Selection of error indicators influencing adaptive remeshing

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.

The following topics are discussed:

Error indicator characteristics
Which fields exist and are of interest
The nature of the loading

Error indicator characteristics

Error indicator output variables provide estimates of solution accuracy (see Error Indicator Output). 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 About adaptive remeshing and Solution-based mesh sizing). 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?), 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 1 lists the error indicator variables applicable to adaptive remeshing and indicates whether they record the solution history.

Table 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 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.

Figure 1. Proportional-loading, linear-response example: small deflection of a cantilever.

Monotonic response example

Figure 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.

Figure 2. Monotonic response example: large deflection of a cantilever.

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. 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.

General response example

Figure 3 illustrates a case where the loading characteristics change dramatically during the analysis.

Figure 3. General response example: block subjected to a rigid indenter.

Your choice of error indicator in this case will depend on the material model. The element energy density error indicator, ENDENERI, will account for the complexity of load history (and lead to an adapted mesh that provides an accurate solution through the analysis) regardless of the material type. If plastic deformation occurs, you also have the option to use the equivalent plastic strain, PEEQERI, or plastic strain, PEERI, error indicators. Plastic strain and the plastic strain error indicator generally do not capture history effects; for example, they do not account for peak straining in models undergoing symmetric strain reversals. This example, however, involves no strain reversals; therefore, PEERI would be a valid error indicator choice.

General multistep response example: die forming and springback

Figure 4 illustrates a further generalization of a general response. Here, a forming operation is simulated, and different steps are used for different stages of the operation.

Figure 4. General multistep response example.

In this case the response of the model varies from step to step. You will typically want the error indicator to capture the extreme of the model's response to the load history adequately. However, you do not know if any particular increment captures this extreme. Therefore, you should select an error indicator variable that records the solution history.