Field Mapper

A field is a physics quantity that spans a numerical domain. The numerical domain can be a set of discrete points associated with a body, a surface on a body, or the volume of a body. In Abaqus discrete points are represented by a node set, a surface domain is represented by a surface definition, and a volume domain is represented by an element set. The field mapper maps fields between domains with dissimilar mesh topologies.

The field mapper supports mapping between similar domain types (point-to-point, surface-to-surface, and volume-to-volume) and mapping between points-to-surfaces and points-to-volume. Mapping involving points limits the mapping algorithms that you can use because no underlying region topology exists and insufficient information is available to accurately interpolate and integrate the fields.

A field is categorized as either extensive or intensive based on the physics properties. For extensive fields, the amount of matter within the body determines the field values. Typically, these are integrated values over the surface or volume of the body. Examples of extensive fields include forces, heat fluxes, and masses, which define a total quantity. For intensive fields, the amount of matter within the body does not influence the field values. Examples of intensive fields include pressure, surface heat flux density, and mass density, which are quantities defined per unit area or volume. Displacement, velocity, and temperature are also examples of intensive fields because these fields do not depend on the amount of matter within the body. The field mapper provides conservative integration techniques for mapping intensive to extensive fields; for example, mapping of a traction field to nodal forces.

Fields can be evaluated at nodes, at the center of surface facets, or at the center or integration points of elements. It is best to evaluate fields where they are computed by the solver because they are most accurate at those locations. For example, stresses in a finite element analysis are most accurate at the integration points where they are computed, while stresses can also exist at nodes for output purposes. However, the stresses at the nodes are extrapolated quantities, and they might subsequently be averaged between adjacent elements before writing output to a results file. For co-simulation, Abaqus always selects the appropriate location to evaluate fields. In a sequential analysis, you must ensure that fields are written at the appropriate locations to the results file in the previous analysis.

When coupling physics to solve a multiphysics or multiscale simulation, you must consider whether the numerical domains overlap or abut to define the domain coupling type. Domain coupling types include point coupling, surface coupling, and volume coupling.

• Point coupling is coupling that occurs at discrete locations associated with a body. An example of point coupling is coupling Abaqus with a one-dimensional (1D) reduced-order model. In this case, the points of the 1D model must correspond with the co-located nodes in the Abaqus model.
• Surface coupling involves distinct domains where fields are exchanged and mapped across a common interface. An example of surface coupling is a fluid-structure simulation, where the fluid and solid domains are distinct, and fields are exchanged and mapped across the interface surface where the fluid and solid adjoin.
• Volume coupling involves domains that overlap and fields that are exchanged and mapped over the volume of a body. An example of volume coupling is a sequential thermal-stress simulation; the temperature field within the body causes thermal expansion, and the thermal and stress domains overlap.

Select the domain coupling type (point, surface, or volume) independent of where the field is evaluated. For example, in a sequential thermal-stress analysis, you should define the volume of the body by providing an element set, although temperature is evaluated at nodes. By specifying a volume, the mapper uses the topology information to provide accurate mapping. If you select points to represent the domain, the mapper uses a less accurate point-cloud algorithm.

Mapping operations consist of two parts:

• a search where an association is made between members (nodes, elements, or integration points) of the source and target meshes; and
• a calculation where field values are transferred from the source to the target meshes using interpolation and integration algorithms.

The search algorithm establishes a one-to-one association between members of the source and target meshes. How such an association is formed and whether members of interest are searched on the source or target mesh depends on the mapping algorithm (see Mapping Algorithms). When coupling surface domains, the surface normal is used to distinguish which faces (SPOS or SNEG) are abutting. The search is performed such that the surface normals of the source and target regions are facing each other.

For discussion purposes, a mapping category defines a set of similar mapping operations performed when mapping a field from the source mesh to the target mesh. The field's physics properties (intensive or extensive) and the location at which it is evaluated define the category (see Table 1). Within a mapping category, there might be one or more algorithms from which you can select.

Four mapping algorithm categories are described below. To simplify the discussion, the term "element" represents an element for a volume domain and a surface facet for a surface domain.

Because the source and target meshes need not be coincident, the search algorithm must determine whether or not to map a member of the target mesh. The distance used to make that determination is referred to as the search position tolerance distance. The default position tolerance is 50% of the average element diagonal length in the domain. In certain circumstances, you might want to modify the search position tolerance distances; for example, if your model has complex geometry or if the mesh topology in one dimension is significantly different in other dimensions.

You can specify four position tolerances.

• Define a search position tolerance distance in the positive surface normal direction for surface domains; only points within the position tolerance normal to the surface are considered.
• Define a search position tolerance distance in the negative surface normal direction for surface domains or a search radius for the point-cloud algorithm for point domains.
• Define a position tolerance for how far a point can be located outside an element for volume coupling or outside a surface facet in the plane of the surface for surface coupling.
• Define a search tolerance radius for the unmapped members treatment (see Nearest Neighbor Method).

You can provide the position tolerance distance as an absolute distance or a relative distance based on the characteristic region dimension. Absolute tolerances might be more appropriate if the mesh discretization varies significantly, such that the characteristic dimension is a poor representation in certain parts of the mesh.

FIELD MAPPER CONTROLS, NAME=controls name, SEARCH TOLERANCE=ABSOLUTE
positive normal distance, negative normal distance or point-cloud radius, distance outside element, nearest neighbor radius

FIELD MAPPER CONTROLS, NAME=controls name, SEARCH TOLERANCE=RELATIVE
positive normal distance tolerance, negative normal distance tolerance or point-cloud radius tolerance, distance tolerance outside element, nearest neighbor radius tolerance

Typically, the search is based on the original nodal coordinates of the source mesh. You might want to use the deformed configuration of the source mesh; for example, in a case where the model is remeshed in the subsequent analysis using the deformed shape of the first analysis.

FIELD MAPPER CONTROLS, NAME=controls name, CONFIGURATION=REFERENCE

FIELD MAPPER CONTROLS, NAME=controls name, CONFIGURATION=DEFORMED

If the search fails to make an association, the field mapper reports unmapped members. For most Abaqus features, the simulation ends, and the unmapped members are reported. Common causes of such failures include:

• The source and target domains use different unit systems.
• The source and target regions are not co-located.
• The target domain is larger than the source domain, requiring extrapolation.
• The search tolerance distances are inadequate for complex geometry or poor mesh topology.

You can try to correct the mesh or adjust the search tolerance distances. If these attempts fail, you can specify how the field mapper treats the unmapped members. Treatment is intended for circumstances where you have only a few unmapped members. You should interpret results carefully in the vicinity of the unmapped members. There are two treatment methods available: the nearest neighbor method and the constant value method.

When mapping tensor quantities, you can specify how to use the averaging technique. You can average the tensor component-by-component, using a technique that preserves the eigenvalues of the tensor, or using a technique that preserves the von Mises invariant.

FIELD MAPPER CONTROLS, TENSOR AVERAGING=COMPONENT

FIELD MAPPER CONTROLS, TENSOR AVERAGING=EIGENVALUE

FIELD MAPPER CONTROLS, TENSOR AVERAGING=INVARIANT