optimism.phasefield package

Subpackages

• optimism.phasefield.test package
  • Submodules
  • optimism.phasefield.test.plotPhaseFieldThresholdModel module
    • PhaseFieldThresholdUniaxialFixture
      • PhaseFieldThresholdUniaxialFixture._classSetupFailed
      • PhaseFieldThresholdUniaxialFixture._class_cleanups
      • PhaseFieldThresholdUniaxialFixture.setUp()
      • PhaseFieldThresholdUniaxialFixture.testUniaxial()
  • optimism.phasefield.test.plotSandiaModelUniaxial module
  • optimism.phasefield.test.test_PhaseFieldLorentzPlastic module
    • GradOfPlasticPhaseFieldModelFixture
      • GradOfPlasticPhaseFieldModelFixture._classSetupFailed
      • GradOfPlasticPhaseFieldModelFixture._class_cleanups
      • GradOfPlasticPhaseFieldModelFixture.setUp()
      • GradOfPlasticPhaseFieldModelFixture.test_elastic_energy()
      • GradOfPlasticPhaseFieldModelFixture.test_plastic_stress()
      • GradOfPlasticPhaseFieldModelFixture.test_rotation_invariance()
      • GradOfPlasticPhaseFieldModelFixture.test_zero_point()
  • optimism.phasefield.test.test_PhaseFieldLorentzPlasticPatch module
    • TestSingleMeshFixture
      • TestSingleMeshFixture._classSetupFailed
      • TestSingleMeshFixture._class_cleanups
      • TestSingleMeshFixture.no_test_uniaxial()
      • TestSingleMeshFixture.setUp()
      • TestSingleMeshFixture.test_constrained_hessian()
      • TestSingleMeshFixture.test_patch_test()
      • TestSingleMeshFixture.test_sparse_hessian_at_nonzero_phase()
      • TestSingleMeshFixture.test_sparse_hessian_at_zero_phase()
  • optimism.phasefield.test.test_PhaseFieldThreshold module
    • PhaseFieldThresholdModelFixture
      • PhaseFieldThresholdModelFixture._classSetupFailed
      • PhaseFieldThresholdModelFixture._class_cleanups
      • PhaseFieldThresholdModelFixture.setUp()
      • PhaseFieldThresholdModelFixture.test_rotation_invariance()
      • PhaseFieldThresholdModelFixture.test_uniaxial_energy()
      • PhaseFieldThresholdModelFixture.test_zero_point()
  • optimism.phasefield.test.test_PhaseFieldThresholdPatch module
    • TestSingleMeshFixture
      • TestSingleMeshFixture._classSetupFailed
      • TestSingleMeshFixture._class_cleanups
      • TestSingleMeshFixture.setUp()
      • TestSingleMeshFixture.test_constrained_hessian()
      • TestSingleMeshFixture.test_patch_test()
      • TestSingleMeshFixture.test_sparse_hessian_at_nonzero_phase()
      • TestSingleMeshFixture.test_sparse_hessian_at_zero_phase()
  • optimism.phasefield.test.test_PhaseFieldThresholdPlastic module
    • GradOfPlasticPhaseFieldModelFixture
      • GradOfPlasticPhaseFieldModelFixture._classSetupFailed
      • GradOfPlasticPhaseFieldModelFixture._class_cleanups
      • GradOfPlasticPhaseFieldModelFixture.no_test_plastic_strain_path()
      • GradOfPlasticPhaseFieldModelFixture.setUp()
      • GradOfPlasticPhaseFieldModelFixture.test_elastic_energy()
      • GradOfPlasticPhaseFieldModelFixture.test_plastic_stress()
      • GradOfPlasticPhaseFieldModelFixture.test_rotation_invariance()
      • GradOfPlasticPhaseFieldModelFixture.test_zero_point()
  • optimism.phasefield.test.test_PhaseFieldUniaxial module
    • PhaseFieldUniaxialFixture
      • PhaseFieldUniaxialFixture._classSetupFailed
      • PhaseFieldUniaxialFixture._class_cleanups
      • PhaseFieldUniaxialFixture.testUniaxial()
    • energy_density()
    • update()
  • Module contents

Submodules

optimism.phasefield.MaterialPointSimulator module

class optimism.phasefield.MaterialPointSimulator.MaterialPointSimulator(materialModel, maxStrain, strainRate, steps=10)

Bases: object

Generates the uniaxial response of a given phase field potential density function

The non-axial strain components are determined by minimizing the potential, which coincides with stress-free conditions for every stress component besides the uniaxial stress.

run():

Launches the simluation with the given parameters

static makeKinematics(unknowns, p)

run()

class optimism.phasefield.MaterialPointSimulator.UniaxialOutput(times, strainHistory, stressHistory, kirchhoffStressHistory, energyHistory, internalVariableHistory, phaseHistory)

Bases: tuple

_asdict()

Return a new dict which maps field names to their values.

