If the nonlinear run stops before reaching the required factored load, you have not shown a converged solution for that load. For an elastic-plastic assessment, solver convergence is not the same as mesh convergence: it means the solver found an equilibrium solution for the load step under its nonlinear solution criteria. Read the load-step and convergence records first; a von Mises stress plot alone does not establish acceptance.
Read a failed run from its last converged load step
Check the analysis log before refining the mesh or changing the material curve. Identify the last load step or increment that converged, the target factored load, and whether the solver stopped because it could not converge or because the run reached its prescribed end.
| What you see | What to check next |
|---|---|
| The run ends before the factored load. | Read the solver message and load-step history. Determine whether equilibrium iterations failed, a step limit was reached, or the model terminated for another stated reason. |
| The run reaches the target and reports convergence. | Confirm that the converged result corresponds to the required load combination and factor, and that the result is a valid equilibrium solution for the modeled constraints. |
| Stress spikes appear at a restraint, sharp corner, or load application. | Check whether the peak is a local singularity or a modeling artifact. Do not use a stress peak by itself to decide elastic-plastic acceptance. |
| Reported von Mises stress exceeds the defined yield stress in an elastic-perfectly-plastic model. | Check whether the displayed value is extrapolated or averaged at nodes, or read directly at material integration points. Then inspect the material definition and solver formulation. |
Do not spend the first troubleshooting pass trying to make every stress contour smooth. Plasticity changes the relevant interpretation: strains, load-step equilibrium, and the solver's convergence record matter more than an isolated stress maximum.
Separate equilibrium convergence from mesh convergence
In a nonlinear finite-element solve, the solver advances the applied load through increments or substeps and iterates toward equilibrium at each one. Convergence means the solver's current solution satisfies its numerical convergence tests, such as the residual or correction criteria configured in that solver. Use the software's solution status and iteration log to establish what happened at each step.
Mesh convergence asks a different question: whether a chosen result changes materially as the mesh is refined. The fact that a finer mesh changes a stress result does not by itself mean the nonlinear solver failed to converge. Likewise, a solver's convergence message does not prove that the mesh, boundary conditions, material curve, or acceptance assessment is correct.
When the code procedure asks whether the analysis converges to a statically permissible solution, follow the applicable Code assessment procedure and the solver's load-step record. Do not substitute a visual judgment of contour smoothness for that decision. The required load factor and acceptance checks depend on the applicable Code provisions and analysis case.
Use strain and load history to interpret plastic response
After yielding, stress no longer serves as a simple pass/fail indicator in the way it does for a linear-elastic assessment. Plastic strain accumulates as the model follows its specified stress-strain response; at factored loads, calculated strains can be theoretical and can extend far along the input curve. Read equivalent plastic strain with the corresponding load step and load factor, not as an isolated color plot.
A concentrated plastic-strain region can point to a local stress concentration or a singularity. Determine whether it affects the assessment required by the Code before changing the model. A singular stress at an idealized sharp feature may have little effect on the overall elastic-plastic result, but that does not excuse a failed solve or establish acceptance on its own.
Keep the two analysis methods distinct. The evidence identifies 1.5 × S as the effective yield stress used in Limit Load Analysis for Protection Against Plastic Collapse under Section VIII, Division 2, paragraph 5.2.3.5, Step 3. That limit-load value is not a default yield stress to insert into the elastic-plastic material curve. For the elastic-plastic model, use the material curve and yield definition required by the applicable Code procedure and the solver's constitutive model.
Run the assessment in a controlled sequence
-
Confirm the governing route. Identify the applicable Code division, edition, assessment route, load case, and required factor. One described Division 1 application used Appendix
46-4(c)(1)(-c)with a factor of3.5; treat that as specific to that application, not a universal factor. - Check the material input. Verify that the stress-strain data follows the applicable Annex 3-D requirements and the solver's input convention. Many nonlinear material interfaces request true stress against plastic strain, with elastic behavior defined separately; if the interface requests total strain instead, follow that definition and the solver documentation. Do not mix total-strain and plastic-strain columns.
