Overcoming Convergence Issues in Abaqus Welding Simulations: A Troubleshooting Guide

1. Systematic Diagnosis: Identifying the Failure Point

When a welding simulation diverges, the first step is to isolate where in the thermomechanical process the failure occurs. Check the .msg, .dat, and .sta files in this order:

1. .msg file: Scan for ***ERROR or ***WARNING near the last increment. Key phrases: “too many attempts,” “time increment required is less than minimum,” “negative eigenvalues.”
2. .sta file: Identify the step and increment where the time increment collapses. A sudden drop to 1E-10 indicates severe instability.
3. .dat file: Look for “zero pivot” warnings, which often point to unconstrained rigid body motion or over-constraint.

Convergence failures in welding simulations typically stem from three sources: material instability at high temperatures, severe distortion causing mesh/contact issues, or numerical ill-conditioning from extreme gradients.

2. Problem 1: Material Instability and Excessive Plastic Flow

The most common cause: material properties become too weak at elevated temperatures, leading to uncontrolled deformation.

2.1. Symptom Pattern

• Failure occurs during the heating phase, often at the first significant temperature rise.
• .msg file shows “excessive distortion at a large number of nodes.”
• Plastic strain (PEEQ) in the weld zone exceeds 1.0 unrealistically early.

2.2. Corrective Actions

Implement a Temperature-Dependent Yield Stress Floor:
In your material definition, ensure yield stress does not drop below a physically realistic value, even above solidus temperature.

fortran

*Plastic, hardening=ISOTROPIC
  450.0, 0.0      ! 20°C
  80.0, 0.0, 800.0
  5.0, 0.0, 1400.0   ! <-- Too low - CAUSES INSTABILITY

See more: Linking Abaqus with Fortran Compiler: step-by-step guide

Change to:

fortran

  25.0, 0.0, 1400.0  ! Minimum yield stress (MPa) for molten material
  25.0, 0.2, 1450.0  ! Small hardening even in "liquid-like" state

Introduce Viscoplastic Regularization:
Add a *CREEP definition with a very small time exponent to provide rate dependence and stabilize the formulation.

*Creep, law=time
  1.0E-5, 1.0, 0.0  ! A, n, m - Small 'A' adds minimal rate effect

This transforms the problem from perfect plasticity to viscoplasticity, often allowing convergence without significantly affecting residual stress results.

Switch to Abaqus/Explicit for the Heating Phase:
For extremely rapid heating (laser welding), use Explicit for the transient heating phase, then import results as a predefined field into a Standard analysis for cooling.

*Transfer, results

3. Problem 2: Contact and Severe Distortion Issues

Contact changes status (open/closed) rapidly during thermal expansion and contraction, causing discontinuities.

3.1. Symptom Pattern

• Convergence fails during cooling or after solidification.
• “Severe discontinuity iterations” appear in .msg.
• Reaction forces oscillate wildly between increments.

3.2. Corrective Actions

Adjust Contact Formulation:
Change from “hard” contact to a softened contact formulation with stabilization.

*Surface Interaction, name=SOFTENED
*Contact
*Contact Stabilization, viscous damping=0.01  ! Adds small damping force
*Contact Controls, stabilize

For fixture contact, use a “softened” exponential pressure-overclosure:

*Surface Behavior, exponential
  1.0, 0.1  ! Nominal pressure, Decay distance

Implement Incremental Constraint Application:
Instead of instantly applying all fixtures, ramp them using an amplitude.

*Amplitude, name=RAMP_UP
  0.0, 0.0, 1.0, 1.0
*Boundary, amplitude=RAMP_UP
  FIXTURE_NODES, 1, 1, 0.0

Refine Mesh at Contact Interfaces:
Use biased meshing to ensure at least 3-4 elements across the contact width in the HAZ.

4. Problem 3: Numerical Ill-Conditioning and Hourglassing

Extreme thermal gradients combined with coarse meshing can lead to zero-energy modes or ill-conditioned stiffness matrices.

4.1. Symptom Pattern

• “Zero pivot” warnings for specific degrees of freedom.
• Hourglass energy (ALLAE) exceeds 10% of internal energy (ALLIE).
• Distortion patterns show “checkerboarding” or unnatural deformation modes.

4.2. Corrective Actions

Enhanced Hourglass Control for Reduced Integration Elements:
If using C3D8R elements (common for efficiency), activate enhanced hourglass control.