_field_defaults = {}

_fields = ('times', 'strainHistory', 'stressHistory', 'kirchhoffStressHistory', 'energyHistory', 'internalVariableHistory', 'phaseHistory')

classmethod _make(iterable)

Make a new UniaxialOutput object from a sequence or iterable

_replace(**kwds)

Return a new UniaxialOutput object replacing specified fields with new values

energyHistory

Alias for field number 4

internalVariableHistory

Alias for field number 5

kirchhoffStressHistory

Alias for field number 3

phaseHistory

Alias for field number 6

strainHistory

Alias for field number 1

stressHistory

Alias for field number 2

times

Alias for field number 0

optimism.phasefield.PhaseField module

class optimism.phasefield.PhaseField.PhaseFieldFunctions(compute_internal_energy, compute_output_energy_densities_and_fluxes, compute_strain_energy_densities, compute_phase_potential_energy, compute_element_stiffnesses, compute_block_diagonal_element_stiffnesses, compute_initial_state, compute_updated_internal_variables, compute_constraint_hessian)

Bases: tuple

_asdict()

Return a new dict which maps field names to their values.

_field_defaults = {}

_fields = ('compute_internal_energy', 'compute_output_energy_densities_and_fluxes', 'compute_strain_energy_densities', 'compute_phase_potential_energy', 'compute_element_stiffnesses', 'compute_block_diagonal_element_stiffnesses', 'compute_initial_state', 'compute_updated_internal_variables', 'compute_constraint_hessian')

classmethod _make(iterable)

Make a new PhaseFieldFunctions object from a sequence or iterable

_replace(**kwds)

Return a new PhaseFieldFunctions object replacing specified fields with new values

compute_block_diagonal_element_stiffnesses

Alias for field number 5

compute_constraint_hessian

Alias for field number 8

compute_element_stiffnesses

Alias for field number 4

compute_initial_state

Alias for field number 6

compute_internal_energy

Alias for field number 0

compute_output_energy_densities_and_fluxes

Alias for field number 1

compute_phase_potential_energy

Alias for field number 3

compute_strain_energy_densities

Alias for field number 2

compute_updated_internal_variables

Alias for field number 7

optimism.phasefield.PhaseField._compute_block_diagonal_element_stiffnesses(U, internalVariables, dt, functionSpace, lagrangian_density, modify_element_gradient)

optimism.phasefield.PhaseField._compute_element_stiffnesses(U, internalVariables, dt, functionSpace, lagrangian_density, modify_element_gradient)

optimism.phasefield.PhaseField.axisymmetric_element_gradient_transformation(elemGrads, elemShapes, elemVols, elemNodalDofs, elemNodalCoords)

optimism.phasefield.PhaseField.axisymmetric_gradient(gradU, U, coord)

optimism.phasefield.PhaseField.compute_element_stiffness_from_global_fields(U, coords, elemInternals, dt, elemConns, elemShapes, elemShapeGrads, elemVols, lagrangian_density, modify_element_gradient)

optimism.phasefield.PhaseField.compute_phase_field_constraint_hessian(Lambda, kappa, constraint, dofManager)

Augmented Lagrange Hessian terms for lower bound constrained phase field models.

Because this is a simple bound constraint, the Hessian terms are diagonal. This function returns just this diagonal, which can be added onto the unconstrained Hessian matrix.

Note that return value is a standard numpy array (with one axis). This is so that it can be added to a sparse matrix without causing an error. Jax numpy arrays do not work with scipy sparse arrays.

