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Abaqus/CAE to create the model and the remeshing rules. A second script allows you to submit the adaptivity process and to view the changing mesh as Abaqus/CAE computes new element sizes.
Example: stress riser
Figure 12.3.1–2 shows how adaptive remeshing generates a high-quality mesh for a typical notched specimen subjected to axial loading.
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original mesh adapted mesh
Figure 12.3.1–2 Stress riser mesh before and after refinement.
Figure 12.3.1–3 shows the effect of these mesh changes on solution accuracy in comparison to the effect of uniform mesh refinement on solution accuracy. Adaptive mesh refinement is much more efficient than uniform mesh refinement at reducing solution error.
Example: plastic hinge
This example, a doubly-notched specimen axially strained until a plastic hinge or band forms, is used to demonstrate how adaptive remeshing will focus a mesh on a plastic hinge. It illustrates the value of adaptive remeshing in cases where the region of interest may not be known a priori. Figure 12.3.1–4 shows the specimen and the region of active yielding. Figure 12.3.1–5 shows the original mesh and the adapted mesh after three adaptive remeshing iterations.
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| Number of elements | Normalized Error in Peak Stress |
|---|---|
| 0 | 0.1 |
| 250 | 0.01 |
| 500 | 0.005 |
| 750 | 0.01 |
| 1500 | 0.005 |
Figure 12.3.1–3 Comparison of adaptive remeshing to uniform mesh refinement based on boundary seeding.
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Pure diagram of a rectangular channel with a shaded central region, no text or symbols present
Figure 12.3.1–4 Region of active yielding in a doubly-notched specimen.
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| Mesh Type | PEEQ (kavg) |
|---|---|
| original mesh | +4.500e-01 |
| adapted mesh | +0.000e+00 |
Figure 12.3.1–5 Mesh of doubly-notched specimen before and after adaptive remeshing.
Preparing your model for adaptive remeshing
You use Abaqus/CAE to do the following when performing adaptive remeshing:
• create the model and specify the boundary conditions and loading history,
• create remeshing rules,
• create an adaptivity process, and
• start and monitor the progress of the adaptivity process.
Creating the model
You do not have to consider adaptive remeshing when you create the model and specify the boundary conditions and loading history; however, before using adaptive remeshing you must do the following:
• create the geometry of the model—you cannot use an orphan mesh part—and
• provide an initial, nominal, mesh. This mesh can be fairly coarse. Providing an extremely coarse mesh, however, can result in more adaptive remesh iterations due to the poor quality of early remesh iteration error indicator calculations. You can, in typical cases, define a reasonable initial mesh by using the default part instance mesh seeding in Abaqus/CAE.
Creating a remeshing rule
You create and configure a remeshing rule using the Mesh module in Abaqus/CAE. See “Creating a remeshing rule,” Section 17.21.1 of the Abaqus/CAE User’s Guide, for details on defining remesh rules. Refer to “Selection of error indicators influencing adaptive remeshing,” Section 12.3.2, and “Solutionbased mesh sizing,” Section 12.3.3, for details on the methods used to determine revised mesh size distributions.
Abaqus/CAE Usage: Mesh module: Adaptivity→Remeshing Rule→Create
Creating an adaptivity process
You create and configure an adaptivity process using the Job module in Abaqus/CAE. When you create an adaptivity process, you can specify the maximum number of remesh iterations to be performed and set various system resource parameters. See “Creating, editing, and manipulating jobs,” Section 19.7 of the Abaqus/CAE User’s Guide, for details.
Abaqus/CAE Usage: Job module: Adaptivity→Create
Performing adaptive remeshing with a provisional analysis
In some cases you will want to determine an adequate mesh for your model prior to conducting a fully detailed analysis, which might include many steps and complex behavior. A “provisional” analysis can often be used, along with adaptive remeshing, to efficiently determine a good mesh for a model. The provisional analysis may include various simplifications of your fully detailed analyis, such as
• replacing your steps with a single linear perturbation step with loading that adequately reflects your more general loading cases,
• removing plasticity and other material nonlinearities, and
• disabling geometric nonlinearity.
The provisional analysis approach may result in a mesh that is not ideally suited to your ultimate choice of loading. However, the cost for obtaining a mesh from a provisional model may be significantly lower than the case where your adaptivity process considers all of the complexity in the fully detailed analysis, and you may find the refined mesh adequate for use in a variety of analysis situations.
Special considerations
In general, the Abaqus adaptive remeshing process iterates automatically toward a better quality mesh; however, you should be aware of certain considerations.
