class ElasticTensorTest(PymatgenTest):
def setUp(self):
self.voigt_1 = [[59.33, 28.08, 28.08, 0, 0, 0],
[28.08, 59.31, 28.07, 0, 0, 0],
[28.08, 28.07, 59.32, 0, 0, 0], [0, 0, 0, 26.35, 0, 0],
[0, 0, 0, 0, 26.35, 0], [0, 0, 0, 0, 0, 26.35]]
mat = np.random.randn(6, 6)
mat = mat + np.transpose(mat)
self.rand_elastic_tensor = ElasticTensor.from_voigt(mat)
self.ft = np.array([[[[59.33, 0, 0], [0, 28.08, 0], [0, 0, 28.08]],
[[0, 26.35, 0], [26.35, 0, 0], [0, 0, 0]],
[[0, 0, 26.35], [0, 0, 0], [26.35, 0, 0]]],
[[[0, 26.35, 0], [26.35, 0, 0], [0, 0, 0]],
[[28.08, 0, 0], [0, 59.31, 0], [0, 0, 28.07]],
[[0, 0, 0], [0, 0, 26.35], [0, 26.35, 0]]],
[[[0, 0, 26.35], [0, 0, 0], [26.35, 0, 0]],
[[0, 0, 0], [0, 0, 26.35], [0, 26.35, 0]],
[[28.08, 0, 0], [0, 28.07, 0], [0, 0, 59.32]]]])
self.elastic_tensor_1 = ElasticTensor(self.ft)
filepath = os.path.join(test_dir, 'Sn_def_stress.json')
with open(filepath) as f:
self.def_stress_dict = json.load(f)
self.structure = self.get_structure("Sn")
warnings.simplefilter("always")
def test_properties(self):
# compliance tensor
self.assertArrayAlmostEqual(np.linalg.inv(self.elastic_tensor_1.voigt),
self.elastic_tensor_1.compliance_tensor)
# KG average properties
self.assertAlmostEqual(38.49111111111, self.elastic_tensor_1.k_voigt)
self.assertAlmostEqual(22.05866666666, self.elastic_tensor_1.g_voigt)
self.assertAlmostEqual(38.49110945133, self.elastic_tensor_1.k_reuss)
self.assertAlmostEqual(20.67146635306, self.elastic_tensor_1.g_reuss)
self.assertAlmostEqual(38.49111028122, self.elastic_tensor_1.k_vrh)
self.assertAlmostEqual(21.36506650986, self.elastic_tensor_1.g_vrh)
self.assertArrayAlmostEqual(self.elastic_tensor_1.kg_average, [
38.49111111111, 22.05866666666, 38.49110945133, 20.67146635306,
38.49111028122, 21.36506650986
])
# universal anisotropy
self.assertAlmostEqual(0.33553509658699,
self.elastic_tensor_1.universal_anisotropy)
# homogeneous poisson
self.assertAlmostEqual(0.26579965576472,
self.elastic_tensor_1.homogeneous_poisson)
# voigt notation tensor
self.assertArrayAlmostEqual(self.elastic_tensor_1.voigt, self.voigt_1)
# young's modulus
self.assertAlmostEqual(54087787667.160583, self.elastic_tensor_1.y_mod)
def test_structure_based_methods(self):
# trans_velocity
self.assertAlmostEqual(1996.35019877,
self.elastic_tensor_1.trans_v(self.structure))
# long_velocity
self.assertAlmostEqual(3534.68123832,
self.elastic_tensor_1.long_v(self.structure))
# Snyder properties
self.assertAlmostEqual(18.06127074,
self.elastic_tensor_1.snyder_ac(self.structure))
self.assertAlmostEqual(
0.18937465, self.elastic_tensor_1.snyder_opt(self.structure))
self.assertAlmostEqual(
18.25064540, self.elastic_tensor_1.snyder_total(self.structure))
# Clarke
self.assertAlmostEqual(
0.3450307,
self.elastic_tensor_1.clarke_thermalcond(self.structure))
# Cahill
self.assertAlmostEqual(
0.37896275,