- Check model setup before solving. Review loads, restraints, contacts if modeled, units, and material assignment. Confirm that supports constrain rigid-body motion without unintentionally preventing the deformation the assessment is intended to evaluate.
- Apply the required load history and factor. Use the load sequence prescribed by the assessment procedure. Record the applied load level for every converged increment and the point at which the solver reports failure or termination.
- Read convergence evidence. Inspect the solver's convergence status and iteration history at the target load. If it stops early, use the stated failure reason to troubleshoot; do not label the target load converged because lower increments succeeded.
- Evaluate the required acceptance quantities. Use the applicable Code criteria and examine strains and other required outputs at the specified load level. Do not infer Code acceptance solely from a von Mises plot or from the fact that the analysis completed.
Check stress-strain and yield definitions before changing the mesh
For a material model based on an elastic-perfectly-plastic response, the idealized constitutive behavior has no post-yield hardening. A stress value above the defined yield in a displayed contour deserves investigation, but the contour's display processing matters. Finite-element software can extrapolate integration-point results to nodes and average them for plotting; those displayed nodal values may not match the unaveraged integration-point values used by the constitutive calculation.
Compare unaveraged integration-point results with the solver's material response and check the yield surface and flow-rule settings. The exact labels and controls vary by software. If integration-point values themselves exceed the expected response, inspect the input curve format, units, elastic modulus, yield definition, and solver's plasticity formulation before concluding that the result is an interpolation artifact.
Do not use mesh refinement to mask an incorrect constitutive definition. Conversely, do not dismiss a nonconverged increment as a harmless singularity without checking the log and the effect of that region on the required assessment.
Verify the result and avoid common false fixes
For a usable result, verify the analysis reached the required factored load with a solver-reported converged solution, confirm the load and material definitions, and review the Code-prescribed acceptance quantities. If the solver does not converge, determine whether the cause is a modeling issue, an unsuitable increment strategy, or difficult nonlinear response; any adjustment must still represent the intended physical model and Code procedure.
- Waste of time: equating a smooth stress plot or an unchanged stress contour after mesh refinement with nonlinear convergence.
-
Waste of time: applying the Limit Load value
1.5 × Sas the elastic-plastic curve's yield stress without a Code basis. - Waste of time: treating completion of a run, without checking its last converged load, as proof the target factor was achieved.
- Useful check: compare solver status, increment history, unaveraged stresses, equivalent plastic strain, and the required assessment outputs at the same load step.
Stop changing solver tolerances or material data when the changes no longer correspond to the documented model and procedure. If the log does not explain convergence failure, or the stress response conflicts with the defined constitutive model at integration points, preserve the model, input curve, and solver log and escalate to the software's official support channel or a qualified pressure-vessel design authority.
Frequently asked questions
What happens if the solver converges but the mesh is not refined?
The solver has met its nonlinear convergence tests for that increment, but mesh adequacy remains a separate question. Check mesh sensitivity for the quantities required by the Code assessment rather than treating refinement as the definition of convergence.
What happens if von Mises stress exceeds yield in an elastic-perfectly-plastic model?
First check whether the plot shows nodally extrapolated or averaged stresses; compare with unaveraged integration-point results. If integration-point values still conflict with the defined model response, inspect the material input and solver formulation.
What happens if my material curve uses plastic strain instead of total strain?
Use the strain measure the material interface requests. If it requests plastic strain, do not enter total strain values; verify how the solver defines elastic behavior and yield separately.
What happens if the analysis will not converge at the factored load?
Use the solver log to identify the last converged increment and its stated failure reason, then check loads, restraints, material input, and nonlinear solution settings. Stop and escalate with the model and log if the cause remains unclear or results contradict the constitutive response.