Singularities
Stress singularities frequently result from geometric abstractions, such as reentrant corners and contact of a sharp edge in elastic materials, and from point loads or abruptly ended distributed load regions. In these situations the stress field near the singularity is unbounded, and no amount of mesh refinement will enable resolution of the correct solution. If you apply the adaptive remeshing process to regions of your
model that include singularities, the process will drive elements near the singularity to very small sizes. The end result may be unacceptably expensive analyses.
You can prevent excessively expensive analyses of models with singularities using the following techniques:
• Exclude the region of the singularity from consideration in the remeshing process. You exclude a region by partitioning the model and assigning remeshing rules only to regions away from the singularity.
• Apply a minimum element size constraint in the remeshing rule. Abaqus/CAE does assign a minimum element size by default, which is a fraction of the default part instance mesh seed. You can modify this constraint to achieve a quality solution near the singularity while avoiding an excessively refined mesh. You can also use the remeshing rule to control the rate at which Abaqus/CAE refines the size of the elements. Element size constraints may prevent an adaptivity process from achieving specified error indicator targets.
• Specify a maximum number of elements for a remeshing rule region. Abaqus/CAE adjusts the mesh sizing such that the generated total number of elements approximately satisfies this constraint.
Convergence issues
Figure 12.3.1–6 shows a typical history of an error indicator and the computational cost, in Abaqus/Standard, versus remesh iteration.
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| Remesh Iteration | Error Indicator | Computational Cost |
|---|---|---|
| 1 | 50% | 1x |
| 2 | ~25% | 2x |
| 3 | ~20% | 2x |
| 4 | ~20% | 3x |
Figure 12.3.1–6 Error indicator and computational cost versus iteration for a model with a 25% error indicator target.
The example in Figure 12.3.1–6 shows a desirable convergence profile. The solution error indicator decreases monotonically and quickly to the desired 25% error indicator target. Accompanying this error indicator decrease is a moderate increase in computational cost, measured either in model degrees of freedom or time in Abaqus/Standard. Certain situations can interfere with this desirable convergence profile, as follows:
• If your initial mesh is too coarse, the error indicator variables may be of insufficient quality to result in a mesh that is sufficiently improved in the next iteration. The adaptive remeshing process typically creates a high-quality mesh eventually even if the initial mesh is quite coarse. However, some mesh iterations can be avoided with a reasonably refined initial mesh.
• Minimum element size constraints and constraints on the maximum number of elements that you specify when creating the remeshing rule can prevent the mesh from achieving sufficient refinement (in the extreme case of singularities this will always be the case) to satisfy your error indicator targets. You may be able to satisfy your targets by relaxing these constraints; for example, by decreasing the minimum element size. For more information, see “What are remeshing rules?,” Section 17.13.1 of the Abaqus/CAE User’s Guide.
• In addition to producing small mesh sizes resulting in a large number of elements, singularities can cause an adaptivity process to fail in achieving the error target or to require more remeshing iterations. As described in “Singularities,” above, you can control the computational cost by specifying a minimum element size constraint or the maximum number of elements. In any case where a singularity exists within a remeshing rule region, you may see poor convergence in the error indicator results.
• Linear elements (C3D4, CPS4, etc.) and modified elements (C3D10M, CPS6M, etc.) converge slowly compared to quadratic elements (C3D10, CPS6, etc.) requiring a relatively large number of elements to achieve a given error target. Hence, you should use quadratic elements whenever possible.
Continuing a stopped adaptive remeshing process
The adaptive remeshing process is designed to be automatic—Abaqus/CAE performs a sequence of analyses as it continues to refine your mesh. However, there are occasions where the process will stop and you will want to continue adaptive remeshing from your most recent mesh:
• when you want to change remeshing rules for later remesh iterations, or
• when the adaptive remesh process fails to complete due to machine resource problems.
You can continue the adaptive remeshing process by resubmitting an existing adaptivity process, creating and submitting a new adaptivity process, or performing manual remeshing. See “Manually resizing and remeshing,” Section 17.21.6 of the Abaqus/CAE User’s Guide.
Limitations
Adaptive remeshing requires the use of Abaqus/CAE, and only Abaqus/Standard procedures are supported. Other specific limitations also apply.
Element types
Abaqus/CAE can perform adaptive remeshing only with elements of the following shapes (see “Which mesh controls can I use with adaptive remeshing?,” Section 17.13.2 of the Abaqus/CAE User’s Guide):
• Planar continuum triangles and quadrilaterals
• Shell triangles and quadrilaterals
• Tetrahedrals
Procedures
Abaqus/CAE can perform remeshing with the following Abaqus/Standard procedures:
• “Static stress analysis,” Section 6.2.2 (general and linear perturbation).