Parameters:

• Lambda (array of constraint forces)

• kappa (array of penalty parameters)

• constraint (values of lower bound constraint functions) – (just unknown nodal phases)

• dofManager (dofManager object for current mesh)

Returns:

d – part of the AL Hessian

Return type:

standard numpy array with one axis representing the constraint

optimism.phasefield.PhaseField.create_phasefield_functions(functionSpace, mode2D, materialModel, pressureProjectionDegree=None)

optimism.phasefield.PhaseField.energy_density_to_lagrangian_density(energy_density)

optimism.phasefield.PhaseField.plane_strain_element_gradient_transformation(elemGrads, elemShapes, elemVols, elemNodalDofs, elemNodalCoords)

optimism.phasefield.PhaseField.plane_strain_gradient(gradU)

optimism.phasefield.PhaseField.unpack_fields_2D(U)

optimism.phasefield.PhaseField.unpack_gradients_2D(gradU)

optimism.phasefield.PhaseFieldClassic module

optimism.phasefield.PhaseFieldLorentzPlastic module

optimism.phasefield.PhaseFieldLorentzPlastic._compute_elastic_linear_strain(dispGrad, state)

optimism.phasefield.PhaseFieldLorentzPlastic._compute_elastic_logarithmic_strain(dispGrad, state)

optimism.phasefield.PhaseFieldLorentzPlastic.compute_elastic_linear_strain(dispGrad, plasticStrain)

optimism.phasefield.PhaseFieldLorentzPlastic.compute_elastic_logarithmic_strain(dispGrad, Fp)

optimism.phasefield.PhaseFieldLorentzPlastic.compute_free_energy_density(elasticStrain, phase, phaseGrad, eqps, eqpsOld, dt, props, hardeningModel)

optimism.phasefield.PhaseFieldLorentzPlastic.compute_state_increment(elasticTrialStrain, phase, stateOld, dt, props, hardeningModel)

optimism.phasefield.PhaseFieldLorentzPlastic.compute_state_new_finite_deformations(dispGrad, phase, phaseGrad, stateOld, dt, props, hardeningModel)

optimism.phasefield.PhaseFieldLorentzPlastic.compute_state_new_small_deformations(dispGrad, phase, phaseGrad, stateOld, dt, props, hardeningModel)

optimism.phasefield.PhaseFieldLorentzPlastic.create_material_model_functions(properties)

properties:

‘elastic modulus’ ‘poisson ratio’ ‘critical energy release rate’ ‘critical strain energy density’ ‘regularization length’ ‘yield strength’ ‘hardening modulus’

optimism.phasefield.PhaseFieldLorentzPlastic.degradation(phase, props)

optimism.phasefield.PhaseFieldLorentzPlastic.dr(elasticTrialStrain, eqps, eqpsOld, phase, dt, props, hardeningModel)

Jacobian of incremental_potential with respect to positional argument(s) (0, 1, 3). Takes the same arguments as incremental_potential but returns the jacobian of the output with respect to the arguments at positions (0, 1, 3).

optimism.phasefield.PhaseFieldLorentzPlastic.elastic_deviatoric_free_energy(elasticStrain, phase, props)

optimism.phasefield.PhaseFieldLorentzPlastic.elastic_volumetric_free_energy(strain, phase, props)

optimism.phasefield.PhaseFieldLorentzPlastic.energy_density_generic(elStrain, phase, phaseGrad, state, dt, props, hardeningModel, doUpdate)

optimism.phasefield.PhaseFieldLorentzPlastic.incremental_potential(elasticTrialStrain, eqps, eqpsOld, phase, dt, props, hardeningModel)

optimism.phasefield.PhaseFieldLorentzPlastic.make_initial_state_finite_deformations(shape=(1,))

optimism.phasefield.PhaseFieldLorentzPlastic.make_initial_state_small_deformations(shape=(1,))

optimism.phasefield.PhaseFieldLorentzPlastic.make_properties(E, nu, Gc, psiC, l, Y0)

optimism.phasefield.PhaseFieldLorentzPlastic.phase_potential_density(phase, gradPhase, props)

optimism.phasefield.PhaseFieldLorentzPlastic.r(elasticTrialStrain, eqps, eqpsOld, phase, dt, props, hardeningModel)

Jacobian of incremental_potential with respect to positional argument(s) 1. Takes the same arguments as incremental_potential but returns the jacobian of the output with respect to the arguments at positions 1.