self.elastic_tensor_1.cahill_thermalcond(self.structure))
# Debye
self.assertAlmostEqual(
247.3058931,
self.elastic_tensor_1.debye_temperature(self.structure))
self.assertAlmostEqual(
189.05670205,
self.elastic_tensor_1.debye_temperature_gibbs(self.structure))
def test_new(self):
self.assertArrayAlmostEqual(self.elastic_tensor_1,
ElasticTensor(self.ft))
nonsymm = self.ft
nonsymm[0, 1, 2, 2] += 1.0
with warnings.catch_warnings(record=True) as w:
ElasticTensor(nonsymm)
self.assertEqual(len(w), 1)
badtensor1 = np.zeros((3, 3, 3))
badtensor2 = np.zeros((3, 3, 3, 2))
self.assertRaises(ValueError, ElasticTensor, badtensor1)
self.assertRaises(ValueError, ElasticTensor, badtensor2)
def test_from_strain_stress_list(self):
strain_list = [
Strain.from_deformation(def_matrix)
for def_matrix in self.def_stress_dict['deformations']
]
stress_list = [stress for stress in self.def_stress_dict['stresses']]
with warnings.catch_warnings(record=True):
et_fl = -0.1 * ElasticTensor.from_strain_stress_list(
strain_list, stress_list).voigt
self.assertArrayAlmostEqual(
et_fl.round(2),
[[59.29, 24.36, 22.46, 0, 0, 0], [
28.06, 56.91, 22.46, 0, 0, 0
], [28.06, 25.98, 54.67, 0, 0, 0], [0, 0, 0, 26.35, 0, 0],
[0, 0, 0, 0, 26.35, 0], [0, 0, 0, 0, 0, 26.35]])
def test_from_stress_dict(self):
stress_dict = dict(
list(
zip([
IndependentStrain(def_matrix)
for def_matrix in self.def_stress_dict['deformations']
], [
Stress(stress_matrix)
for stress_matrix in self.def_stress_dict['stresses']
])))
minimal_sd = {
k: v
for k, v in stress_dict.items()
if (abs(k[k.independent_deformation] - 0.015) < 1e-10
or abs(k[k.independent_deformation] - 0.01005) < 1e-10)
}
with warnings.catch_warnings(record=True):
et_from_sd = ElasticTensor.from_stress_dict(stress_dict)
et_from_minimal_sd = ElasticTensor.from_stress_dict(minimal_sd)
self.assertArrayAlmostEqual(et_from_sd.voigt_symmetrized.round(2),
self.elastic_tensor_1)
self.assertAlmostEqual(50.63394169, et_from_minimal_sd[0, 0, 0, 0])
def test_energy_density(self):
film_elac = ElasticTensor.from_voigt(
[[324.32, 187.3, 170.92, 0., 0., 0.],
[187.3, 324.32, 170.92, 0., 0., 0.],
[170.92, 170.92, 408.41, 0., 0., 0.],
[0., 0., 0., 150.73, 0., 0.], [0., 0., 0., 0., 150.73, 0.],
[0., 0., 0., 0., 0., 238.74]])
dfm = Deformation([[-9.86004855e-01, 2.27539582e-01, -4.64426035e-17],
[-2.47802121e-01, -9.91208483e-01, -7.58675185e-17],
[-6.12323400e-17, -6.12323400e-17, 1.00000000e+00]])
self.assertAlmostEqual(
film_elac.energy_density(dfm.green_lagrange_strain),
0.000125664672793)
film_elac.energy_density(
Strain.from_deformation([[0.99774738, 0.11520994, -0.],
[-0.11520994, 0.99774738, 0.],
[
-0.,
-0.,
1.,
]]))
@unittest.skipIf(not sympy, "sympy not present, skipping toec_fit test")
def test_toec_fit(self):
with open(os.path.join(test_dir, 'test_toec_data.json')) as f:
toec_dict = json.load(f)
strains = [Strain(sm) for sm in toec_dict['strains']]
