porepy.models.contact_mechanics_model module

This is a setup class for solving linear elasticity with contact mechanics governing the relative motion of fracture surfaces.

The setup handles parameters, variables and discretizations. Default (unitary-like) parameters are set.

For a description of the mathematical model, see e.g. the tutorials and the PhD thesis of Hüeber (2008): https://elib.uni-stuttgart.de/handle/11682/4854

class ContactMechanics(params=None)

Bases: AbstractModel

This is a shell class for contact mechanics problems.

Setting up such problems requires a lot of boilerplate definitions of variables, parameters and discretizations. This class is intended to provide a standardized setup, with all discretizations in place and reasonable parameter and boundary values. The intended use is to inherit from this class, and do the necessary modifications and specifications for the problem to be fully defined. The minimal adjustment needed is to specify the method create_grid().

Parameters

params (Optional[Dict]) –

displacement_variable

Name assigned to the displacement variable in the highest-dimensional subdomain. Will be used throughout the simulations, including in ParaView export.

Type

str

mortar_displacement_variable

Name assigned to the displacement variable on the fracture walls. Will be used throughout the simulations, including in ParaView export.

Type

str

contact_traction_variable

Name assigned to the variable for contact forces in the fracture. Will be used throughout the simulations, including in ParaView export.

Type

str

mechanics_parameter_key

Keyword used to define parameters and discretizations for the mechanics problem.

Type

str

friction_coupling_term

Keyword used to define parameters and discretizations for the friction problem.

Type

str

params

Dictionary of parameters used to control the solution procedure. Default parameters are set in AbstractModel

Type

dict

mdg

Mixed-dimensional grid. Should be set by a method create_grid which should be provided by the user.

Type

pp.MixedDimensionalGrid

convergence_status

Whether the non-linear iterations has converged.

Type

bool

linear_solver

Specification of linear solver. Only known permissible value is ‘direct’

Type

str

All attributes are given natural values at initialization of the class.

after_newton_convergence(solution, errors, iteration_counter)

Parameters

• solution (ndarray) –

• errors (float) –

• iteration_counter (int) –

Return type

None

after_newton_iteration(solution_vector)

Extract parts of the solution for current iterate.

The iterate solutions in d[pp.STATE][pp.ITERATE] are updated for the mortar displacements and contact traction are updated. Method is a tailored copy from assembler.distribute_variable.

Parameters

solution_vector (np.array) – solution vector for the current iterate.

Return type

None

after_simulation()

Called after a time-dependent problem

Return type

None

before_newton_iteration()

Return type

None

before_newton_loop()

Will be run before entering a Newton loop. Discretize time-dependent quantities etc.

check_convergence(solution, prev_solution, init_solution, nl_params)

Check whether the solution has converged by comparing values from the two most recent iterations.

Tailored implementation if AD is not used. Else, the generic check in AbstractModel is used.

Parameters

• solution (array) – solution of current iteration.

• solution – solution of previous iteration.

• solution – initial solution (or from beginning of time step).

• nl_params (dictionary) – assumed to have the key nl_convergence_tol whose value is a float.

• prev_solution (ndarray) –

• init_solution (ndarray) –

Return type

Tuple[float, bool, bool]

prepare_simulation()

Is run prior to a time-stepping scheme. Use this to create a (mixed-dimensional) grid, initialize variables, parameters, equations, discretizations, export for visualization, linear solvers etc.

The ordering of operations may be significant. For instance, defining initial condition before parameters allows the latter to depend on the former.

Return type

None

reconstruct_local_displacement_jump(intf, projection, from_iterate=True)

Reconstruct the displacement jump in local coordinates.

Parameters

• grid (intf represented by a mortar) –

• projection (TangentialNormalProjection) –

• pp.contact_conditions.set_projections (obtained by calling) –

• intf (MortarGrid) –

• projection –

• from_iterate (bool) –

Returns

ambient_dim x sd_l.num_cells. First 1-2 dimensions are in the tangential direction of the fracture, last dimension is normal.

Return type

(np.array)

reconstruct_stress(previous_iterate=False)

Compute the stress in the highest-dimensional grid based on the displacement states in that grid, adjacent interfaces and global boundary conditions.

The stress is stored in the data dictionary of the highest-dimensional grid, in [pp.STATE][‘stress’].

Parameters

previous_iterate (boolean, optional) – If True, use values from previous iteration to compute the stress. Defaults to False.

Return type

None

class ContactMechanicsAdObjects

Bases: object

Storage class for ad related objects.

Stored objects include variables, compound ad operators and projections.

contact_force: Variable

contact_traction: Operator

displacement: Variable

interface_displacement: Variable

internal_boundary_vector_to_outwards: Matrix

local_fracture_coord_transformation: Matrix

local_fracture_coord_transformation_normal: Matrix

mortar_projections_vector: MortarProjections

normal_component_frac: Matrix

normal_to_tangential_frac: Matrix

subdomain_projections_vector: SubdomainProjections

tangential_component_frac: Matrix