Defining Adaptive Mesh Refinement in the Eulerian Domain

In a traditional Eulerian analysis the topology of the Eulerian mesh does not change during the analysis. Although the Eulerian mesh motion feature allows the Eulerian mesh to move in space to cover areas of interest, its ability to create a nonuniformly refined mesh that changes with time is limited. The adaptive mesh refinement feature can locally refine the mesh by subdividing elements identified by user-defined criteria. This refinement can be removed automatically during the analysis once the criteria are no longer satisfied. This feature offers great savings in computational cost compared to a uniformly refined mesh. See Impact of a copper rod for an example of using the adaptive mesh refinement feature.

In some cases Eulerian material may penetrate through the Lagrangian contact surface, which could result in the leakage of liquid or gas through the Lagrangian contact surface. To prevent this, an enhanced contact formulation is available to improve the contact between the Eulerian material and the Lagrangian contact surface. This enhanced contact formulation is more expensive than the default contact algorithm and should be activated only when required.

You can independently activate adaptive mesh refinement for each Eulerian section in a model. The feature applies to all the elements specified in the element set; all the elements in the element set have to be in the same Eulerian section.

You can activate the enhanced contact formulation for an Eulerian domain. However, if you use the enhanced contact formulation, you cannot specify adaptive mesh refinement criteria.

When adaptive mesh refinement occurs, elements are added to the Eulerian mesh. You can limit how many elements can be created by specifying an upper bound ratio of added elements to original elements. The default value of this upper bound ratio is 8.0 if you deactivate the enhanced contact formulation, and the default value is 1.0 if you activate the enhanced contact formulation. When you activate the enhanced contact formulation, Abaqus/Explicit adds elements along the Eulerian-Lagrangian interface only if they are needed. You can reduce the computational cost of the analysis by limiting how many elements are created.

With one level of refinement, each time a user-defined Eulerian element is refined, it is equally divided into eight subelements. These subelements can subsequently be divided again if you allow two levels of refinement and so forth. You can set a limit on the maximum number of levels of refinement. The default maximum level is one. This setting is relevant only when you deactivate the enhanced contact formulation.

You can specify whether refinement can be removed when the refinement criteria are no longer met. This setting is relevant only when the enhanced contact formulation is deactivated.

You must specify at least one refinement criterion unless the enhanced contact formulation is activated. An element will be selected for refinement if any of the criteria is met. To reduce the numerical artifacts at the mesh transition boundaries (where a fine mesh meets a coarse mesh), the elements adjacent to the selected elements are also refined. The elements are coarsened once the refinement criteria are no longer met. Each selected element can be refined or coarsened by only one level in every increment. Table 1 lists all the refinement criteria available in Abaqus/Explicit.

Table 1. Refinement criteria.

Refinement criterion description	Refinement criterion label	User-specified values
Refine elements containing material interfaces	VF	N/A
Refine elements that are in contact with Lagrangian bodies	CONT	You can specify the value ALL to refine all elements intersecting the Lagrangian surfaces even if contact has not occurred; using this option avoids frequent refining and coarsening with chattering contact. You can also specify the value MAT to refine only elements containing materials that are in contact with the Lagrangian surfaces. If no values are specified, MAT will be used except for materials with Mie-Grüneisen equations of state.
Refine elements in which significant plastic deformation occurs. Not supported for the critical state (clay) plasticity model.	PEEQ	Critical value of the equivalent plastic strain
Refine elements near a sharp density gradient	DENSITY	You can specify two values for this criterion. The first value is the critical value of the density gradient, computed as the ratio between the change of density across element faces and the density of the material inside the element; the second value is the critical density. For an element to be selected, both the density and the density gradient must exceed the critical value.
Refine elements near a sharp pressure gradient	PRESS	You can specify two values for this criterion. The first value is the critical value of the pressure gradient, computed as the ratio between the change of pressure across element faces and the pressure of the material inside the element; the second value is the critical pressure. For an element to be selected, both the pressure and the pressure gradient must exceed the critical value.

When adaptive mesh refinement is specified in an Eulerian section that is involved in general contact, dynamic seeding is activated by default. Dynamic seeding allows more seeds to be created once the Eulerian elements near a Lagrangian face are refined; these seeds will be deleted once these Eulerian elements are coarsened.

Dynamic seeding can also be useful for Eulerian analyses with no adaptive mesh refinement.

You cannot apply adaptive mesh refinement on elements where Eulerian mesh motion is also applied.