pk_stresses = [Stress(d) for d in toec_dict['pk_stresses']]
reduced = [(strain, pks) for strain, pks in zip(strains, pk_stresses)
if not (abs(abs(strain) - 0.05) < 1e-10).any()]
with warnings.catch_warnings(record=True) as w:
c2, c3 = toec_fit(strains,
pk_stresses,
eq_stress=toec_dict["eq_stress"])
self.assertArrayAlmostEqual(c2.voigt, toec_dict["C2_raw"])
self.assertArrayAlmostEqual(c3.voigt, toec_dict["C3_raw"])
# Try with reduced data set
r_strains, r_pk_stresses = zip(*reduced)
c2_red, c3_red = toec_fit(r_strains,
r_pk_stresses,
eq_stress=toec_dict["eq_stress"])
self.assertArrayAlmostEqual(c2, c2_red, decimal=0)
self.assertArrayAlmostEqual(c3, c3_red, decimal=-1)
class ElasticTensorTest(PymatgenTest):
def setUp(self):
self.voigt_1 = [[59.33, 28.08, 28.08, 0, 0, 0],
[28.08, 59.31, 28.07, 0, 0, 0],
[28.08, 28.07, 59.32, 0, 0, 0],
[0, 0, 0, 26.35, 0, 0],
[0, 0, 0, 0, 26.35, 0],
[0, 0, 0, 0, 0, 26.35]]
mat = np.random.randn(6, 6)
mat = mat + np.transpose(mat)
self.rand_elastic_tensor = ElasticTensor.from_voigt(mat)
self.ft = np.array([[[[59.33, 0, 0],
[0, 28.08, 0],
[0, 0, 28.08]],
[[0, 26.35, 0],
[26.35, 0, 0],
[0, 0, 0]],
[[0, 0, 26.35],
[0, 0, 0],
[26.35, 0, 0]]],
[[[0, 26.35, 0],
[26.35, 0, 0],
[0, 0, 0]],
[[28.08, 0, 0],
[0, 59.31, 0],
[0, 0, 28.07]],
[[0, 0, 0],
[0, 0, 26.35],
[0, 26.35, 0]]],
[[[0, 0, 26.35],
[0, 0, 0],
[26.35, 0, 0]],
[[0, 0, 0],
[0, 0, 26.35],
[0, 26.35, 0]],
[[28.08, 0, 0],
[0, 28.07, 0],
[0, 0, 59.32]]]])
self.elastic_tensor_1 = ElasticTensor(self.ft)
filepath = os.path.join(test_dir, 'Sn_def_stress.json')
with open(filepath) as f:
self.def_stress_dict = json.load(f)
self.structure = self.get_structure("Sn")
warnings.simplefilter("always")
def test_properties(self):
# compliance tensor
self.assertArrayAlmostEqual(np.linalg.inv(self.elastic_tensor_1.voigt),
self.elastic_tensor_1.compliance_tensor)
# KG average properties
self.assertAlmostEqual(38.49111111111, self.elastic_tensor_1.k_voigt)
self.assertAlmostEqual(22.05866666666, self.elastic_tensor_1.g_voigt)
self.assertAlmostEqual(38.49110945133, self.elastic_tensor_1.k_reuss)
self.assertAlmostEqual(20.67146635306, self.elastic_tensor_1.g_reuss)
self.assertAlmostEqual(38.49111028122, self.elastic_tensor_1.k_vrh)
self.assertAlmostEqual(21.36506650986, self.elastic_tensor_1.g_vrh)
self.assertArrayAlmostEqual(self.elastic_tensor_1.kg_average,
[38.49111111111,
22.05866666666,
38.49110945133,
20.67146635306,
38.49111028122,
21.36506650986])
# universal anisotropy
self.assertAlmostEqual(0.33553509658699,
self.elastic_tensor_1.universal_anisotropy)
# homogeneous poisson
self.assertAlmostEqual(0.26579965576472,
self.elastic_tensor_1.homogeneous_poisson)
# voigt notation tensor
self.assertArrayAlmostEqual(self.elastic_tensor_1.voigt,
self.voigt_1)
# young's modulus
self.assertAlmostEqual(54087787667.160583,
self.elastic_tensor_1.y_mod)