optimism.phasefield.PhaseFieldLorentzPlastic.r_and_deqps(elasticTrialStrain, eqps, eqpsOld, phase, dt, props, hardeningModel)

Value and gradient of incremental_potential with respect to positional argument(s) 1. Takes the same arguments as incremental_potential but returns a two-element tuple where the first element is the value of incremental_potential and the second element is the gradient, which has the same shape as the arguments at positions 1.

optimism.phasefield.PhaseFieldLorentzPlastic.strain_energy_density(elasticStrain, phase, props)

optimism.phasefield.PhaseFieldLorentzPlastic.update_state(elasticTrialStrain, stateOld, stateNewGuess, phase, dt, props, hardeningModel)

optimism.phasefield.PhaseFieldMaterialModel module

class optimism.phasefield.PhaseFieldMaterialModel.MaterialModel(compute_energy_density, compute_output_energy_density, compute_strain_energy_density, compute_phase_potential_density, compute_initial_state, compute_state_new)

Bases: tuple

_asdict()

Return a new dict which maps field names to their values.

_field_defaults = {}

_fields = ('compute_energy_density', 'compute_output_energy_density', 'compute_strain_energy_density', 'compute_phase_potential_density', 'compute_initial_state', 'compute_state_new')

classmethod _make(iterable)

Make a new MaterialModel object from a sequence or iterable

_replace(**kwds)

Return a new MaterialModel object replacing specified fields with new values

compute_energy_density

Alias for field number 0

compute_initial_state

Alias for field number 4

compute_output_energy_density

Alias for field number 1

compute_phase_potential_density

Alias for field number 3

compute_state_new

Alias for field number 5

compute_strain_energy_density

Alias for field number 2

optimism.phasefield.PhaseFieldThreshold module

class optimism.phasefield.PhaseFieldThreshold.Properties(E, nu, mu, kappa, Gc, l)

Bases: tuple

E

Alias for field number 0

Gc

Alias for field number 4

_asdict()

Return a new dict which maps field names to their values.

_field_defaults = {}

_fields = ('E', 'nu', 'mu', 'kappa', 'Gc', 'l')

classmethod _make(iterable)

Make a new Properties object from a sequence or iterable

_replace(**kwds)

Return a new Properties object replacing specified fields with new values

kappa

Alias for field number 3

l

Alias for field number 5

mu

Alias for field number 2

nu

Alias for field number 1

optimism.phasefield.PhaseFieldThreshold.compute_linear_strain(dispGrad)

optimism.phasefield.PhaseFieldThreshold.compute_logarithmic_strain(dispGrad)

optimism.phasefield.PhaseFieldThreshold.create_material_model_functions(properties)

properties:

‘elastic modulus’: real ‘poisson ratio’: real ‘critical energy release rate’: real ‘regularization length’: real ‘kinematics’: string

Value ‘large deformations’ or ‘small deformations’

optimism.phasefield.PhaseFieldThreshold.degradation(phase)

optimism.phasefield.PhaseFieldThreshold.elastic_deviatoric_free_energy(strain, phase, props)

optimism.phasefield.PhaseFieldThreshold.elastic_volumetric_free_energy(strain, phase, props)

optimism.phasefield.PhaseFieldThreshold.energy_density(strain, phase, phaseGrad, props)

optimism.phasefield.PhaseFieldThreshold.initial_state(shape)

optimism.phasefield.PhaseFieldThreshold.make_properties(E, nu, Gc, l)

optimism.phasefield.PhaseFieldThreshold.phase_potential_density(phase, gradPhase, props)

optimism.phasefield.PhaseFieldThreshold.state_new(strain, phase, props)

optimism.phasefield.PhaseFieldThreshold.strain_energy_density(strain, phase, props)

optimism.phasefield.PhaseFieldThresholdPlastic module

class optimism.phasefield.PhaseFieldThresholdPlastic.Properties(E, nu, mu, kappa, Gc, l, Y0, H)

Bases: tuple

E

Alias for field number 0

Gc

Alias for field number 4

H

Alias for field number 7

Y0

Alias for field number 6

_asdict()

Return a new dict which maps field names to their values.

