def test_convert_strain_to_deformation(self):
strain = Tensor(np.random.random((3, 3))).symmetrized
while not (np.linalg.eigvals(strain) > 0).all():
strain = Tensor(np.random.random((3, 3))).symmetrized
upper = convert_strain_to_deformation(strain, shape="upper")
symm = convert_strain_to_deformation(strain, shape="symmetric")
self.assertArrayAlmostEqual(np.triu(upper), upper)
self.assertTrue(Tensor(symm).is_symmetric())
for defo in upper, symm:
self.assertArrayAlmostEqual(defo.green_lagrange_strain, strain)
def get_symmetric_wallace_tensor(self, tau):
"""
Gets the symmetrized wallace tensor for determining
yield strength criteria.
Args:
tau (3x3 array-like): stress at which to evaluate
the wallace tensor.
"""
wallace = self.get_wallace_tensor(tau)
return Tensor(0.5 * (wallace + np.transpose(wallace, [2, 3, 0, 1])))
def process_item(self, item):
"""
Process the tasks and materials into a dielectrics collection
Args:
item dict: a dict of material_id, structure, and tasks
Returns:
dict: a dieletrics dictionary
"""
def poly(matrix):
diags = np.diagonal(matrix)
return np.prod(diags) / np.sum(
np.prod(comb) for comb in combinations(diags, 2))
d = {self.dielectric.key: item[self.materials.key]}
structure = Structure.from_dict(item["structure"])
if item.get("dielectric", False):
ionic = Tensor(
item["dielectric"]["ionic"]).symmetrized.fit_to_structure(
structure).convert_to_ieee(structure)
static = Tensor(
item["dielectric"]["static"]).symmetrized.fit_to_structure(
structure).convert_to_ieee(structure)
total = ionic + static
d["dielectric"] = {
"total": total,
"ionic": ionic,
"static": static,
"e_total": poly(total),
"e_ionic": poly(ionic),
"e_static": poly(static)
}
sga = SpacegroupAnalyzer(structure)
# Update piezo if non_centrosymmetric
if item.get("piezo", False) and not sga.is_laue():
static = PiezoTensor.from_voigt(np.array(
item['piezo']["static"])).symmetrized.fit_to_structure(
structure).convert_to_ieee(structure).voigt
ionic = PiezoTensor.from_voigt(np.array(
item['piezo']["ionic"])).symmetrized.fit_to_structure(
structure).convert_to_ieee(structure).voigt
total = ionic + static
directions, charges, strains = np.linalg.svd(total)
max_index = np.argmax(np.abs(charges))
d["piezo"] = {
"total": total,
"ionic": ionic,
"static": static,
"e_ij_max": charges[max_index],
"max_direction": directions[max_index],
"strain_for_max": strains[max_index]
}
if len(d) > 1:
return d
return None
def process_item(self, item):
"""
Process the tasks and materials into a dielectrics collection
Args:
item dict: a dict of material_id, structure, and tasks
Returns:
dict: a dieletrics dictionary
"""
def poly(matrix):
diags = np.diagonal(matrix)
return np.prod(diags) / np.sum(
np.prod(comb) for comb in combinations(diags, 2))
d = {"material_id": item["material_id"]}
structure = Structure.from_dict(item["structure"])
if item.get("dielectric") is not None:
ionic = Tensor(d["dielectric"]["ionic"])
static = Tensor(d["dielectric"]["static"])
total = ionic + static
d["dielectric"] = {
"total":
total.symmetrized.fit_to_structure(structure).convert_to_ieee(
structure),
"ionic":
ionic.symmetrized.fit_to_structure(structure).convert_to_ieee(
structure),
"static":
static.symmetrized.fit_to_structure(structure).convert_to_ieee(
structure),
"e_total":
poly(total),
"e_ionic":
poly(ionic),
"e_static":
poly(static)
}
# Update piezo if non_centrosymmetric
if item.get("piezo") is not None:
static = PiezoTensor.from_voigt(
np.array(item['piezo']["piezo_tensor"]))
ionic = PiezoTensor.from_voigt(
np.array(item['piezo']["piezo_ionic_tensor"]))
total = ionic + static
d["piezo"] = {
"total":
total.symmetrized.fit_to_structure(structure).convert_to_ieee(
structure).voigt,
"ionic":
ionic.symmetrized.fit_to_structure(structure).convert_to_ieee(
structure).voigt,
"static":
static.symmetrized.fit_to_structure(structure).convert_to_ieee(
structure).voigt,
"e_ij_max":
np.max(total.voigt)
}
# TODO Add in more analysis: v_max ?
# TODO: Add in unstable phonon mode analysis of piezoelectric for potentially ferroelectric
if len(d) > 1:
return d
return None