaceCenteredCubic('Au', size=[1,1,1],
# latticeconstant=a0, directions=x),
# EAM(potential='Au-Grochola-JCP05.eam.alloy') ),
]:
a = make_atoms(None, [[1,0,0], [0,1,0], [0,0,1]])
a.set_calculator(calc)
FIRE(StrainFilter(a, mask=[1,1,1,0,0,0]), logfile=None) \
.run(fmax=self.fmax)
latticeconstant = np.mean(a.cell.diagonal())
C6 = measure_triclinic_elastic_constants(a, delta=self.delta,
fmax=self.fmax)
C11, C12, C44 = Voigt_6x6_to_cubic(C6)/GPa
el = CubicElasticModuli(C11, C12, C44)
C_m = measure_triclinic_elastic_constants(a, delta=self.delta,
fmax=self.fmax)/GPa
self.assertArrayAlmostEqual(el.stiffness(), C_m, tol=0.01)
for directions in [ [[1,0,0], [0,1,0], [0,0,1]],
[[0,1,0], [0,0,1], [1,0,0]],
[[1,1,0], [0,0,1], [1,-1,0]],
[[1,1,1], [-1,-1,2], [1,-1,0]] ]:
a, b, c = directions
directions = np.array([ np.array(x)/np.linalg.norm(x)
for x in directions ])
a = make_atoms(latticeconstant, directions)
a.set_calculator(calc)
C = el.rotate(directions)
C_check = el._rotate_explicit(directions)
C_check2 = rotate_cubic_elastic_constants(C11, C12, C44,
directions)
C_check3 = \
rotate_elastic_constants(cubic_to_Voigt_6x6(C11, C12, C44),
directions)
self.assertArrayAlmostEqual(C, C_check, tol=1e-6)
self.assertArrayAlmostEqual(C, C_check2, tol=1e-6)
self.assertArrayAlmostEqual(C, C_check3, tol=1e-6)
C_m = measure_triclinic_elastic_constants(a, delta=self.delta,
fmax=self.fmax)/GPa
self.assertArrayAlmostEqual(C, C_m, tol=1e-2)
def __init__(self,
crack_surface,
crack_front,
C11=None,
C12=None,
C44=None,
stress_state=PLANE_STRAIN,
C=None,
Crot=None):
"""
Initialize a crack in a cubic crystal with elastic constants C11, C12
and C44 (or optionally a full 6x6 elastic constant matrix C).
The crack surface is given by crack_surface, the cracks runs
in the plane given by crack_front.
"""
# x (third_dir) - direction in which the crack is running
# y (crack_surface) - free surface that forms due to the crack
# z (crack_front) - direction of the crack front
third_dir = np.cross(crack_surface, crack_front)
third_dir = np.array(third_dir) / np.sqrt(np.dot(third_dir, third_dir))
crack_surface = np.array(crack_surface) / \
np.sqrt(np.dot(crack_surface, crack_surface))
crack_front = np.array(crack_front) / \
np.sqrt(np.dot(crack_front, crack_front))
A = np.array([third_dir, crack_surface, crack_front])
if np.linalg.det(A) < 0:
third_dir = -third_dir
A = np.array([third_dir, crack_surface, crack_front])
if Crot is not None:
C6 = Crot
elif C is not None:
C6 = rotate_elastic_constants(C, A)
else:
C6 = rotate_cubic_elastic_constants(C11, C12, C44, A)
self.crack = RectilinearAnisotropicCrack()
S6 = inv(C6)
self.C = C6
self.S = S6
if stress_state == PLANE_STRESS:
self.crack.set_plane_stress(S6[0, 0], S6[1, 1], S6[0, 1], S6[0, 5],
S6[1, 5], S6[5, 5])
elif stress_state == PLANE_STRAIN:
self.crack.set_plane_strain(S6[0, 0], S6[1, 1], S6[2, 2], S6[0, 1],
S6[0, 2], S6[1, 2], S6[0, 5], S6[1, 5],
S6[2, 5], S6[5, 5])
def __init__(self, crack_surface, crack_front, C11=None, C12=None,
C44=None, stress_state=PLANE_STRAIN, C=None, Crot=None):
"""
Initialize a crack in a cubic crystal with elastic constants C11, C12
and C44 (or optionally a full 6x6 elastic constant matrix C).