_field_defaults = {}

_fields = ('E', 'nu', 'mu', 'kappa', 'Gc', 'l', 'Y0', 'H')

classmethod _make(iterable)

Make a new Properties object from a sequence or iterable

_replace(**kwds)

Return a new Properties object replacing specified fields with new values

kappa

Alias for field number 3

l

Alias for field number 5

mu

Alias for field number 2

nu

Alias for field number 1

optimism.phasefield.PhaseFieldThresholdPlastic.compute_elastic_strain(dispGrad, state)

optimism.phasefield.PhaseFieldThresholdPlastic.compute_element_energy(compute_free_energy_density, U, state, shapeGrad, conn)

optimism.phasefield.PhaseFieldThresholdPlastic.compute_state_increment(elasticTrialStrain, phase, stateOld, props)

optimism.phasefield.PhaseFieldThresholdPlastic.compute_state_new(dispGrad, phase, phaseGrad, stateOld, props)

optimism.phasefield.PhaseFieldThresholdPlastic.compute_total_energy(compute_free_energy_density, U, states, mesh)

optimism.phasefield.PhaseFieldThresholdPlastic.degradation(phase)

optimism.phasefield.PhaseFieldThresholdPlastic.dr(elasticTrialStrain, eqps, eqpsOld, phase, props)

Jacobian of incremental_potential with respect to positional argument(s) (0, 1, 3). Takes the same arguments as incremental_potential but returns the jacobian of the output with respect to the arguments at positions (0, 1, 3).

optimism.phasefield.PhaseFieldThresholdPlastic.dr_dstrain_and_deqps(elasticTrialStrain, eqps, eqpsOld, phase, props)

Jacobian of incremental_potential with respect to positional argument(s) (0, 1). Takes the same arguments as incremental_potential but returns the jacobian of the output with respect to the arguments at positions (0, 1).

optimism.phasefield.PhaseFieldThresholdPlastic.elastic_deviatoric_free_energy(elasticStrain, phase, props)

optimism.phasefield.PhaseFieldThresholdPlastic.elastic_volumetric_free_energy(strain, phase, props)

optimism.phasefield.PhaseFieldThresholdPlastic.energy_density(dispGrad, phase, phaseGrad, state, props, doUpdate=True)

optimism.phasefield.PhaseFieldThresholdPlastic.energy_density_generic(elStrain, phase, phaseGrad, state, props, doUpdate)

optimism.phasefield.PhaseFieldThresholdPlastic.flow_stress(eqps, props)

Jacobian of hardening_energy_density with respect to positional argument(s) 0. Takes the same arguments as hardening_energy_density but returns the jacobian of the output with respect to the arguments at positions 0.

optimism.phasefield.PhaseFieldThresholdPlastic.hardening_energy_density(eqps, props)

optimism.phasefield.PhaseFieldThresholdPlastic.incremental_potential(elasticTrialStrain, eqps, eqpsOld, phase, props)

optimism.phasefield.PhaseFieldThresholdPlastic.interpolate_element_kinematics(U, shapeGrad, conn)

optimism.phasefield.PhaseFieldThresholdPlastic.interpolate_kinematics(mesh, U)

optimism.phasefield.PhaseFieldThresholdPlastic.make_initial_state(shape=(1,))

optimism.phasefield.PhaseFieldThresholdPlastic.make_properties(E, nu, Gc, l, Y0, H)

optimism.phasefield.PhaseFieldThresholdPlastic.phase_potential_density(phase, gradPhase, props)

optimism.phasefield.PhaseFieldThresholdPlastic.r(elasticTrialStrain, eqps, eqpsOld, phase, props)

Jacobian of incremental_potential with respect to positional argument(s) 1. Takes the same arguments as incremental_potential but returns the jacobian of the output with respect to the arguments at positions 1.

optimism.phasefield.PhaseFieldThresholdPlastic.r_and_deqps(elasticTrialStrain, eqps, eqpsOld, phase, props)

Value and gradient of incremental_potential with respect to positional argument(s) 1. Takes the same arguments as incremental_potential but returns a two-element tuple where the first element is the value of incremental_potential and the second element is the gradient, which has the same shape as the arguments at positions 1.

optimism.phasefield.PhaseFieldThresholdPlastic.strain_energy_density(elasticStrain, phase, props)

optimism.phasefield.PhaseFieldThresholdPlastic.update_state(elasticTrialStrain, stateOld, stateNewGuess, phase, props)

Module contents