def test_structure_based_methods(self):
# trans_velocity
self.assertAlmostEqual(1996.35019877,
self.elastic_tensor_1.trans_v(self.structure))
# long_velocity
self.assertAlmostEqual(3534.68123832,
self.elastic_tensor_1.long_v(self.structure))
# Snyder properties
self.assertAlmostEqual(18.06127074,
self.elastic_tensor_1.snyder_ac(self.structure))
self.assertAlmostEqual(0.18937465,
self.elastic_tensor_1.snyder_opt(self.structure))
self.assertAlmostEqual(18.25064540,
self.elastic_tensor_1.snyder_total(self.structure))
# Clarke
self.assertAlmostEqual(0.3450307,
self.elastic_tensor_1.clarke_thermalcond(self.structure))
# Cahill
self.assertAlmostEqual(0.37896275,
self.elastic_tensor_1.cahill_thermalcond(self.structure))
# Debye
self.assertAlmostEqual(247.3058931,
self.elastic_tensor_1.debye_temperature(self.structure))
self.assertAlmostEqual(189.05670205,
self.elastic_tensor_1.debye_temperature_gibbs(self.structure))
def test_new(self):
self.assertArrayAlmostEqual(self.elastic_tensor_1,
ElasticTensor(self.ft))
nonsymm = self.ft
nonsymm[0, 1, 2, 2] += 1.0
with warnings.catch_warnings(record=True) as w:
ElasticTensor(nonsymm)
self.assertEqual(len(w), 1)
badtensor1 = np.zeros((3, 3, 3))
badtensor2 = np.zeros((3, 3, 3, 2))
self.assertRaises(ValueError, ElasticTensor, badtensor1)
self.assertRaises(ValueError, ElasticTensor, badtensor2)
def test_from_strain_stress_list(self):
strain_list = [Strain.from_deformation(def_matrix)
for def_matrix in self.def_stress_dict['deformations']]
stress_list = [stress for stress in self.def_stress_dict['stresses']]
with warnings.catch_warnings(record=True):
et_fl = -0.1*ElasticTensor.from_strain_stress_list(strain_list,
stress_list).voigt
self.assertArrayAlmostEqual(et_fl.round(2),
[[59.29, 24.36, 22.46, 0, 0, 0],
[28.06, 56.91, 22.46, 0, 0, 0],
[28.06, 25.98, 54.67, 0, 0, 0],
[0, 0, 0, 26.35, 0, 0],
[0, 0, 0, 0, 26.35, 0],
[0, 0, 0, 0, 0, 26.35]])
def test_from_stress_dict(self):
stress_dict = dict(list(zip([IndependentStrain(def_matrix) for def_matrix
in self.def_stress_dict['deformations']],
[Stress(stress_matrix) for stress_matrix
in self.def_stress_dict['stresses']])))
with warnings.catch_warnings(record = True):
et_from_sd = ElasticTensor.from_stress_dict(stress_dict)
self.assertArrayAlmostEqual(et_from_sd.voigt_symmetrized.round(2),
self.elastic_tensor_1)
def test_energy_density(self):
film_elac = ElasticTensor.from_voigt([
[324.32, 187.3, 170.92, 0., 0., 0.],
[187.3, 324.32, 170.92, 0., 0., 0.],
[170.92, 170.92, 408.41, 0., 0., 0.],
[0., 0., 0., 150.73, 0., 0.],
[0., 0., 0., 0., 150.73, 0.],
[0., 0., 0., 0., 0., 238.74]])
dfm = Deformation([[ -9.86004855e-01,2.27539582e-01,-4.64426035e-17],
[ -2.47802121e-01,-9.91208483e-01,-7.58675185e-17],
[ -6.12323400e-17,-6.12323400e-17,1.00000000e+00]])
self.assertAlmostEqual(film_elac.energy_density(dfm.green_lagrange_strain),
0.000125664672793)