The crack surface is given by crack_surface, the cracks runs
in the plane given by crack_front.
"""
# x (third_dir) - direction in which the crack is running
# y (crack_surface) - free surface that forms due to the crack
# z (crack_front) - direction of the crack front
third_dir = np.cross(crack_surface, crack_front)
third_dir = np.array(third_dir) / np.sqrt(np.dot(third_dir,
third_dir))
crack_surface = np.array(crack_surface) / \
np.sqrt(np.dot(crack_surface, crack_surface))
crack_front = np.array(crack_front) / \
np.sqrt(np.dot(crack_front, crack_front))
A = np.array([third_dir, crack_surface, crack_front])
if np.linalg.det(A) < 0:
third_dir = -third_dir
A = np.array([third_dir, crack_surface, crack_front])
if Crot is not None:
C6 = Crot
elif C is not None:
C6 = rotate_elastic_constants(C, A)
else:
C6 = rotate_cubic_elastic_constants(C11, C12, C44, A)
self.crack = RectilinearAnisotropicCrack()
S6 = inv(C6)
self.C = C6
self.S = S6
if stress_state == PLANE_STRESS:
self.crack.set_plane_stress(S6[0, 0], S6[1, 1], S6[0, 1],
S6[0, 5], S6[1, 5], S6[5, 5])
elif stress_state == PLANE_STRAIN:
self.crack.set_plane_strain(S6[0, 0], S6[1, 1], S6[2, 2],
S6[0, 1], S6[0, 2], S6[1, 2],
S6[0, 5], S6[1, 5], S6[2, 5],
S6[5, 5])
size=(1, 1, 1),
symbol='Si',
pbc=True,
latticeconstant=a0)
if (hasattr(params, 'check_rotated_elastic_constants') and
# Check that elastic constants of the rotated system
# lead to same Young's modulus and Poisson ratio
params.check_rotated_elastic_constants):
unit_slab.set_calculator(params.calc)
C_r1 = measure_triclinic_elastic_constants(unit_slab,
optimizer=FIRE,
fmax=params.bulk_fmax)
R = np.array([np.array(x) / np.linalg.norm(x) for x in directions])
C_r2 = rotate_elastic_constants(C, R)
for C_r in [C_r1, C_r2]:
S_r = np.linalg.inv(C_r)
E_r = 1. / S_r[1, 1]
print('Young\'s modulus from C_r: %.1f GPa' % (E_r / units.GPa))
assert (abs(E_r - E) / units.GPa < 1e-3)
nu_r = -S_r[1, 2] / S_r[1, 1]
print('Possion ratio from C_r: %.3f' % (nu_r))
assert (abs(nu_r - nu) < 1e-3)
print('Unit slab with %d atoms per unit cell:' % len(unit_slab))
print(unit_slab.cell)
print('')
pbc=True,
latticeconstant=a0)
if (hasattr(params, 'check_rotated_elastic_constants') and
# Check that elastic constants of the rotated system
# lead to same Young's modulus and Poisson ratio
params.check_rotated_elastic_constants):
unit_slab.set_calculator(params.calc)
C_r1 = measure_triclinic_elastic_constants(unit_slab,
optimizer=FIRE,
fmax=params.bulk_fmax)
R = np.array([ np.array(x)/np.linalg.norm(x) for x in directions ])
C_r2 = rotate_elastic_constants(C, R)
for C_r in [C_r1, C_r2]:
S_r = np.linalg.inv(C_r)
E_r = 1./S_r[1,1]
print('Young\'s modulus from C_r: %.1f GPa' % (E_r / units.GPa))
assert (abs(E_r - E)/units.GPa < 1e-3)
nu_r = -S_r[1,2]/S_r[1,1]
print('Possion ratio from C_r: %.3f' % (nu_r))
assert (abs(nu_r - nu) < 1e-3)
print('Unit slab with %d atoms per unit cell:' % len(unit_slab))
print(unit_slab.cell)
print('')
