Published on May 22nd, 2018 | by özgün


Submodeling with Boundary Contact Surfaces

Calculating localized peak stresses used in determining fatigue life can be very computationally expensive with large complex finite element models.  When including the fidelity of mesh needed to capture the local stress concentration, the global model often becomes either impossible to solve or very inefficient.  This scenario is particularly a problem for nonlinear analyses, where often, numerous contact surfaces require a very large number of analysis iterations.

Engineers often turn to submodeling as a means of obtaining detailed stresses using an independent finite element model.  The submodel’s displacement boundary conditions are extracted from the global model via displacement interpolations and the submodel is solved as an independent simulation.  In general, one should avoid having the submodel intersect with a contact region, but often this can be geometrically challenging.  This post shows that it is possible to use the submodeling procedure where the cut boundary displacements cut through a nonlinear contact surface, provided the analyst carefully follows the methodology outlined herein.

Figure 1, above, illustrates the demonstration global model, where a nonlinear contact surface extends along the entire pipe-flange external boundary.  Successful submodeling requires a 5 step procedure as outlined below to be successful when contact is present on the cut boundary.

1)  Build and analyze the global model:

a.  The global model mesh must be fine enough to capture the global stiffness with a reasonable representation of the displacement response throughout.  For contact submodeling, extra attention should be given to assure that a fine enough mesh is in place along the boundary where the contact cut-boundary edges will occur.  If the global model mesh is too coarse, artificial stress concentrations will occur in the submodel at the boundary contact interface.

b.  Be sure to store the displacement history for all load and substeps in the global analysis results file, such that a consistent set of incremental submodel displacement files can be created.

c.  In most cases, I would suggest activating large deflections to assure that any contact gaps are accurately computed in both models.

d.  Solve the global analysis and postprocess to determine peak stress areas and areas of relatively low stress gradients.  The low stress areas are ideal locations where the submodel geometry boundaries can be formed.  Make sure that if the boundary contact region includes a partially open connection so that there are enough elements along the boundary to provide a reasonable prediction of transition from open to closed contact.

2)  Build the submodel:

a.  The independent submodel region geometry boundaries should be located away from the areas where peak stresses are needed.  Ideally, they should be in areas of relatively low stress gradients.  Figure 2 illustrates the submodel mesh used in the example.  In addition to matching geometry, materials and loading sequence, one must also match the contact settings (friction, stiffness controls, etc.) for the boundary contact elements.  This is key, since displacements will be imposed from the global analysis on these nodes thus the stiffness of the global and submodels must match.  Interior to the submodel, local fillets can be added if needed, but these must be far away from any boundaries.

Figure 2 – Submodel of Center Bolt Assembly with Refined Mesh
Submodel of Center Bolt Assembly with Refined Mesh | FEA Consultant

b.  Groups of nodes on the cut-boundaries should be extracted independently for each part of the assembly.  This is key to retrieving the correct interpolated displacements from the global analysis since any interpolations across the contact boundary will create errors.

3)  Interpolation of displacements from the global analysis:

a.  Interpolation of displacements from the global analysis onto the submodel boundary nodes should be performed independently for each body.  This will assure that the displacements from the adjacent part are not averaged across the contact boundary.  The node group from the submodel should be matched with the element group in the global model from which the interpolated displacement history is extracted.  Figure 3 illustrates independent displacement interpolations for each body.

Figure 3 – Example Cut Boundary Displacements Extracted from each Global Model Body Independently
Figure 3 - Example Cut Boundary Displacements Extracted from Each Global Model Body | FEA Consulting

b.  Since the contact status on the boundary may change between solution steps, it is particularly important that independent boundary displacement files be created for every load and substep of the global analysis, such that each analysis will follow the same contact status changes at the boundary.

4)  Submodel solution:

a.  The submodel load stepping response should follow the same setup as the global analysis. There are often many load steps in a complex nonlinear analyses that need to be tracked. The most accurate results are achieved when these load steps and substeps are identical in both the global and submodels. Changes in substepping, however, can sometimes be used in the submodel to enhance convergence provided consistent displacement loading interpolation is applied and there are not any sudden contact status changes on the boundary that are missed.

5)  Checking results:

a.  It is essential to validate all submodel simulations. Submodels with contact require extra diligence since getting the correct displacements and corresponding loading sequence is often challenging.

b.  Before conquering that million element solution, I would suggest one perfect the methodology on a much smaller scale such as the example solution illustrated in this blog.

c.  Artificially high stresses on the submodel boundary are the most common sign of a modeling error.

d.  Validating the contact submodel can be done in a similar manner to single part submodeling. The only difference being, in addition to inspecting the entire model all at once – checking net forces, stress paths etc. on a part by part basis should be performed. Figure 4 illustrates a comparative stress distribution in both the global and submodels in a section cut through the center of the submodel.  Notice, away from the local hot spot, the identical color bands between the global and local submodel.

Figure 4 – Global Model vs. Submodel Von Mises Stress (psi) featuring Combined Bolt Pre-Load & Internal Pressure Loading
Global Model vs. Submodel Von Mises Stress (psi) Featuring Combined Bolt Pre-Load & Internal Pressure Loading | FEA Consulting

Have you ever tried to perform submodeling where contact elements were part of the boundary?  I would welcome others experiences to this complex analysis procedure.


By: Peter Barrett from

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Researcher Solid Mechanics, Finite Element and Material Science

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