*Solid Section, elset=WELD_REGION, hourglass=ENHANCED

Alternatively, switch to incompatible mode elements (C3D8I) in the weld zone, which resist hourglassing naturally but increase cost.

Apply Selective Subcycling:
Use *CONTROLS,PARAMETERS=FIELD to apply smaller time increments only in regions of high temperature gradient.

*Controls, parameters=field
  0.25, 0.75  ! More conservative field variable scaling

Improve Mesh Design:
Maintain element aspect ratio < 10:1 in the HAZ. For the moving heat source, element size should be ≤ 1/3 of the heat source radius (b or c from Goldak model).

5. Advanced Stabilization Techniques

5.1. Artificial Damping for Quasi-Static Analyses

For sequentially coupled analyses where inertia is negligible but stability is problematic:

*Static, stabilize=0.0002, allsdtol=0.05
  0.01, 1.0, 1e-08, 0.1

The stabilize parameter introduces a small viscous damping force proportional to the displacement rate. Monitor the dissipated energy (ALLSD) in the .sta file—it should be < 1% of internal energy (ALLIE).

5.2. Adaptive Remeshing Workaround

While Abaqus/Standard doesn’t have adaptive remeshing, you can manually implement a form:

1. Run analysis until distortion becomes severe (but before divergence).
2. Export deformed mesh and state variables (*RESTART, WRITE).
3. Import deformed geometry as new mesh, mapping results via *IMPORT.
4. Continue analysis.

5.3. Material State Regularization via User Subroutine

In a UMAT or VUMAT, add a small strain-rate dependence to the plastic flow rule even for static analyses:

fortran code:

      if (dtime .gt. 0.0) then
        effRate = dplas/dtime
        sigY = sigY0 * (1.0 + 0.001*(effRate/1.0)**0.1)  ! Minimal rate effect
      endif

6. Step-by-Step Debugging Protocol

When faced with a non-converging model, follow this sequence:

1. Run a Thermal-Only Check: Disable mechanical response and verify the temperature field is stable and physically reasonable.
2. Isolate the Step: If using multiple steps (heating, cooling, clamp removal), run them individually to identify which causes failure.
3. Simplify the Model:
   • Replace complex material with linear elastic, temperature-independent properties.
   • Remove all contact, replacing with tied constraints.
   • If it converges, reintroduce complexity incrementally.
4. Monitor Key Variables: Use *MONITOR to track temperature, displacement, and reaction force at critical nodes during the solve.
5. Extreme Increment Control: For the problematic step, set extremely conservative increments:text*Static 1E-5, 1E-10, 1E-5, 0.01 ! Initial, Min, Max, Total step time

7. Prevention: Best Practices in Model Setup

7.1. Material Property Definition

• Ensure smooth transitions in temperature-dependent properties—use *SMOOTH STEP or spline interpolation in user subroutines.
• Always include thermal expansion coefficients; omitting them creates artificial stress constraints.
• For steels, implement phase transformation effects gradually via field variables rather than step changes.

7.2. Load and Boundary Condition Application

• Apply thermal loads via *DFLUX with a smooth start-up amplitude to avoid thermal shock.
• Use *RAMP amplitude over first 0.1% of step time for mechanical loads.
• Never fix all DOFs of a surface; use coupling constraints or reference points instead.

7.3. Solver Settings for Welding

*CONTROLS, ANALYSIS=DISCONTINUOUS
*CONTROLS, PARAMETERS=TIME INCREMENTATION
  15, 20, , , , 10, 8, 20  ! I1-I8: More aggressive cutbacks allowed

These settings tell Abaqus to expect severe nonlinearities and to be more aggressive with time increment management.

8. Conclusion: Building Robust Welding Simulations

Convergence in welding simulations is not merely a numerical challenge—it’s a test of how well the computational model represents physical reality. The most robust solutions come from combining physically realistic material modeling (avoiding non-physical softness), appropriate numerical stabilization (damping, regularization), and incremental complexity in model development.

When standard techniques fail, consider hybrid approaches: run the violent heating phase in Explicit, use Arbitrary Lagrangian-Eulerian (ALE) methods for severe deformation available in Abaqus/Explicit with CEL, or decompose the problem into smaller, manageable domains via submodeling.

The ultimate validation of any convergence “fix” is that it should not significantly alter the final mechanical results—residual stresses and distortions should remain within the expected physical range and, ideally, match experimental validation data. Document all stabilization parameters used, as they become part of the methodological chain of evidence for your simulation’s credibility.