Phase-Field#

Input Class#

Input: Phase-Field#

class phasefieldx.Element.Phase_Field.Input.Input(l=1.0, save_solution_xdmf=False, save_solution_vtu=True, results_folder_name='results')[source]#

Bases: object

Class for managing phase-field simulation parameters.

This class encapsulates parameters related to phase-field fracture simulations and provides methods for setting, logging, and exporting these parameters.

Attributes:

lfloat: Length scale parameter.
save_solution_xdmfbool: Indicates whether to save solutions in XDMF format.
save_solution_vtubool: Indicates whether to save solutions in VTU format.
results_folder_namestr: Name of the folder to save simulation results.

Methods

__init__(l=1.0, save_solution_xdmf=False, save_solution_vtu=True, results_folder_name=”results”)	Initialize the Input class with default parameters.
save_log_info(logger)	Log the simulation parameters using the provided logger.
save_parameters_to_csv(filename=”parameters.input”)	Save the simulation parameters to a two-column text file (tab-separated) for easy loading with pandas.
__str__()	Return a string representation of the simulation parameters.

save_log_info(logger)[source]#

Log the simulation parameters using the provided logger.

Parameters:: logger: An instance of a logging object.

save_parameters_to_csv(filename='parameters.input')[source]#

Save the simulation parameters to a CSV file for easy loading with pandas.

Parameters:: filename (str): The name of the CSV file to save the parameters.

Solver#

Solver: Phase-field#

phasefieldx.Element.Phase_Field.solver.solver.solve(Data, msh, final_time, V_Φ, bc_list_phi=[], update_boundary_conditions=None, update_loading=None, ds_bound=None, dt=1.0, path=None, quadrature_degree=2, case='AT2', V_gradient_Φ=None)[source]#

Solver for phase-field problems.

Parameters:

Dataphasefieldx.Data: Data object containing simulation parameters.
mshdolfinx.cpp.mesh.Mesh: Mesh object defining the computational domain.
final_timefloat: Final pseudo time for the simulation.
V_Φdolfinx.fem.FunctionSpace: Function space for the phase field variable Φ.
bc_list_philist of dolfinx.fem.DirichletBC, optional: List of Dirichlet boundary conditions for Φ (default is []).
update_boundary_conditionsfunction, optional: Function to update boundary conditions based on time (default is None).
update_loadingfunction, optional: Function to update external loading conditions based on time and spatial coordinates (default is None).
ds_boundnumpy.ndarray, optional: Array containing boundary descriptions for reaction forces (default is None).
dtfloat, optional: Time step size (default is 1.0).
pathstr, optional: Path to store simulation results (default is current working directory).
quadrature_degreeint, optional: Quadrature degree for numerical integration (default is 2).

Returns:

None

Notes

This function initializes and solves the phase-field problem for the given phase-field variable Φ, updating it over the specified time period using a Newton-type solver. It logs simulation progress, saves results, and manages output using Paraview-compatible formats.

Examples

# Initialize Data, msh, V_Φ, bc_list_phi, and optionally update functions solve(Data, msh, 10.0, V_Φ, bc_list_phi, update_boundary_conditions, update_loading)

# This will simulate the phase-field evolution in time, saving results in the current directory.

Energy#

phasefieldx.Element.Phase_Field.energy.calculate_crack_surface_energy(Φ, l, comm, case='AT2', dx=Measure('cell', subdomain_id='everywhere'))[source]#

Calculates the total crack surface energy in a phase-field model.

This function computes the integral of the crack surface energy density functional, which regularizes a sharp crack over a finite width. The functional is expressed as:

Ψ_c = ∫_Ω [ (1 / (c₀ * l)) * w(Φ) + (l / c₀) * |∇Φ|² ] dΩ

where w(Φ) is the geometric crack function (e.g., Φ² for the AT2 model, Φ for the AT1 model), l is the length scale parameter, and Φ is the phase-field variable. The calculation is performed in parallel using the provided MPI communicator.

Φdolfinx.fem.Function: The phase-field variable, representing the crack state.
lfloat: The length scale parameter, controlling the regularization width.
commmpi4py.MPI.Comm: The MPI communicator for parallel computation.
casestr, optional: The phase-field model type, which determines the geometric crack function. Common values are ‘AT1’ or ‘AT2’. Defaults to ‘AT2’.
dxufl.Measure, optional: The UFL integration measure over the domain. Defaults to ufl.dx.
tuple[float, float, float]: A tuple containing: - The total crack surface energy (scalar value). - The contribution from the geometric crack function term. - The contribution from the phase-field gradient term.

Geometric Crack#

Geometric Crack functions#

phasefieldx.Element.Phase_Field.geometric_crack.geometric_crack_coefficient(case='AT2')[source]#

Returns the geometric coefficient c_w for the crack surface density function.

This coefficient ensures that the integral of the dissipation function w(phi) over the crack length equals 1.

Parameters:

casestr, optional: The phase-field model. Supported values are ‘AT2’, ‘AT1’, ‘Wu’, ‘DOUBLE’. Default is ‘AT2’.

Returns:

float: The geometric coefficient.

phasefieldx.Element.Phase_Field.geometric_crack.geometric_crack_function(phi, case='AT2')[source]#

Computes the geometric function alpha(phi) for various phase-field models.

Parameters:

phifloat or array_like: Phase-field variable.
casestr, optional: The phase-field model. Supported values are ‘AT2’, ‘AT1’, ‘WU’, ‘DOUBLE’. Default is ‘AT2’.

Returns:

float or array_like: The value of the geometric function.

phasefieldx.Element.Phase_Field.geometric_crack.geometric_crack_function_derivative(phi, case='AT2')[source]#

Computes the derivative of the geometric function, alpha’(phi).

Parameters:

phifloat or array_like: Phase-field variable.
casestr, optional: The phase-field model. Supported values are ‘AT2’, ‘AT1’, ‘WU’, ‘DOUBLE’. Default is ‘AT2’.

Returns:

float or array_like: The derivative of the geometric function.