• “Quasi-static analysis,” Section 6.2.5.
• “Uncoupled heat transfer analysis,” Section 6.5.2.
• “Fully coupled thermal-stress analysis,” Section 6.5.3.
• “Coupled thermal-electrical analysis,” Section 6.7.3.
• “Coupled pore fluid diffusion and stress analysis,” Section 6.8.1.
12.3.2 SELECTION OF ERROR INDICATORS INFLUENCING ADAPTIVE REMESHING
Products: Abaqus/Standard Abaqus/CAE
References
• “Error indicator output,” Section 4.1.4
• “Adaptive remeshing: overview,” Section 12.3.1
• “Abaqus/Standard output variable identifiers,” Section 4.2.1
• *CONTACT OUTPUT
• *ELEMENT OUTPUT
• “Understanding adaptive remeshing,” Section 17.13 of the Abaqus/CAE User’s Guide
• “Controlling adaptive remeshing,” Section 17.21 of the Abaqus/CAE User’s Guide
Overview
Your selection of which error indicator variables to use in adaptive remeshing rules for a particular analysis should take into consideration:
• characteristics of the error indicator variables;
• which fields exist and are of interest; and
• the nature of the loading.
Error indicator characteristics
Error indicator output variables provide estimates of solution accuracy (see “Error indicator output,” Section 4.1.4). In the context of adaptive remeshing, error indicators help determine where the mesh should be refined or coarsened to achieve the specified accuracy targets (see “Adaptive remeshing: overview,” Section 12.3.1 and “Solution-based mesh sizing,” Section 12.3.3). This Section discusses additional characteristics of error indicators in the context of how well-suited they are for influencing adaptive remeshing in various analysis types.
Which fields exist and are of interest
Certain variables apply naturally to certain types of analyses. For example, the heat flux indicator (HFLERI) is used in analyses with temperature degrees of freedom. When selecting error indicator variables in the Remeshing Rule editor in Abaqus/CAE (see “What are remeshing rules?,” Section 17.13.1 of the Abaqus/CAE User’s Guide), your choices will be restricted to variables available for the selected procedure type.
The nature of the loading
Some error indicator variables only indicate discretization error at the current analysis time—the particular increment in a step. Other error indicator variables provide a record of the solution history
up to the current analysis time. For example, if your simulation involves non-proportional loading or a significantly nonlinear response, you will typically see better adaptive remeshing results when using error indicator variables that record the solution history. Table 12.3.2–1 lists the error indicator variables applicable to adaptive remeshing and indicates whether they record the solution history.
Table 12.3.2–1 Error indicator variables applicable to adaptive remeshing that record the solution history.
| Solution Quantity | Error indicator variable ( $c_e$ ) | Records the solution history? |
| Element energy density | ENDENERI | Yes |
| Mises stress | MISESERI | No |
| Equivalent plastic strain | PEEQERI | Yes |
| Plastic strain | PEERI | No |
| Creep strain | CEERI | No |
| Heat flux | HFLERI | No |
| Electric flux | EFLERI | No |
| Electric potential gradient | EPGERI | No |
By default, when you create a remeshing rule, error indicators are specified for the final increment of the final step of your analysis and adaptive remeshing is based on error indicators in this final increment. When you select an error indicator that records the solution history, this default error indicator specification is appropriate for almost all analyses. However, for other error indicator variables that do not record the solution history, you may find it appropriate (for multistep cases with non-proportional loading, for example) to define mutiple remeshing rules for the same region, with each rule applied to a different step.
The examples that follow provide simple illustrations of typical cases and show appropriate choices of error indicator output variables.
Linear response example
Figure 12.3.2–1 illustrates the simplest load case, where the load is proportional to the step time and the model’s response is linear. In this case the solution at the final increment would be proportional to any other increment. Therefore, it is appropriate to base the remeshing on the value of the error indicator in the last increment for any choice of error indicator variable.
Monotonic response example
Figure 12.3.2–2 illustrates a more general case, where the model has a nonlinear response—in this case resulting from a geometric nonlinearity—and the loading is monotonic but not generally proportional to the step time. The response of the model is slightly more general because the solution at a particular increment is not proportional to the solution at the final increment. However, the value of the error indicator output in the final increment still reflects the extreme of the model’s response to the load history.