Output And Postprocessing

Sources. custom_strategies/custom_convergencecriterias/base_mortar_criteria.h (gidio_debug), mortar_and_criteria.h (table, condition number), python_scripts/search_base_process.py and alm_contact_process.py (debug_mode), the variables header; thesis §4.3.3.5 (Fig. 4.18), §4.3.4.4 (Fig. 4.23), §4.5.6 (energy conservation, Fig. 4.64).

Contact results available on the nodes

On the pair conditions of ComputingContact the flags ACTIVE, SLIP, RIGID and MODIFIED are also available; the conditions themselves carry no result variables.

Writing the results

VTK (vtk_output_process)

"output_processes" : {
    "vtk_output" : [{
        "python_module" : "vtk_output_process",
        "kratos_module" : "KratosMultiphysics",
        "process_name"  : "VtkOutputProcess",
        "Parameters"    : {
            "model_part_name"                    : "Structure",
            "output_control_type"                : "step",
            "output_interval"                    : 1,
            "file_format"                        : "binary",
            "output_path"                        : "vtk_output",
            "nodal_solution_step_data_variables" : ["DISPLACEMENT", "REACTION", "NORMAL", "LAGRANGE_MULTIPLIER_CONTACT_PRESSURE", "WEIGHTED_GAP"],
            "nodal_data_value_variables"         : ["AUGMENTED_NORMAL_CONTACT_PRESSURE", "NORMAL_GAP", "NODAL_H"],
            "nodal_flags"                        : ["ACTIVE", "SLAVE", "MASTER"],
            "gauss_point_variables_in_elements"  : ["VON_MISES_STRESS"]
        }
    }]
}

For frictional cases replace the multiplier by VECTOR_LAGRANGE_MULTIPLIER, add WEIGHTED_SLIP to the historical list, AUGMENTED_TANGENT_CONTACT_PRESSURE to the non-historical list and SLIP to the flags. output_sub_model_parts: true writes the Contact and ComputingContact sub-model-parts separately, which is convenient to inspect the interface alone.

GiD (gid_output_process)

The test cases keep a GiD block (as _output_processes, disabled by the leading underscore) that can be reused directly:

"nodal_results"               : ["DISPLACEMENT", "NORMAL", "REACTION", "LAGRANGE_MULTIPLIER_CONTACT_PRESSURE", "WEIGHTED_GAP"],
"nodal_nonhistorical_results" : ["AUGMENTED_NORMAL_CONTACT_PRESSURE"],
"nodal_flags_results"         : ["ACTIVE", "SLAVE"],
"gauss_point_results"         : ["VON_MISES_STRESS", "PK2_STRESS_TENSOR"]

The pair conditions of ComputingContact are written with the mesh; with clear_inactive_for_post (default true) the inactive pairs are removed before the output step so that only the current active interface appears.

JSON output / checks

json_output_process and from_json_check_result_process (Kratos core) work with the contact variables as with any other; the test suite uses them with "historical_value": false for AUGMENTED_NORMAL_CONTACT_PRESSURE (see the _json_output_process blocks of the test parameter files and Test suite reference).

Reading the convergence table

With fancy_convergence_criterion (default) every Newton iteration prints one row of a table built by MortarAndConvergenceCriteria (TABLE_UTILITY). Frictionless ALM example (from the tutorial):

CONVERGENCE CHECK	STEP: 1	TIME: 5.0050e-01	DELTA TIME: 5.0050e-01
|ITER|  DP RATIO|  EXP. RAT|       ABS|  EXP. ABS|  LM RATIO|  EXP. RAT|       ABS|  EXP. ABS|    CONVERGENCE|ACTIVE SET CONV|
|   1| 1.000E+00| 1.000E-04| 1.882E-07| 1.000E-09| 1.000E+00| 1.000E-04| 1.988E-06| 1.000E-09|   Not achieved|   Not achieved|
|   4| 4.167E-06| 1.000E-04| 7.842E-13| 1.000E-09| 2.606E-05| 1.000E-04| 5.180E-11| 1.000E-09|       Achieved|       Achieved|

The step is converged only when all columns are achieved in the same iteration (thesis Algorithms 2 and 3). The thesis shows the same tables in Figs. 4.18 (frictionless) and 4.23 (frictional):

Figure: convergence table of a frictionless contact step as printed by Kratos (thesis Fig. 4.18).

Figure: convergence table of a frictional contact step with the two active-set columns (thesis Fig. 4.23).

Typical patterns: a multiplier ratio that grows in the first iterations while ACTIVE SET CONV is Not achieved is normal (nodes entering or leaving contact); a table that alternates Achieved / Not achieved in the active-set column for many iterations indicates chattering (see Tips and troubleshooting); once the set is fixed the ratios should drop quadratically.

Debug outputs

Post-processing recipes

Contact pressure. Plot AUGMENTED_NORMAL_CONTACT_PRESSURE (negative = compression). If you need the multiplier itself, remember the scaling: pressure \(=\) SCALE_FACTOR \(\times\) LAGRANGE_MULTIPLIER_CONTACT_PRESSURE (or \(\times\,\mathbf{n}\cdot\)VECTOR_LAGRANGE_MULTIPLIER). The scale factor is printed at start-up and stored in ProcessInfo[SCALE_FACTOR].

Resultant contact force. Either sum the REACTION of a fixed body, or integrate the pressure on the slave side:

import KratosMultiphysics as KM
import KratosMultiphysics.ContactStructuralMechanicsApplication as CSMA
contact = model["Structure.Contact"]
force = sum(n.GetValue(KM.NODAL_AREA) * n.GetValue(CSMA.AUGMENTED_NORMAL_CONTACT_PRESSURE)
            for n in contact.Nodes if n.Is(KM.SLAVE) and n.Is(KM.ACTIVE))

(NODAL_AREA is filled by the explicit contribution of the mortar conditions on the slave nodes.)

Contact area / half-width. Count or locate the ACTIVE slave nodes, or integrate NODAL_AREA over them.

Gap history. WEIGHTED_GAP keeps its previous value in buffer position 1 (GetSolutionStepValue(WEIGHTED_GAP, 1)), which is how ComputeDynamicFactorProcess measures the approach velocity of the surfaces.

Energy conservation (dynamics). The thesis checks the formulation on a cylinder bouncing inside a ring (§4.5.6): the total energy must stay constant apart from the contact impulses. With compute_dynamic_factor and an implicit scheme the displacement and energy evolution follow the analytical solution:

Figure: displacement and energy evolution of the energy-conservation test compared with the analytical solution (thesis Fig. 4.64).

The kinetic and strain energies can be obtained with the StructuralMechanicsApplication utilities (EnergyCalculationUtilities) or from the STRAIN_ENERGY / KINETIC_ENERGY element results; the work of the contact tractions is \(\sum\) AUGMENTED_NORMAL_CONTACT_PRESSURE \(\times\) NODAL_AREA \(\times\) gap increment on the slave nodes.

Comparing with an analytical solution. See the tutorial for a complete example (Hertz pressure distribution) and Benchmarks for the reference solutions of every thesis example.

Thesis figures © Vicente Mataix Ferrándiz, PhD thesis “Innovative mathematical and numerical models for studying the deformation of shells during industrial forming processes with the Finite Element Method”, UPC 2020, reproduced by the author. Figures marked “inspired by” are the author’s redrawings of the cited sources.