def apply_plasticity_enr(self, mask_mesh, delta_t):
"""
Apply plasticity treatment if criterion is activated :
- compute yield stress
- tests plasticity criterion
- compute plastic strain rate for plastic cells
"""
mask = np.logical_and(self.plastic_enr_cells, mask_mesh)
if not mask.any():
return
# Right part : right part of enriched cells is plastic ? => self.plastic_enr_cells
invariant_j2_el = np.sqrt(
compute_second_invariant(self.enr_deviatoric_stress_new[mask]))
yield_stress = self.enr_yield_stress.new_value[mask]
shear_modulus = self.enr_shear_modulus.new_value[mask]
radial_return = self._compute_radial_return(invariant_j2_el,
yield_stress)
dev_stress = self._enr_deviatoric_stress_new[mask]
self._enr_plastic_strain_rate[mask] = \
self._compute_plastic_strain_rate_tensor(radial_return, shear_modulus,
delta_t, dev_stress)
self._enr_equivalent_plastic_strain_rate[mask] = \
self._compute_equivalent_plastic_strain_rate(invariant_j2_el, shear_modulus,
yield_stress, delta_t)
self._enr_deviatoric_stress_new[mask] *= radial_return[np.newaxis].T
def check_criterion(self, cells):
"""
Return the mask of the cells where the VonMises plasticity criterion is verified
:param cells: cells on which to check the criterion
:return: the mask of the cells where the VonMises plasticity criterion is verified
"""
return (compute_second_invariant(cells.deviatoric_stress_new) >
cells.yield_stress.new_value**2)
def test_apply_plastic_correction_on_enriched_deviatoric_stress_tensor(self):
"""
Test of the method apply_plastic_correction_on_enriched_deviatoric_stress_tensor
"""
deviatoric_stress_new = np.array([[5., -2.5, -2.5], ])
j2 = np.sqrt(compute_second_invariant(deviatoric_stress_new))
yield_stress = np.array([10.])
exact_deviator_plastic_right = np.array([[6.666667, -3.333333, -3.333333]])
radial_return = self.my_cells._compute_radial_return(j2, yield_stress)
deviatoric_stress_new *= radial_return[np.newaxis].T
np.testing.assert_allclose(deviatoric_stress_new, exact_deviator_plastic_right, rtol=1.e-5)
def check_criterion_on_right_part_cells(cells):
"""
Return the mask of the cells where the VonMises plasticity criterion is verified
:param cells: cells on which to check the criterion
:return: the mask of the cells where the VonMises plasticity criterion is verified
"""
if not cells.enriched.any():
return
return (compute_second_invariant(cells.enr_deviatoric_stress_new) >
cells.enr_yield_stress.new_value**2)
def test_compute_enriched_equivalent_plastic_strain_rate(self):
"""
Test of the method compute_enriched_equivalent_plastic_strain_rate
"""
dt = 1. # pylint: disable=invalid-name
exact_equivalent_plastic_strain_rate_right = np.array([0.33333333333333331])
deviatoric_stress_new = np.array([[4, -2., -2.]])
j2 = np.sqrt(compute_second_invariant(deviatoric_stress_new))
shear_modulus = np.array([4.])
yield_stress = np.array([2.])
res = self.my_cells._compute_equivalent_plastic_strain_rate(j2, shear_modulus, yield_stress, dt)
np.testing.assert_allclose(res, exact_equivalent_plastic_strain_rate_right)
def test_apply_plastic_corrector_on_deviatoric_stress_tensor(self):
"""
Test of the method apply_plastic_corrector_on_deviatoric_stress_tensor
"""
mask = np.array([True, True, False, False])
deviatoric_stress_new = np.array([[8e+9, -4e+9, -4e+9],
[5e+8, -2.5e+8, -2.5e+8],
[1.e+2, -5e+1, -5e+1],
[4e+9, -2e+9, -2e+9]])
j2 = np.sqrt(compute_second_invariant(deviatoric_stress_new))
yield_stress = np.ones(
self.nbr_cells
) * self.test_data.material_target.initial_values.yield_stress_init
radial_return = self.my_cells._compute_radial_return(j2, yield_stress)
deviatoric_stress_new[mask] *= radial_return[mask][np.newaxis].T
expected_value = np.array(
[[8.000000e+07, -4.000000e+07, -4.000000e+07],
[8.000000e+07, -4.000000e+07, -4.000000e+07],
[1.e+2, -5e+1, -5e+1], [4e+9, -2e+9, -2e+9]])
np.testing.assert_allclose(deviatoric_stress_new, expected_value)
def test_compute_equivalent_plastic_strain_rate(self):
"""
Test of the method compute_equivalent_plastic_strain_rate
"""
mask = np.array([True, True, False, False])
delta_t = 1.
deviatoric_stress = np.array([[8e+9, -4e+9, -4e+9],
[5e+8, -2.5e+8, -2.5e+8],
[1.e+2, -5e+1, -5e+1],
[4e+9, -2e+9, -2e+9]])
j2 = np.sqrt(compute_second_invariant(deviatoric_stress))
shear_modulus = np.ones(
self.nbr_cells
) * self.test_data.material_target.initial_values.shear_modulus_init
yield_stress = np.ones(
self.nbr_cells
) * self.test_data.material_target.initial_values.yield_stress_init
obtained = self.my_cells._compute_equivalent_plastic_strain_rate(
j2[mask], shear_modulus[mask], yield_stress[mask], delta_t)
np.testing.assert_allclose(obtained,
np.array([0.08301887, 0.00440252]),
rtol=1.e-5)
def apply_plasticity(self, mask, delta_t):
"""
Apply plasticity treatment if criterion is activated :
- compute yield stress
- tests plasticity criterion
- compute plastic strain rate for plastic cells
:param mask: boolean array to identify cells to be computed
:param dt: time step
"""
invariant_j2_el = np.sqrt(
compute_second_invariant(self.deviatoric_stress_new[mask, :]))
yield_stress = self.yield_stress.new_value[mask]
shear_modulus = self.shear_modulus.new_value[mask]
radial_return = self._compute_radial_return(invariant_j2_el,
yield_stress)
dev_stress = self.deviatoric_stress_new[mask]
self._plastic_strain_rate[
mask] = self._compute_plastic_strain_rate_tensor(
radial_return, shear_modulus, delta_t, dev_stress)
self._equivalent_plastic_strain_rate[
mask] = self._compute_equivalent_plastic_strain_rate(
invariant_j2_el, shear_modulus, yield_stress, delta_t)
self._deviatoric_stress_new[mask] *= radial_return[np.newaxis].T